Experiment – Helene Intraub The Representational Momentum Experiment – Jennifer

Human visual cognition has historically been characterized through the metaphor of optical instrumentation, likened across centuries to a camera obscura, a photographic plate, or a passive sensor recording sensory photons upon the retinal surface. This structuralist framework presumed that perception establishes an internal, veridical replica of external reality, and that visual memory operates as an archival repository dedicated to preserving these sensory snapshots. However, pioneering empirical paradigms initiated in the late twentieth century systematically dismantled this static paradigm. Through the groundbreaking empirical work of cognitive psychologists Jennifer J. Freyd and Helene Intraub, cognitive science recognized that perceptual representations are inherently dynamic, proactive, and predictive. Rather than registering an inert snapshot of the environment, human visual cognition actively extrapolates physical properties across both time and space, continuously anticipating the unfolding states of the physical world.

Jennifer Freyd’s discovery of representational momentum in 1984 revealed that memory for the final location of a dynamically moving or rotationally implied object is systematically displaced forward along its trajectory of motion. The mental representation of an entity does not freeze instantly upon its perceptual offset; instead, it exhibits properties analogous to physical momentum, carrying the mental state forward in time. Concurrently, Helene Intraub’s discovery of boundary extension in 1989 uncovered a complementary spatial extrapolation: when observers view a photographic scene depicting a close-up or medium view of an ecological environment, their memory systematically extends beyond the physical borders of the image, leading them to remember having seen a wider, more expansive field of view than was physically exposed. Together, these two paradigms represent a foundational shift toward understanding visual cognition as an anticipatory simulation engine designed for real-time biological agency.

The convergence of Freyd’s temporal extrapolation and Intraub’s spatial extrapolation provides a unified window into how the human brain reconciles the severe physiological latencies of neural transmission with the urgent behavioral demands of dynamic environmental navigation. By examining the empirical architectures, psychophysical parameters, neurobiological substrates, computational models, and ecological implications of both representational momentum and boundary extension, this analysis investigates how the nervous system constructs continuous, coherent conscious experience from discrete, fragmentary, and delayed sensory inputs. Through these paradigms, memory distortions cease to be viewed as systemic cognitive failures; instead, they emerge as profound, evolutionary signatures of an adaptive, predictive perceptual architecture.

1. Introduction to Dynamic Mental Representations: Freyd and Intraub

1.1 Conceptual Convergence of Perceptual Extrapolation

The transition from classical models of static mental imagery to continuous, dynamic spatial cognition represents one of the most critical conceptual evolutions in contemporary cognitive science. Early computational and cognitive models, heavily influenced by the modular architectures of the 1960s and 1970s, conceptualized visual perception as an episodic pipeline wherein a sensory array is digitized, stored in a transient buffer, and subsequently retrieved by higher-order cognitive faculties as a fixed internal icon. This structuralist perspective assumed that the visual system prioritizes veridical fidelity, preserving the exact geometry and physical coordinates of sensory inputs. However, this classical model proved fundamentally inadequate for explaining how biological organisms interact with non-static, rapidly evolving environments characterized by constant motion, spatial occlusions, and relentless kinematic flux.

The epistemological overlap between Jennifer Freyd’s representational momentum and Helene Intraub’s boundary extension emerges directly from their mutual rejection of static representational models. Both researchers identified systemic, directional memory displacements that operate below conscious awareness, demonstrating that internal representations are fundamentally dynamic constructions. While Freyd focused on the temporal dimension—demonstrating that mental representations carry an internal analog of physical momentum that propels the remembered position of an object along its implied kinematic vector—Intraub focused on the spatial dimension, showing that mental representations of scenes project outward beyond visual apertures to construct a coherent, anticipated spatial layout. Both phenomena demonstrate that human memory does not record a terminal sensory state, but rather projects the immediate future or surrounding spatial context.

These anticipatory perceptual mechanisms play an indispensable role in real-time environmental navigation. Biological neural pathways exhibit inherent conduction delays ranging from tens to hundreds of milliseconds. If an organism’s internal model of the world relied solely on unextrapolated sensory feedback, its behavioral reactions to dynamic stimuli—such as a fast-moving predator, an airborne projectile, or rapid shifts in self-motion—would constantly lag behind physical reality. Consequently, these systematic memory distortions represent an adaptive, evolutionary feature rather than a processing deficiency. By proactively projecting the spatial and kinematic coordinates of the external world, the human visual system effectively eliminates computational and neural latency, allowing organisms to interact with their environment in real time.

1.2 The Evolution of Spatial and Kinematic Memory Paradigms

To contextualize the revolutionary nature of Freyd’s and Intraub’s discoveries, one must trace the historical paradigms of psychophysics and visual memory that preceded them. Traditional psychophysics, grounded in the nineteenth-century methodologies of Ernst Heinrich Weber and Gustav Fechner, sought to quantify the precise mathematical relationships between physical stimuli and internal sensation. These early models treated perception as a discrete mapping problem. Structuralist perception theories, championed by Wilhelm Wundt and Edward Titchener, further fragmented sensory experience into elemental, non-overlapping sensory atoms, viewing memory for visual scenes as an aggregation of these discrete physical sensations. Under this framework, cognitive processing was strictly reactive, proceeding unidirectionally from sensory reception to retrospective memory consolidation.

Although early twentieth-century Gestalt psychology challenged this atomistic paradigm by demonstrating that visual processing is governed by holistic principles such as closure, proximity, and good continuation, Gestalt models remained predominantly static. They illustrated how spatial arrays are organized simultaneously, yet they rarely addressed how these configurations evolve across temporal intervals or how incomplete visual scenes are dynamically extrapolated beyond their visible framing. It was not until the cognitive revolution gathered momentum in the late twentieth century that researchers began investigating the predictive capacity of cognitive processing. The emergence of predictive coding paradigms suggested that the brain operates not as an empirical recorder, but as a hierarchical inference engine generating continuous hypotheses about sensory inputs.

When Jennifer Freyd published her foundational findings on representational momentum in the mid-1980s, followed closely by Helene Intraub’s initial demonstration of boundary extension in 1989, the cognitive science community initially met these phenomena with both fascination and skepticism. Prevailing orthodoxies attributed apparent memory displacements to post-perceptual biases, demand characteristics, or imprecise psychophysical calibration. However, through rigorous empirical replications, precise tachistoscopic presentations, and stringent control conditions, both Freyd and Intraub conclusively proved that these extrapolative phenomena were robust, pervasive, and rooted in deep cognitive and neural architectures. Their work catalyzed a profound theoretical paradigm shift, establishing that dynamic extrapolation is a core computational operation of human visual cognition.

1.3 Scope and Taxonomy of Perceptual Extrapolation Experiments

Perceptual extrapolation can be organized into a comprehensive taxonomy spanning temporal, kinematic, spatial, and scene-based dimensions. Temporal extrapolation centers primarily on the continuous projection of an object’s future position based on its historical trajectory and implied physical dynamics. Within this domain, research investigates kinematic variables such as implied linear velocity, angular velocity during mental rotation, and uniform versus non-uniform acceleration vectors. Researchers examine how internal representations inherently incorporate Newtonian principles, demonstrating that mental trajectories do not terminate instantaneously at the physical point of stimulus offset, but instead execute a continuous decelerative glide path within psychological representational space.

Conversely, spatial extrapolation centers on the structural and layout-based projection of visual scenes. This taxonomy encompasses peripheral visual completion, panoramic context expansion, and the anticipatory generation of occluded or out-of-frame environmental coordinates. Helene Intraub’s boundary extension paradigms systematically delineate how the cognitive apparatus resolves the visual system’s “aperture problem”—the reality that the eye takes in scenes through discrete, highly localized fixations and artificial framing, while the physical world extends seamlessly and continuously. Spatial extrapolation bridges these discrete inputs by internally generating the panoramic space immediately adjacent to the visible borders, maintaining a continuous representation of environmental context.

Synthesizing Jennifer Freyd’s kinematic models with Helene Intraub’s ecological scene models yields a unified theoretical framework: the *anticipatory perceptual simulation hypothesis*. Under this synthetic framework, representational momentum and boundary extension are recognized as complementary manifestations of a single, highly integrated predictive engine. Freyd’s paradigm explains how the visual brain predicts “what will happen next” along an object’s trajectory of motion, while Intraub’s paradigm reveals how the visual brain predicts “what lies just beyond” the current field of view. Together, they confirm that spatial and temporal visual representations are intrinsically coupled, predictive, and continuously updated to support behavioral action.

2. Theoretical Foundations of Representational Momentum: Freyd’s Paradigm

2.1 Physical Invariants and Mental Kinematics

The foundational premise of Jennifer Freyd’s theoretical paradigm is that the physical invariants of the external macroscopic world—principles such as inertia, momentum, velocity, acceleration, and gravity—are deeply internalized within the functional architecture of the human visual system. In their seminal 1984 paper, Jennifer J. Freyd and Ronald A. Finke advanced the revolutionary hypothesis that dynamic continuity is an obligatory, intrinsic dimension of mental representations. They argued that when an observer perceives a sequence of static images that imply continuous physical motion, the internal cognitive representation does not simply transition through discrete symbolic states; rather, it participates in a continuous, analog transformation that possesses mental momentum.

To establish this hypothesis, Freyd and her colleagues had to distinguish representational momentum from known physiological and retinal phenomena, most notably iconic memory decay, afterimages, and visible retinal persistence. Retinal persistence operates over very brief temporal intervals (typically under 100 to 250 milliseconds) and is retinotopically mapped, decaying passively in the earliest stages of sensory transduction. In contrast, representational momentum persists over substantially longer temporal intervals, operates across spatial transformations independent of precise retinal locus, and scales directly with the conceptual and physical meaning of the stimulus display. It reflects a high-order cognitive simulation of dynamic motion rather than a lingering sensory afterimage in the photoreceptor array.

This formulation directly challenged the classical computational view of the mind championed by symbolic processing theorists, who posited that visual memory consists of propositional or discrete algorithmic descriptions. Freyd asserted the continuous transformation hypothesis: mental space functions as an analog simulation medium wherein dynamic variables are continuously represented. When an object in motion suddenly ceases to be visible, its internal representation cannot stop instantaneously because the cognitive system simulates the physical property of inertia. Consequently, the internal state continues along its trajectory of transformation, displacing the remembered final position in the direction of the implied physical vector.

2.2 The Probe-Comparison Methodology of Jennifer Freyd

The empirical verification of representational momentum required an ingenious psychophysical paradigm capable of measuring sub-degree spatial and angular memory distortions with microsecond temporal accuracy. Freyd and Finke developed the *inducing-sequence and probe-comparison paradigm*, which has since become the gold standard in kinematic cognitive psychology. In a prototypical experiment, an observer is presented with a rapid, stroboscopic sequence of static visual frames depicting an object (such as a geometric rectangle or dot pattern) appearing in successive positions that imply a coherent directional rotation or linear trajectory. The sequence typically consists of three inducing stimuli: an initial inducing frame, a transitional inducing frame, and a final terminal inducing frame.

Following the presentation of the terminal inducing stimulus, a precise temporal delay known as the inter-stimulus interval (ISI) is introduced, typically calibrated between 200 and 500 milliseconds. Immediately after this retention interval, a fourth visual stimulus—the probe—is presented to the observer. The probe can appear in one of three spatial configurations: in the exact, identical physical location occupied by the terminal inducing stimulus (“same”), in a position slightly displaced forward along the trajectory of implied motion (“forward displacement”), or in a position slightly displaced backward along the trajectory (“backward displacement”). The participant’s task is to make a speeded, forced-choice recognition judgment, determining whether the probe stimulus is in the identical physical position as the final inducing stimulus.

The empirical findings revealed a striking and highly systematic asymmetry. Observers consistently and overwhelmingly exhibited higher error rates and prolonged reaction times when rejecting forward-displaced probes compared to backward-displaced probes. Forward-displaced probes were routinely misidentified as being the “same” as the final inducing stimulus, whereas identical probes were frequently rejected as being “backward” relative to the remembered terminal position. By plotting the probability of a “same” response across a continuum of probe displacements, Freyd generated psychophysical response distributions whose peaks were systematically shifted in the direction of implied motion. This forward displacement error served as direct quantitative evidence that the mental representation had carried forward past the physical offset point.

2.3 Modulating Factors in Momentum Extrapolation

Subsequent psychophysical investigations revealed that the magnitude of representational momentum is not a fixed perceptual constant; rather, it is systematically modulated by the physical invariants implied by the visual stimulus. Primary among these modulators is implied velocity. When the temporal interval between inducing frames is decreased or the spatial distance between them is increased—thereby simulating a higher physical speed—the magnitude of the forward memory displacement increases proportionally. This linear scaling provides compelling confirmation of Freyd’s hypothesis that internal mental transformations mirror the continuous kinematic laws of physical mechanics: greater implied momentum results in greater cognitive extrapolation.

Beyond basic velocity, cognitive scientists demonstrated that internal dynamic simulations incorporate complex multidimensional physical constraints, including friction, gravity, and environmental centripetal forces. In groundbreaking experiments involving simulated projectile motion, researchers observed that the forward displacement of an object moving horizontally across a display exhibited a downward parabolic drift, mimicking the influence of gravitational acceleration on physical trajectories. Similarly, when an object was depicted sliding along an implied surface, the forward displacement was significantly attenuated if the surface was textured to imply high friction, as opposed to a smooth surface implying low friction. The cognitive simulation engine automatically integrates context-dependent environmental dynamics into its predictive projections.

Crucially, the magnitude and fidelity of representational momentum are also constrained by attentional deployment and cognitive load. The forward projection of a dynamic trajectory is an active, resource-demanding simulation process. When observers are subjected to concurrent secondary cognitive tasks—such as maintaining a complex auditory digit span in working memory or performing peripheral visual search during the inducing sequence—the magnitude of representational momentum is systematically attenuated or disrupted. If visual attention is diverted from the moving entity prior to the offset of the terminal inducing frame, the cognitive extrapolation cannot proceed efficiently, demonstrating that representational momentum relies on continuous focal attention directed along the vector of implied motion.

3. Theoretical Foundations of Boundary Extension: Intraub’s Paradigm

3.1 Ecological Scene Perception and the Aperture Problem

While Jennifer Freyd was uncovering the dynamic kinematic properties of object representations, Helene Intraub was fundamentally reinterpreting how the human mind perceives and remembers naturalistic scenes. In their classic 1989 paper, Helene Intraub and Michael Richardson documented a pervasive, unidirectional visual memory distortion which they termed boundary extension. When observers view a photograph or bounded visual display depicting a naturalistic scene, their internal memory of the scene consistently and reliably encompasses a wider angle of view, mentally reconstructing the continuous world that lay just beyond the physical edges of the photographic aperture.

To understand the theoretical necessity of boundary extension, one must consider the ecological aperture problem inherent in human vision. In the physical world, space is continuous, panoramic, and unbounded. However, biological vision is inherently constrained by physiological and structural apertures: the human eye possesses a limited visual field governed by retinal geometry, high-acuity foveal vision spans only about two degrees of visual angle, and natural scenes are continually interrupted by foreground occlusions, physiological blinks, and saccadic eye movements. Furthermore, modern visual communication routinely presents scenes within artificial boundaries, such as the borders of photographs, television monitors, and computer screens.

Intraub proposed that to bridge these discrete, truncated sensory fixations into a coherent, unbroken representation of reality, the visual cognitive system relies on *integrative scene schemas*. When a person glances at an image of a scene—for example, a close-up photograph of a telephone on a desktop—the visual system does not treat the edge of the photographic print as the absolute termination of the physical world. Instead, higher-order top-down scene schemas immediately and automatically activate, projecting an anticipatory representation of the unseen adjacent spatial coordinates (such as the rest of the desk, the wall behind it, and the floor below). Boundary extension is therefore the memory manifestation of this proactive spatial layout projection: the observer later misremembers the internal projection as having been part of the physical sensory input.

3.2 Experimental Methodologies: Drawing, Rating, and Reconstruction

To substantiate the reality of boundary extension and eliminate the possibility of experimental artifact, Helene Intraub and her collaborators developed a suite of robust, complementary empirical methodologies. The earliest and most intuitive of these was the *rapid scene drawing protocol*. Participants were exposed to photographs of natural scenes for brief intervals, after which the image was removed. Participants were then provided with blank templates possessing the identical aspect ratio and boundary dimensions of the original photograph and instructed to draw the scene exactly as they remembered it, with rigorous instructions regarding fidelity and spatial placement.

The quantitative evaluation of these drawings revealed a striking pattern: participants consistently drew the primary objects of the scenes at a significantly reduced relative scale, pulling the boundaries outward to include surrounding environmental context that was completely absent from the original photographic stimulus. To eliminate potential motor, artistic, or reproduction biases associated with drawing, Intraub pioneered the *camera-distance rating paradigm*. In this psychophysical design, observers view an initial target photograph, undergo a variable retention interval, and are subsequently shown a test probe that is either physically identical to the original, cropped closer (narrower angle of view), or expanded (wider angle of view). Observers rate the probe relative to the study picture on an asymmetrical rating scale (e.g., indicating whether the probe appears “too close,” “same,” or “too far”).

The results of the camera-distance rating paradigm provided irrefutable psychophysical proof: physically identical probes are consistently rated as being “too close” or “zoomed in,” because the observer’s internal memory representation has expanded, requiring a wider test picture to visually match the remembered mental layout. To refine this measurement further, Intraub and her colleagues developed *computerized border-adjustment techniques*. In these paradigms, participants use a physical interface (such as a mouse or dial) to dynamically expand or contract the visible borders of a digital photograph until it matches their internal memory. Participants systematically contract the borders of test images, demonstrating that their memory contains an extended representation of the peripheral field. Control conditions evaluating isolated objects lacking an ecological background confirmed that boundary extension is uniquely triggered by scene context, demonstrating that the effect depends on an activated spatial frame rather than generic object mislocalization.

3.3 Temporal Persistence and Invariance Across Exposure Durations

A remarkable finding emerging from Intraub’s experimental corpus is the extreme temporal speed with which boundary extension is generated. Traditional models of reconstructive memory, such as those popularized by Sir Frederic Bartlett, suggested that memory distortions emerge slowly over time as sensory traces decay and top-down cultural or semantic schemas gradually overwrite veridical details. Intraub challenged this view by presenting photographic scenes under ultra-brief tachistoscopic exposures, reducing presentation times down to a mere 40 milliseconds, followed immediately by masked visual retention intervals as brief as 42 milliseconds.

Remarkably, boundary extension manifests robustly even under these ultra-brief, masked conditions. Within a fraction of a single second—far faster than the time required to execute a cognitive plan or engage in conscious deliberative recall—the visual system has already deployed an anticipatory spatial schema that integrates with the feedforward sensory input, producing an extrapolated mental representation. This demonstrates that boundary extension is an online, perceptual-level phenomenon rather than a slow, post-perceptual reconstructive memory decay.

Furthermore, boundary extension exhibits profound temporal persistence. While it appears nearly instantaneously, the resulting boundary-extended mental representation remains stable across short-term, working-memory, and multi-day long-term memory retention intervals. It does not dissipate as the image memory solidifies; rather, it becomes the permanent foundational trace of the observed visual event. Intraub also demonstrated that boundary extension is distinctly different from the classical psychophysical phenomenon of *regression to the central tendency*, wherein memories for extreme stimuli drift toward an average mean. When observers are shown extremely wide-angle panoramic photographs, they do not exhibit boundary contraction (which central tendency regression would predict); instead, they continue to demonstrate boundary extension or veridical boundary retention, confirming that the directional bias is uniquely tied to spatial scene completion.

4. Comparative Analysis: Representational Momentum versus Boundary Extension

4.1 Spatiotemporal Trajectories versus Static Scene Framing

While representational momentum and boundary extension both belong to the overarching category of predictive cognitive phenomena, they operate across fundamentally different representational dimensions and respond to distinct visual properties. Freyd’s representational momentum is fundamentally kinematic and temporal: it depends upon the perception or conceptual implication of continuous, directional change across time. The underlying vector of distortion is collinear with the trajectory of physical displacement, governed by an internal simulation of velocity, acceleration, and inertia. The cognitive system anticipates “t + Δt”—the immediate, imminent temporal future of an object traversing coordinate space.

In direct contrast, Intraub’s boundary extension operates over static spatial layouts and panoramic scene geography. It does not require motion, temporal sequencing, or kinematic velocity to manifest; a single, static photograph viewed for a few milliseconds is sufficient to trigger the phenomenon. The vector of distortion in boundary extension is spatial and centrifugal: it expands omnidirectionally outward from the focal center toward and beyond the bounding apertures of the visual frame. The cognitive system anticipates “s + Δs”—the continuous environmental layout immediately adjacent to the current sensory window.

These distinct functional profiles correspond to different processing systems within the primate visual brain. Representational momentum is primarily engaged by the magnocellular pathway and the dorsal visual processing stream, which specialize in processing motion, velocity vectors, spatial coordinates, and dynamic motor affordances. Boundary extension, while relying on the dorsal stream for coordinate mapping, critically depends on specialized high-order ventral and medial-temporal scene-processing structures that encode environmental geometry, panoramic space, and ecological context. Thus, while both paradigms demonstrate anticipatory extrapolation, they execute these predictions through distinct cognitive and neural pathways.

4.2 Shared Adaptive Architecture in Visual Memory

Despite their operational distinctions, representational momentum and boundary extension share a profound, foundational architecture rooted in evolutionary adaptation. Both phenomena reject the naive assumption that the primary function of memory is to produce a retrospective, veridical archive of past sensory states. Instead, both paradigms provide compelling empirical proof that memory is inherently prospective. The brain constantly generates proactive, anticipatory simulations of the external environment to facilitate rapid, effective physical action.

This shared adaptive architecture directly addresses the critical challenge of biological latency. In real-world environments, an organism that relied entirely on lagging sensory feedback would suffer severe behavioral disadvantages. In dynamic motor scenarios—such as intercepting an escaping target, evading an attacking predator, or dodging falling debris—internal representational momentum bridges the temporal delay between photon absorption in the retina and somatic motor execution, allowing an individual to target where the moving entity *will be* rather than where it *was*. Similarly, during ecological visual exploration, boundary extension bridges the gaps created by rapid saccadic eye movements. Humans make saccades three to four times per second, rendering the incoming foveal visual input a series of disjointed, narrow sensory fragments. Boundary extension provides a pre-activated, extrapolated spatial context around each fixation, enabling the visual cortex to seamlessly integrate disjointed sensory glances into a continuous, stable representation of panoramic space.

A second striking commonality between Freyd’s and Intraub’s paradigms is their near-total cognitive impenetrability and resistance to conscious metacognitive correction. Even when experimental participants are explicitly informed of the existence of representational momentum or boundary extension, instructed on the precise mathematical nature of the memory distortions, and offered financial incentives to make veridical judgments, the extrapolative errors persist. Observers cannot willfully turn off the forward momentum of a moving target, nor can they prevent their scene schemas from expanding the boundaries of a photographic image. This conscious uncontrollability proves that both mechanisms operate at a mandatory, pre-attentive, architectural level of the cognitive processing stream.

4.3 Contrasting Vulnerabilities and Modulation

The structural divergence between representational momentum and boundary extension becomes particularly evident when examining how each phenomenon reacts to experimental perturbations, visual masking, and semantic contextual modifications. Representational momentum is acutely vulnerable to disruptions in temporal continuity and attentional allocation. If an inducing motion sequence is interrupted by an unexpected temporal pause (an extended inter-stimulus interval exceeding 500 to 1000 milliseconds) or if an unrelated visual distractor appears along the trajectory path, the mental momentum rapidly decays, halts, or even reverses toward the veridical terminal position. Furthermore, the introduction of a visual mask that overwrites the spatial coordinates of the terminal inducing frame can extinguish representational momentum, resetting the dynamic tracking mechanisms of the dorsal stream.

Conversely, boundary extension exhibits extraordinary resilience to visual masking and temporal interruptions. Helene Intraub demonstrated that presenting high-contrast, high-entropy visual masks (such as random noise patterns or scrambled scene fragments) between the study image and the test probe does not abolish boundary extension; in many instances, it actively amplifies the spatial extrapolation by disrupting transient iconic representations that might otherwise anchor the exact photographic edges. Similarly, while representational momentum is highly sensitive to the semantic identity and perceived physical mass of the moving object (e.g., an animated image of a heavy cannonball exhibits different forward displacement than an image of a ping-pong ball), boundary extension is primarily governed by spatial layout geometry. It occurs whether the scene depicts a natural landscape, an artificial domestic interior, or a synthetic computer-rendered environment, provided the visual cues imply continuous ground surfaces extending beyond the frame.

Furthermore, these two cognitive mechanisms interface differently with transsaccadic visual processing. Intra-saccadic momentum progression requires the dynamic vector calculation to remain locked to the moving object’s frame of reference, often surviving saccadic eye movements if the target continues its implied trajectory in retinotopic or spatiotopic space. Boundary extension, on the other hand, operates as a spatial integration mechanism precisely designed for transsaccadic vision, continually maintaining the coordinate transform from retinotopic visual inputs to spatiotopic environmental memory. These functional differences are systematically summarized below:

Comparative Parameter	Representational Momentum (Freyd)	Boundary Extension (Intraub)
Primary Dimension	Temporal / Kinematic ($t + \Delta t$)	Spatial / Layout ($s + \Delta s$)
Direction of Displacement	Forward along the implied physical trajectory	Centrifugal expansion beyond photographic borders
Triggering Stimulus	Sequential or implied directional motion	Static photograph or view of an ecological scene
Primary Cortical Pathways	Dorsal Stream, MT+/V5, Intraparietal Sulcus	Ventral/Medial-Temporal, PPA, RSC, OPA
Vulnerability to Visual Masking	High; visual masks frequently abolish or disrupt momentum	Extremely low; visual masks preserve or amplify extrapolation
Metacognitive Modifiability	Impenetrable; resistant to conscious cognitive control	Impenetrable; resistant to conscious cognitive control
Ecological Function	Compensation for neural latency during dynamic tracking	Seamless integration of discrete saccades into panoramic context

5. Cognitive and Psychophysical Mechanisms of Perceptual Prediction

5.1 Predictive Coding and the Bayesian Visual Brain

The contemporary cognitive architecture that best synthesizes the findings of Jennifer Freyd and Helene Intraub is the framework of predictive coding and Bayesian perceptual inference. Under this neurocomputational paradigm, championed by cognitive neuroscientists such as Karl Friston, the brain is modeled as a hierarchical Helmholtz machine. Rather than passively waiting to be stimulated by bottom-up sensory photons, the visual brain constantly generates top-down generative predictions regarding the current state and imminent trajectory of the physical environment. Sensory input arriving via afferent pathways does not get transcribed directly into conscious memory; rather, it is compared against this top-down prediction to calculate a prediction error.

Within this Bayesian formulation, representational momentum and boundary extension represent scenarios where powerful, evolutionary environmental priors systematically override noisy, ambiguous, or truncated bottom-up sensory data. In the case of Freyd’s representational momentum, the visual system operates under a deeply embedded physical prior: objects in motion continue in motion unless acted upon by an external force. When the visual stimulus abruptly ceases, the bottom-up sensory signal indicates the sudden disappearance of the object. However, the system’s dynamic prior calculates that an instantaneous cessation of momentum is physically improbable in macroscopic mechanics. The Bayesian posterior distribution—the resulting conscious perceptual representation—is therefore shifted forward along the trajectory, reflecting an optimal balance between incoming sensory data and internal kinematic priors.

Similarly, boundary extension is governed by a fundamental spatial prior: the natural physical world is spatially continuous and does not terminate at the arbitrary rectangular edges of an optical aperture. When an observer views a photographic print, the sensory input registers sharp rectangular boundaries. However, the scene-processing hierarchy applies an ecological prior of environmental continuity. The resulting top-down generative prediction fills in the adjacent spatial context. Because the brain minimizes prediction error by integrating the generative spatial hypothesis with the sensory input, the remembered mental state inevitably incorporates this peripheral expansion, yielding boundary extension as an optimal Bayesian inference.

5.2 Schema Theory and Spatial Frame Systems

To fully delineate the internal mechanics of boundary extension, Helene Intraub formulated the *Multisource Model of Scene Perception*. This model asserts that our conscious visual experience of a scene is not derived from visual sensory inputs alone. Instead, it is an emergent synthesis constructed from three distinct information streams: bottom-up visual sensory input (the literal pixels or photons reaching the retina), top-down scene schemas (amodal cognitive structures that store general knowledge about how spatial environments are configured), and egocentric spatial frameworks (internal coordinate systems that track observer position relative to the environment).

When an observer looks at a photograph, these three streams converge rapidly within working memory. The scene schema instantly activates to fill in missing information, projecting an anticipatory representation of the wider layout. Boundary extension occurs as a consequence of a *source monitoring error* within this multisource integration. When asked to evaluate a memory probe or reconstruct the scene, the cognitive system fails to reliably distinguish between the spatial information derived directly from the sensory input and the spatial information self-generated by the amodal schema. The self-generated contextual projection is misattributed to the sensory source, resulting in the subjective certainty that the extended scene boundaries were physically present in the original stimulus.

In Freyd’s paradigm, dynamic representational schemas execute an analogous coordinate frame transformation. When observing sequential inducing stimuli, the visual cognitive architecture translates discrete retinotopic coordinates into an internal, continuous spatiotopic coordinate system. Within this dynamic coordinate frame, physical affordances—such as directional vectors, kinetic energy, and structural resistance—are operationalized into an internal mental simulation. The dynamic representational schema actively drives the spatiotopic coordinates forward, ensuring that subsequent perceptual matching tasks operate against a predictive mental canvas rather than an outdated, historical sensory trace.

5.3 The Role of Attentional Deployment and Working Memory

The operational boundaries of both representational momentum and boundary extension are intimately bound to the mechanics of visual attention and working memory capacity. In representational momentum, attentional deployment must be sharply focused upon the moving target. Psychophysical experiments tracking eye fixations and covert spatial attention demonstrate that the visual system focuses attention immediately ahead of a moving object’s current position, actively pre-allocating neural resources to the anticipated spatial coordinates. When visual working memory is taxed by competing cognitive loads, the precision of this forward vector calculation degrades, demonstrating that mental kinematics requires continuous attentional resources.

In contrast, boundary extension exhibits a radically different relationship with visual working memory and attentional deployment. Research has consistently demonstrated that the magnitude of boundary extension does not correlate with an individual’s visual working memory capacity. Whether an individual possesses high or low visual working memory spans, boundary extension occurs with near-identical magnitude and fidelity. Even more remarkably, depleting visual working memory through severe cognitive dual-task paradigms does not abolish boundary extension; in some experimental configurations, it actively increases the magnitude of boundary extension, as the cognitive system relies more heavily on default spatial schemas when working memory buffers are saturated.

Furthermore, attentional distribution across the visual scene reveals a critical divergence between focal target processing and global layout analysis. Representational momentum requires focal concentration along a specific kinematic path. If attention is broadly distributed across unrelated background elements, momentum extrapolation decreases. Conversely, boundary extension thrives on panoramic, global scene viewing. If an observer is instructed to focus tightly and exclusively on an isolated internal feature of an image (such as the texture of a button on a jacket), boundary extension of the surrounding scene frame is attenuated, because the global scene schema was not fully activated. The deployment of visual attention thus modulates these two anticipatory mechanisms in distinct ways: representational momentum depends on focal, vector-aligned attention, while boundary extension depends on global, schema-activating scene processing.

6. Experimental Methodologies: Structural Designs and Control Paradigms

6.1 Stimulus Construction and Psychophysical Calibration

The empirical validity of both Freyd’s and Intraub’s discoveries depends on meticulous stimulus design and precise psychophysical calibration. In representational momentum experiments, researchers must exercise extraordinary control over visual variables to prevent low-level sensory artifacts from contaminating high-level kinematic simulations. Stimulus sequences must carefully control for luminance, contrast, edge sharpness, and spatial frequency to ensure that apparent motion is not confused with true representational momentum. The classic design utilizes simple geometric polygons, alphanumeric characters, or dot configurations presented against uniform backgrounds, thereby eliminating confounding semantic variables.

The velocity gradients and temporal sequences of the inducing frames must be calibrated down to the millisecond. In a typical rotational momentum experiment, an inducing rectangle might be presented at angles of $\theta_1 = 0^circ$, $\theta_2 = 17^circ$, and $\theta_3 = 34^circ$, with an exposure duration of precisely 250 milliseconds per frame and an inter-stimulus interval of 250 milliseconds. The critical experimental challenge is distinguishing between *apparent motion* (the classic Phi phenomenon, where the brain perceives continuous motion across sequential flashes) and *conceptual implied motion* (where the mind calculates a physical trajectory). Freyd addressed this by demonstrating that even when the sequence is presented with temporal intervals too long to sustain low-level apparent motion, the systematic forward memory displacement persists, proving that representational momentum operates at a higher cognitive level than basic retinal motion detectors.

For Intraub’s boundary extension paradigms, stimulus construction demands an entirely different set of rigorous controls. Photographic scenes must be calibrated across multiple viewing metrics, including visual angle, camera-to-subject distance, focal length, and the specific ratio of primary subject area to surrounding background space. A primary methodological challenge in boundary extension is ensuring that the effect is not merely an artifact of photographic edge contrast or simple center-surround retinotopic adaptation. Intraub resolved this by employing rigorous control conditions featuring isolated objects presented against blank, untextured backgrounds. When observers view an isolated object devoid of environmental context, boundary extension drops to near zero; in fact, isolated objects often exhibit slight *boundary restriction* (being remembered as larger than they were). Boundary extension emerges exclusively when the stimulus provides sufficient ecological cues to activate a spatial scene schema, proving it is a property of scene perception rather than low-level edge processing.

6.2 Response Capture Paradigms and Artifact Minimization

Capturing uncorrupted internal memory representations requires sophisticated psychophysical response paradigms designed to isolate perceptual extrapolation from post-perceptual response biases. In early representational momentum studies, critics suggested that forward memory errors might reflect an observer’s motor delay or a general tendency to guess in the direction of motion. To eliminate this alternative explanation, researchers integrated Signal Detection Theory (SDT) into the probe-comparison paradigm. By calculating sensitivity ($d’$) and response bias ($\beta$ or $c$) across varying probe displacements, researchers proved that the forward displacement error represents a genuine shift in perceptual sensitivity—the point of subjective equality (PSE)—rather than a mere cognitive response bias.

In boundary extension research, response capture methodologies have evolved across multiple distinct experimental designs to rule out task-specific artifacts:

• Forced-Choice Probe Matching: Observers are presented with the original image alongside altered versions (slightly wider or slightly closer) and must select the exact match. Observers consistently select the slightly wider image as the original, proving that the internal representation is expanded.
• Continuous Border Adjustment: Observers use digital controls to expand or contract image boundaries in real time, eliminating categorical response biases and providing fine-grained, continuous metric data on spatial displacement.
• Standardized Grid-Based Drawing Tasks: Drawings produced by participants are scanned, digitized, and scored using automated spatial metrics and blinded inter-rater reliability protocols, verifying that the scale of drawn objects is systematically reduced and drawn boundaries are expanded.
• Transsaccadic Change Detection: During a brief saccadic eye movement, the image boundaries are expanded or contracted. Observers are blind to expansions (as the change matches their top-down expectation) but highly sensitive to contractions, providing direct psychophysical evidence of predictive boundary generation during active viewing.

6.3 Technological Evolution in Experimental Delivery

The historical trajectory of both experimental paradigms has been profoundly shaped by the rapid technological evolution of cognitive psychology laboratories over the past four decades. When Jennifer Freyd conducted her early investigations in the 1980s, the presentation of dynamic sequences relied on mechanical tachistoscopes, slide projectors equipped with high-speed electronic shutters, and early cathode-ray tube (CRT) monitors driven by basic microcomputers. These early systems required continuous calibration to ensure that phosphors decayed rapidly enough to prevent physical ghosting from mimicking representational momentum. Similarly, Helene Intraub’s early boundary extension experiments utilized physical carousel slide projectors, printed photographic stimuli, and manual drawing protocols with physical paper and pencils.

The advent of modern computing transformed the precision and ecological validity of both paradigms. High-refresh-rate CRT and low-persistence OLED monitors operating at 144Hz to 240Hz, synchronized with sub-millisecond hardware timers, allowed researchers to map the micro-temporal decay and progression of representational momentum with absolute precision. Concurrently, the integration of high-speed, pupil-tracking infrared eye-trackers allowed researchers to monitor the exact point of foveal gaze during both the encoding and retrieval phases of boundary extension experiments. Eye-tracking conclusively demonstrated that boundary extension does not depend on observers physically looking at the edges of the image; in fact, observers spend the vast majority of their visual fixations on the central subject, while peripheral boundary extrapolation occurs amodally in the unattended visual periphery.

In recent years, the paradigms have expanded into fully immersive Virtual Reality (VR) and stereoscopic augmented reality environments. In these 360-degree digital spaces, researchers can study representational momentum along three-dimensional vectors ($x$, $y$, $z$) involving depth motion, looming stimuli, and active head rotations. Similarly, VR allows the investigation of boundary extension beyond the arbitrary frame of a flat screen, revealing how the cognitive system extrapolates spatial layouts when observers physically rotate their heads within simulated omnidirectional environments. These modern neurotechnological paradigms continue to confirm and expand upon the core principles originally formulated by Freyd and Intraub.

7. Neurobiological Substrates and Functional Neuroanatomy

7.1 Cortical Loci of Representational Momentum

Advances in functional neuroimaging (fMRI), magnetoencephalography (MEG), and transcranial magnetic stimulation (TMS) have mapped the specific neurobiological networks that implement representational momentum in the human brain. Unsurprisingly, the central cortical locus for representational momentum is the human **MT+/V5 complex** (middle temporal / visual area 5), located in the lateral occipitotemporal cortex. Area MT+/V5 is the brain’s specialized visual motion processing center, containing direction-selective neurons that process both real physical motion and implied motion depicted in static imagery.

Neuroimaging experiments demonstrate that when observers view static images implying directional motion—or when they perform probe-comparison tasks evaluating representational momentum—area MT+/V5 exhibits robust blood-oxygen-level-dependent (BOLD) activation. Crucially, applying repetitive TMS over area MT+/V5 temporarily disrupts this activation, causing a significant attenuation or complete abolition of representational momentum. When MT+/V5 is temporarily inhibited, observers judge terminal positions with near-veridical accuracy. This proves that the forward memory displacement is not an abstract, post-perceptual reasoning error; rather, it is actively generated by the visual motion processing hardware of the extrastriate cortex.

Furthermore, representational momentum engages a broader dorsal-stream network encompassing the **Intraparietal Sulcus (IPS)** and the **Frontal Eye Fields (FEF)**. The intraparietal sulcus is critically involved in dynamic spatial computation, coordinate transformations, and vector tracking. The IPS processes the spatial trajectory of the inducing stimuli, calculating an anticipatory vector that is projected to the prefrontal cortex for action planning. This dynamic dorsal pathway functions in functional dissociation from the ventral stream (object identity): while ventral structures recognize *what* the object is, the dorsal stream (MT+/V5, IPS) actively extrapolates *where* the object is heading, driving the cognitive forward displacement observed in Freyd’s paradigm.

7.2 Neural Mechanisms of Boundary Extension

The functional neuroanatomy underlying Helene Intraub’s boundary extension is localized within a specialized network of scene-selective cortical areas residing within the ventral and medial temporal lobes. Functional neuroimaging studies have definitively identified three critical nodes responsible for processing scenes and extrapolating their spatial boundaries:

• The Parahippocampal Place Area (PPA): Situated along the collateral sulcus in the parahippocampal gyrus, the PPA is profoundly sensitive to environmental layouts, spatial geometry, and background surfaces. Landmark fMRI adaptation studies show that the PPA responds to a wide-angle test image as if it has already seen it when preceded by a close-up image, demonstrating that the PPA internally generates the extrapolated boundary layout during initial encoding.
• The Retrosplenial Complex (RSC): Located in the posterior cingulate cortex, the RSC serves as the crucial computational interface between local scene representations and global, panoramic spatial memory. The RSC translates the viewer-centered (egocentric) coordinates of the current visual input into world-centered (allocentric) cognitive maps, driving the amodal completion of the surrounding environment beyond the physical frame.
• The Occipital Place Area (OPA): Situated in the transverse occipital sulcus, the OPA encodes the immediate navigational affordances and visible boundaries of the surrounding space, projecting boundaries outwards and calculating navigable pathways through the anticipated peripheral context.

Helene Intraub, in collaboration with cognitive neuroscientists, provided functional neuroimaging proof that boundary extension involves rapid top-down feedback from these scene-processing areas to early retinotopic visual cortex. Using fMRI pattern classification, researchers demonstrated that the PPA and RSC rapidly project the anticipated spatial layout back down to primary visual cortex (V1/V2), effectively pre-activating the retinotopic coordinates that would correspond to the unseen peripheral scene. Consequently, boundary extension represents a profound neurobiological loop wherein higher-order spatial schemas actively shape the sensory representations in early visual areas.

7.3 Electrophysiological Markers (ERP) and Time Course Dynamics

While fMRI excels at spatial localization, event-related potential (ERP) and electroencephalography (EEG) methodologies provide the millisecond-level temporal resolution necessary to track the emergence of dynamic extrapolation in real time. Electrophysiological investigations of representational momentum reveal that the anticipatory projection begins within the earliest sensory-processing latencies. When observers evaluate memory probes following an inducing motion sequence, the early sensory-evoked potentials—specifically the **P1** (occurring approximately 100 milliseconds post-stimulus) and the **N1** (occurring around 150–200 milliseconds)—are directly modulated by the spatial congruence of the probe.

Forward-displaced probes elicit significantly smaller N1 and mismatch negativity amplitudes compared to backward-displaced probes. Because the N1 component reflects the detection of physical sensory change or violation of sensory expectation, the attenuated N1 for forward probes confirms that the visual cortex treats the forward-displaced location as the *expected* sensory baseline. Conversely, probes placed in the historically veridical position elicit sharp mismatch negativities, confirming that the early visual system considers the veridical coordinate to be an error relative to its forward-projected simulation.

Similarly, electrophysiological investigations of boundary extension demonstrate the remarkably early emergence of spatial schematic completion. When observers view test probes that are cropped closer versus expanded wider, early ERP components show asymmetric modulation within 150 to 250 milliseconds of image onset. Furthermore, the late positive complex—most notably the **P300** and late positive potential (**LPP**), which index conscious memory mismatch, cognitive surprise, and context updating—is selectively magnified when observers are presented with a probe that physically matches the original study image. Observers exhibit electrophysiological surprise when shown the identical picture, because their internal representation has already expanded; a wider-angle image, by contrast, matches their top-down expectation, eliciting a blunted P300 component. These electrophysiological markers provide definitive proof that dynamic extrapolation occurs within the initial feedforward-feedback sweeps of visual perception.

8. Developmental Trajectories and Lifespan Variations

8.1 Ontogeny of Spatial and Dynamic Extrapolation in Infancy

A central question in cognitive science is whether dynamic perceptual extrapolation is an innate architectural feature of the human nervous system or a learned heuristic acquired through months or years of interacting with the physical world. To answer this question, developmental psychologists adapted Jennifer Freyd’s and Helene Intraub’s experimental paradigms for non-verbal human infants using visual habituation and preferential looking methodologies.

In developmental investigations of representational momentum, infants as young as four to six months old were habituated to visual displays of geometric objects moving along continuous trajectories before undergoing sudden occlusions. When the occluder was removed to reveal the object either in its forward-projected kinematic position or in a backward-displaced position, infants looked significantly longer at the backward-displaced configurations. In infant psychophysics, prolonged looking time reflects cognitive surprise and the violation of expectation. This preferential looking indicates that infants as young as four months of age expect moving objects to exhibit physical momentum, projecting dynamic trajectories forward through space and time before they have developed advanced manual motor skills.

Similarly, developmental research conducted by Helene Intraub and her colleagues demonstrated that boundary extension is present in pre-verbal infants within the first few months of life. In habituation-dishabituation studies using photographic scenes, infants habituated to a scene showed greater dishabituation (longer looking times) when presented with a cropped, closer-up version of the scene than when shown a wider-angle version. The wider-angle version was treated as familiar because the infants had already mentally extended the boundaries of the habituated image. The manifestation of boundary extension in pre-verbal infants proves that this spatial extrapolation is not an acquired cultural habit derived from viewing bordered photographic prints or television screens. Rather, it is a foundational, innate property of the visual system’s integrative scene schema, designed to construct continuous spatial models from birth.

8.2 Age-Related Stability and Cognitive Senescence

As the human brain traverses the lifespan into late adulthood, cognitive systems undergo substantial neurobiological restructuring, often accompanied by marked declines in executive function, processing speed, and episodic working memory capacity. However, investigations into how normal cognitive senescence affects representational momentum and boundary extension reveal a striking pattern of functional preservation, alongside specific kinematic modulations.

Remarkably, Helene Intraub demonstrated that boundary extension remains entirely robust and preserved across healthy aging. Older adults, despite showing typical age-related declines in the detailed recall of local scene objects and significant reductions in visual working memory capacity, demonstrate identical or slightly heightened levels of boundary extension compared to young college-aged adults. Because boundary extension relies on automated, feedforward-feedback loops between scene-selective cortex (PPA, RSC) and early visual cortex rather than resource-intensive prefrontal executive control, the core schematic projection of spatial boundaries remains impervious to normal age-related cognitive decline.

In contrast, representational momentum exhibits interesting modulations in older adult populations. While the core directional forward displacement error persists across the lifespan, the precise scaling of momentum relative to implied velocity changes. Older adults frequently demonstrate a reduced magnitude of forward displacement at high implied velocities, yet an exaggerated forward displacement at slower, moderate velocities. This alteration is directly linked to age-related changes in the temporal processing speed of the magnocellular pathway and structural alterations within cortical area MT+/V5. Because the aging visual cortex requires longer temporal windows to integrate sequential kinematic cues, the internal velocity calculation runs at a modified gain, altering the mathematical scaling of the forward projection while preserving the fundamental dynamic forward bias.

8.3 Neurodevelopmental Variations and Clinical Populations

Studying dynamic spatial extrapolation across clinical and neurodevelopmental populations provides profound insights into atypical cognitive architectures. A particularly compelling line of research focuses on individuals diagnosed with Autism Spectrum Disorder (ASD). One of the dominant theoretical models of autistic perception is the *weak central coherence* hypothesis, which posits that autistic visual processing is biased toward hyper-veridical local detail extraction at the expense of holistic, global context integration.

When tested in boundary extension paradigms, individuals with ASD exhibit a striking, atypical profile: they demonstrate significantly attenuated boundary extension, and in some experimental tasks involving high-detail scenes, they exhibit near-veridical boundary memory. Because autistic cognition prioritizes high-fidelity local features and displays reduced reliance on top-down amodal schemas, the visual system does not automatically project the panoramic spatial frame to the same degree as neurotypical observers. This reduced boundary extension provides a rare, objective cognitive marker of how altered top-down schematic weighting directly alters the internal representation of the visual world.

In clinical populations characterized by executive dysfunction and motor planning impairments, such as Developmental Coordination Disorder (DCD) and spatial processing deficits, representational momentum is frequently disrupted. Individuals with DCD show irregular, non-linear forward displacement errors that fail to scale with implied velocity, reflecting a breakdown in the internal mental models of physical kinematics. Even more dramatically, individuals with schizophrenia demonstrate profound impairments in forward predictive modeling. Due to systemic disruptions in predictive coding, NMDA receptor hypofunction, and impaired corollary discharge signaling, patients with schizophrenia struggle to generate accurate forward projections of dynamic visual trajectories. This failure of predictive extrapolation causes the visual world to appear disjointed and erratic, directly contributing to perceptual fragmentation and positive symptoms such as delusions of control.

9. Computational Models and Mathematical Parameterizations

9.1 Mathematical Formulation of Momentum Displacements

To transition from qualitative descriptions of representational momentum to precise quantitative predictions, mathematical psychologists formulated differential equations that parameterize psychological velocity, acceleration, and deceleration functions. In Freyd’s framework, the internal representation of an object’s position $x$ at time $t$ can be modeled as a dynamic state variable undergoing continuous transformation in an internal psychological phase space.

The forward displacement $\Delta x$ (the magnitude of representational momentum) is mathematically defined as a function of the implied physical velocity $v$, the inter-stimulus interval or retention retention duration $\Delta t$, and an internal friction or deceleration coefficient $k$. The basic linear displacement can be expressed through the following formulation:

$\Delta x = \int_{0}^{\Delta t} v(t) , dt – \frac{1}{2} k (\Delta t)^2$

In this equation, the internal psychological velocity $v(t)$ carries forward from the terminal inducing stimulus. However, because the physical stimulus is no longer present, the cognitive system applies an internal dampening force—analogous to physical friction—represented by the decelerative constant $k$. As the retention interval $\Delta t$ increases, the forward displacement initially grows linearly, reaches an asymptotic peak (typically between 200 and 400 milliseconds), and then gradually declines toward baseline as the dampening term overtakes the initial momentum.

When acceleration is implied in the inducing sequence, the mathematical model must incorporate higher-order derivative terms. If the inducing sequence implies a constant acceleration $a$, the forward displacement incorporates the change in velocity:

$\Delta x = v_0 \Delta t + \frac{1}{2} (a – k) (\Delta t)^2$

Psychophysical experiments confirm that when the implied acceleration $a$ exceeds the internal dampening coefficient $k$, the magnitude of the forward memory shift increases exponentially before leveling off, confirming that human visual memory mathematically parameterizes Newtonian mechanics within its internal representational algorithms.

9.2 Neural Network Architectures for Scene Completion

In computational neuroscience and artificial intelligence, researchers have engineered artificial neural network architectures that simulate and replicate Helene Intraub’s boundary extension. Modern deep learning architectures—most notably Generative Adversarial Networks (GANs), deep convolutional autoencoders, and predictive coding Recurrent Neural Networks (RNNs)—provide powerful computational analogies for how biological brains extrapolate spatial layouts.

In an algorithmic sense, boundary extension is analogous to the computational process of *image outpainting* (the inverse of inpainting). When a deep convolutional autoencoder is trained on large datasets of naturalistic ecological scenes, its latent space develops high-order structural abstractions of environmental layouts. If the network is presented with a cropped, bounded input image and tasked with optimizing predictive spatial representations, it uses its latent priors to generate the most probable surrounding pixels. The generative network does not simply mirror the existing edge pixels; it extrapolates continuous ground planes, walls, horizons, and contextually probable objects.

However, computational comparisons reveal critical structural disparities between artificial AI inpainting algorithms and biological boundary extension:

• Amodal versus Modal Rendering: Artificial inpainting engines synthesize high-frequency, literal pixel values across the extended borders. Human boundary extension, in contrast, operates primarily as an *amodal* spatial representation; observers do not hallucinate explicit, high-resolution photographic pixels in their sensory field, but rather generate a high-confidence structural framework of the adjacent layout.
• Centrifugal Geometry: Deep neural networks often show edge artifacts or blurring at image boundaries. Biological boundary extension exhibits a smooth, scale-invariant centrifugal expansion that seamlessly preserves the spatial perspective and vanishing points of the original camera angle.
• Speed of Generation: Recurrent predictive coding networks require multiple iterative cycles of backpropagation and error minimization to reconstruct missing borders, whereas the human visual brain generates boundary extension within a single feedforward-feedback pass spanning less than 50 milliseconds.

9.3 Parameter Estimation via Bayesian Inference

To mathematically formalize boundary extension within a probabilistic computational framework, cognitive modelers employ Bayesian inference models. Under this formulation, the remembered boundary coordinate $B_{mem}$ is treated as a maximum a posteriori (MAP) estimate derived from two competing probability distributions: the noisy sensory measurement of the physical boundary $B_{sens}$, and the internal environmental prior distribution $B_{prior}$, which dictates that scenes are continuous panoramic layouts.

We can parameterize this interaction using Gaussian probability densities. Let the sensory evidence be distributed as:

$P(B_{sens} | B) \sim \mathcal{N}(B_{true}, \sigma_{sens}^2)$

where $B_{true}$ represents the true physical boundary coordinate of the photograph, and $\sigma_{sens}^2$ represents the sensory noise or uncertainty in the visual representation. Concurrently, the internal spatial prior is distributed as:

$P(B) \sim \mathcal{N}(B_{panoramic}, \sigma_{prior}^2)$

where $B_{panoramic}$ is an expanded spatial coordinate representing the wider continuous world, and $\sigma_{prior}^2$ represents the variance or strength of the spatial schema. According to Bayes’ rule, the posterior distribution of the remembered boundary is obtained by multiplying the likelihood by the prior, yielding an optimal posterior mean:

$B_{mem} = \frac{\sigma_{prior}^2}{\sigma_{sens}^2 + \sigma_{prior}^2} B_{true} + \frac{\sigma_{sens}^2}{\sigma_{sens}^2 + \sigma_{prior}^2} B_{panoramic}$

This mathematical formulation elegantly captures every empirical finding of boundary extension. When an image is exposed for long durations with high clarity, sensory noise $\sigma_{sens}^2$ is small, and $B_{mem}$ remains closer to the true physical boundary $B_{true}$ (though boundary extension still occurs due to the fundamental strength of the ecological prior). However, when exposure duration is ultra-brief, when visual masks introduce high noise, or when the retention interval is extended, $\sigma_{sens}^2$ increases dramatically. As a mathematical consequence, the weighting shifts decisively toward $B_{panoramic}$, causing the magnitude of boundary extension to increase. Bayesian parameter estimations across diverse empirical image sets have validated this model, proving that boundary extension reflects mathematically optimal spatial inference under uncertainty.

10. Ecological Validity, Environmental Context, and Real-World Paradigms

10.1 Naturalistic versus Artificial Stimuli Dynamics

A critical evolutionary frontier in both representational momentum and boundary extension research involves evaluating how these cognitive mechanisms operate when tested with highly complex, naturalistic ecological stimuli compared to simplified laboratory abstractions. In Jennifer Freyd’s early experiments, stimuli were predominantly restricted to high-contrast geometric forms—rectangles, circles, and arrowheads—rotating in empty, featureless display space. While these minimalist designs were essential for eliminating semantic confounds, subsequent research demonstrated that ecological and semantic context profoundly shapes dynamic extrapolation.

When researchers replace abstract geometric shapes with photorealistic depictions of animate entities (such as a running cheetah, a diving hawk, or a sprinting human athlete), the magnitude of representational momentum increases significantly compared to inanimate mechanical objects (such as an automobile, an airplane, or a rolling sphere) moving at identical implied velocities. The visual brain applies biological motion heuristics: animate entities are recognized as self-propelled agents capable of internal acceleration, requiring the cognitive simulation engine to extrapolate their trajectories with greater predictive urgency. Furthermore, if an animate target is depicted in a biomechanical posture implying imminent deceleration (such as a runner planting their feet to stop), the forward displacement is appropriately truncated, proving that representational momentum is deeply sensitive to naturalistic biomechanical and contextual constraints.

Similarly, Helene Intraub demonstrated that boundary extension is intrinsically tied to the ecological realism of the visual scene. When an object is depicted in a natural, highly cluttered ecological environment—such as a kitchen counter filled with utensils, a dense forest floor, or a crowded city street—boundary extension is robust and pronounced. The continuous ground surfaces, depth planes, and structural affordances provide rich contextual cues that activate extensive spatial schemas. If the exact same object is presented in a sanitized, visually impoverished setting—such as floating in empty white space or placed against a flat, textureless artificial plane—boundary extension vanishes or converts into boundary restriction. The phenomenon is therefore not a generic visual distortion, but an ecologically driven mechanism explicitly designed to process complex, multi-layered environments.

10.2 Haptic and Auditory Cross-Modal Extrapolations

Perhaps the most extraordinary proof that representational momentum and boundary extension reflect foundational, amodal properties of human cognition—rather than idiosyncrasies of the retinal visual system—comes from cross-modal research spanning the auditory and haptic (tactile) sensory modalities. Cognitive science has revealed that both dynamic forward extrapolation and peripheral spatial completion operate seamlessly across non-visual senses.

In the auditory domain, researchers established the existence of *auditory representational momentum*. When listeners are presented with rapid sequences of discrete auditory tones that imply a continuous sweep in pitch (ascending or descending frequency) or continuous motion across spatial acoustic space (via stereo panning), their memory for the terminal tone is systematically shifted forward in the direction of the implied pitch or spatial trajectory. Listeners misremember the final sound as being higher in pitch for ascending sequences, or further to the left/right for spatial sweeps. This proves that representational momentum represents a general cognitive computation that applies to continuous physical variables across both auditory and visual domains.

Even more remarkably, Helene Intraub, in collaboration with cognitive researchers, demonstrated the existence of **haptic boundary extension**. In these groundbreaking experiments, blindfolded sighted participants—as well as congenitally blind individuals who had no visual experience whatsoever—were presented with bounded three-dimensional scenes that they explored exclusively through touch. Participants rested their hands inside a bounded box containing a tangible three-dimensional display (such as a miniature scene with a sculpted tree mounted on a textured ground surface surrounded by a physical boundary wall). After a retention interval, participants adjusted the boundary walls or evaluated probe scenes using haptic exploration.

The results were unequivocal: both sighted and congenitally blind participants exhibited robust haptic boundary extension. When reconstructing or recognizing the scenes through touch, participants remembered the physical boundary walls as being further away from the central object than they actually were, believing the ground surface extended across a wider tactile expanse. The discovery of haptic boundary extension in congenitally blind individuals definitively proves that boundary extension does not rely on visual imagery, photographic optics, or retinal processing. Instead, it is an amodal, fundamental property of the brain’s spatial cognition engine, which automatically extends the perceived borders of continuous space regardless of the sensory channel through which that space is apprehended.

10.3 Environmental Affordances and Action Planning

To fully grasp the ecological imperative behind both representational momentum and boundary extension, one must view these phenomena through the theoretical lens of James J. Gibson’s ecological approach to visual perception, with its central concept of affordances—the actionable properties and possibilities offered by the physical environment to an acting organism. Visual cognition did not evolve to generate passive, aesthetically pleasing pictures of reality; it evolved to facilitate rapid, effective physical action, locomotion, and survival.

In motor action planning, representational momentum provides the computational foundation for effective manual interception, grasping, and catching. When an individual attempts to catch a moving baseball, grab a falling glass, or strike a fleeing target, the physical neuromuscular execution requires an extended time window: somatic motor commands take between 100 and 200 milliseconds to travel from the primary motor cortex through the spinal cord to the musculoskeletal effectors. If the motor system targeted the veridical location where the object was sensed when the motor plan was formulated, every manual interception would fall behind the target. Representational momentum shifts the cognitive and neurological representation forward, automatically feeding the motor cortex an extrapolated coordinate that corresponds to where the object *will be* when the hand arrives, enabling successful physical interception.

Similarly, boundary extension provides an indispensable computational foundation for locomotor spatial updating and navigation. As an animal or human moves through an environment, physical obstacles, terrain changes, and navigational affordances are continuously moving into and out of the immediate field of view. Boundary extension ensures that the spatial representations of these layouts do not drop off abruptly at the edges of current gaze. By maintaining an amodally extended framework of what lies just beyond the immediate perceptual horizon, the visual brain enables the motor system to plan walking paths, anticipate stepping locations, and maintain spatial orientation across continuous active locomotion through complex physical terrains.

11. Applied Implications: Human Factors, Forensics, and Technology

11.1 Eyewitness Testimony and Forensic Reconstruction

The realization that human visual memory systematically and unconsciously distorts the spatial boundaries and physical coordinates of perceived events has profound, disruptive implications for legal jurisprudence, forensic reconstruction, and the evaluation of eyewitness testimony. In criminal trials and legal proceedings, courts historically treat confident eyewitness memory as a reliable record of a crime scene or vehicular accident. However, the robust realities of representational momentum and boundary extension demonstrate that even highly confident, completely sober eyewitnesses are subject to predictable, involuntary memory extrapolations.

In forensic scenarios involving high-velocity vehicular collisions, representational momentum introduces dangerous systematic distortions. An eyewitness observing a speeding automobile just prior to a catastrophic collision does not remember the vehicle at its true terminal braking point; instead, the dynamic momentum carries the mental image forward along its trajectory. Consequently, eyewitnesses consistently overestimate the vehicle’s speed, place the vehicle further into an intersection than it physically was, and misremember the exact point of impact. In aviation and transit disaster investigations, survivor and observer testimonies regarding the final trajectories of descending aircraft routinely display severe forward displacement errors, which can lead accident investigators astray if physical flight-recorder telemetry is unavailable.

Similarly, boundary extension profoundly impacts crime scene eyewitness testimony regarding visibility, proximity, and spatial line of sight. When a witness is shown a photograph of a crime scene (e.g., an alleyway, an entrance, or a room) or when they view an event through a restricted aperture (such as an open doorway, a window frame, or the gap between two buildings), their memory automatically expands the boundaries. During cross-examination or police interviews, witnesses routinely testify with absolute conviction that they “saw” an accomplice standing in the peripheral background, an exit door, or an identifying landmark that was, in physical reality, completely occluded or outside their actual physical field of view. These unconscious, schematic source monitoring errors can lead to wrongful identifications, false corroborations, and erroneous judicial conclusions if forensic investigators do not account for natural boundary extrapolation.

11.2 Aviation, Driving, and Complex Interface Design

In high-stakes aerospace, automotive, and industrial engineering contexts, understanding human dynamic perceptual extrapolation is a life-or-death requirement for human factors engineers and interface designers. Modern pilots and automobile operators are required to monitor complex, dynamic visual displays—such as Primary Flight Displays (PFDs), electronic flight instrument systems, heads-up displays (HUDs), and digital automotive dashboards—that present rapid, high-density kinematic information.

If an avionics display presents a digital indicator (such as an altimeter tape, an airspeed gauge, or a navigational vector) that moves dynamically, representational momentum causes the human pilot to perceive and remember the indicator as having progressed further along its path than it actually has. In high-workload, rapid-descent flight scenarios, this forward extrapolation can lead a pilot to overcorrect controls, inducing Pilot-Induced Oscillations (PIO) or mistakenly believing an altitude limit has already been breached. Human factors engineers must intentionally design digital instruments with dynamic damping, predictive visual cues, or discrete digital readouts to counteract the pilot’s internal kinematic momentum.

Furthermore, in the design of automotive Heads-Up Displays and Autonomous Vehicle (AV) sensor visualizations, boundary extension plays a critical role. When autonomous vehicles present video feeds or digitized spatial reconstructions of the surrounding road on an in-cockpit screen, the driver’s brain automatically extends the boundaries of that screen. If the interface cuts off a pedestrian or cyclist at the digital border, the driver assumes the space immediately outside the screen is clear based on their internal schema. Interface designers must explicitly visualize the *uncertainty zone* at display boundaries, ensuring that autonomous vehicle human-machine interfaces match human operator perceptual expectations and prevent catastrophic misjudgments regarding adjacent vehicular blind spots.

11.3 Virtual Reality, Visual Media, and Cinematic Editing

The entertainment industry, cinematographers, and virtual reality (VR) developers have intuitively exploited representational momentum and boundary extension for decades to craft compelling, immersive visual experiences. In traditional filmmaking and cinematic editing, the foundational technique of the *continuity cut* relies directly on these perceptual extrapolation mechanisms. When an editor cuts from a medium shot of an actor looking off-screen to a close-up shot of an object, the viewer’s brain utilizes boundary extension and implied trajectory to seamlessly bridge the two shots, creating the illusion of a continuous, coherent three-dimensional space.

Cinematographic panning and rapid cuts exploit representational momentum: when a camera pans rapidly across a landscape and cuts to a new angle, the viewer’s dynamic visual simulation carries across the cut. If the editor mismatches the implied momentum vectors—cutting to a shot moving in the opposite direction without a neutral transitional frame—the viewer experiences a jarring cognitive disorientation known as a “jump cut” or directional violation. Master directors and editors deliberately align the dynamic vectors of motion across cuts, allowing the viewer’s representational momentum to glide effortlessly from one visual scene to the next, sustaining deep narrative immersion.

In modern Virtual Reality and Augmented Reality (AR) systems, the failure to accommodate these internal extrapolation engines is a primary cause of *simulator sickness* (cybersickness). When an individual wears a VR head-mounted display, the visual hardware tracks head motion and renders digital space. If there is even a minor latency mismatch between the user’s physical head rotation and the digital rendering, or if the field of view (FOV) is artificially restricted by narrow headset lenses without proper boundary softening, a violent sensory conflict occurs. The user’s vestibular system and internal representational momentum predict where the visual field *should* be, but the lagging display presents an unextrapolated image. This computational mismatch between top-down predictive simulation and lagging sensory feedback triggers nausea, disorientation, and headaches, driving VR engineers to develop predictive display algorithms that render anticipated frames ahead of time.

12. Synthesis and Future Directions in Dynamic Spatial Representation

12.1 Unification of Cognitive Extrapolation Theories

As cognitive science advances into the twenty-first century, the historical separation between Jennifer Freyd’s representational momentum and Helene Intraub’s boundary extension is dissolving into a comprehensive, unified theory of *dynamic spatial cognition*. Rather than viewing temporal extrapolation and spatial layout completion as isolated psychological oddities, contemporary cognitive theorists recognize them as dual manifestations of a single, continuous predictive simulation engine that operates across all levels of human consciousness.

This synthetic framework demonstrates that human mental representation exists along a multidimensional continuum of mental simulation. At the local, fine-grained end of the spectrum, the brain simulates the kinematic properties, velocity vectors, and physical dynamics of individual objects (representational momentum). At the global, contextual end of the spectrum, the brain simulates the panoramic spatial layout, continuous ground surfaces, and environmental affordances of surrounding ecological scenes (boundary extension). Both mechanisms are governed by identical computational imperatives: minimizing prediction error, bridging biological transmission delays, integrating discrete sensory inputs into coherent perceptual wholes, and optimizing real-time behavioral affordances.

This unification resolves long-standing debates regarding whether visual memory is fundamentally *implicit* (perceptual and automatic) or *explicit* (reconstructive and deliberative). The synthesis reveals that the initial generation of both representational momentum and boundary extension is strictly implicit, automatic, and embedded in the early feedforward-feedback architecture of the visual cortex. However, once generated, these anticipatory projections are integrated into the explicit memory trace, becoming indistinguishable from genuine sensory inputs. Human memory does not archive what the eyes saw; it archives what the brain predicted.

12.2 Emerging Neurotechnological Paradigms

The next frontier in unraveling the neural mechanics of representational momentum and boundary extension is being driven by cutting-edge neurotechnological methodologies that surpass the spatial and temporal limits of traditional neuroimaging. Primary among these is the deployment of **high-density intracranial electrophysiology** in presurgical epileptic patients. By placing electrode grids and depth probes directly onto the human cortex—specifically targeting the MT+/V5 complex, the Parahippocampal Place Area, the Retrosplenial Cortex, and early visual areas (V1, V2, V4)—neuroscientists can track the activity of single neurons and local field potentials during extrapolative memory tasks.

These intracranial recordings are beginning to answer precisely when and where top-down predictions overwrite bottom-up inputs. Early data suggests that within 60 to 90 milliseconds of stimulus onset, parahippocampal neurons transmit low-frequency theta and alpha-band traveling waves backward toward the occipital pole, literally pre-activating the retinotopic peripheral neurons before the next saccade or probe appears. Simultaneously, optogenetic and advanced multi-focal Transcranial Magnetic Stimulation (TMS) paradigms are allowing researchers to causally perturb specific nodes within this predictive network, isolating the precise feedback loops responsible for boundary projection and kinematic momentum.

Furthermore, the advent of **ultra-high field 7-Tesla (7T+) functional MRI** is unlocking the ability to map cortical activity at the *layer-specific* (laminar) level. Laminar fMRI allows cognitive neuroscientists to separate sensory feedforward signals arriving in cortical layer IV from top-down feedback signals terminating in superficial (layers I/II) and deep (layers V/VI) cortical layers. Laminar studies of boundary extension and representational momentum are currently testing the core hypothesis of predictive coding: demonstrating that forward displacements and extended scene boundaries correspond directly to elevated BOLD activity in the feedback-receiving superficial layers of early visual cortex, confirming that dynamic extrapolation is driven by top-down cortical projections.

12.3 Open Empirical Questions and Decadal Research Agendas

Despite four decades of intensive research, profound empirical questions remain open for the next generation of cognitive scientists. The decadal research agenda for dynamic mental representations centers on three critical frontiers:

1. The Mathematical Boundary between Perception and Decay: Where is the exact phase transition between predictive perceptual inference and post-perceptual memory decay? Developing mathematical models that unify the microsecond forward projection of momentum with the long-term temporal drift of episodic memory remains an elusive computational goal.
2. Comparative Cross-Species Evolutionary Conservation: To what degree are representational momentum and boundary extension conserved across the animal kingdom? While preliminary studies show dynamic tracking in primates and certain bird species, comprehensive comparative studies examining whether non-mammalian species (such as cephalopods, reptiles, and insects) exhibit boundary extension or representational momentum will illuminate how early these predictive architectures evolved in biological nervous systems.
3. Translational Neurotechnology and Visual Prosthetics: In the biomedical realm, engineers developing cortical visual prosthetics (retinal implants and direct V1 intracortical microelectrode arrays) face a monumental challenge: biological vision relies on automatic predictive extrapolation, whereas artificial cameras provide purely passive, lagging digital frames. If visual prosthetics fail to incorporate the anticipatory forward modeling discovered by Freyd and Intraub, prosthetic users will struggle with severe disorientation, navigational lag, and motion sickness. Future translational neuroengineering must build real-time predictive algorithms directly into the hardware of neural prosthetics, ensuring that artificial vision restores not merely the ability to see the world as it was, but the vital biological capacity to anticipate the world as it will be.

Conclusion

The pioneering empirical paradigms of Jennifer Freyd and Helene Intraub dismantled the long-standing scientific misconception that human visual memory functions as an optical recorder. By uncovering representational momentum and boundary extension, their research revealed that the human mind does not passively reflect physical reality; it actively and predictive models it. Perception and memory are inextricably unified within an anticipatory cognitive architecture that continuously projects dynamic trajectories forward through time and expands bounded vistas outward through space.

These systematic cognitive distortions—once dismissed as minor perceptual bugs or laboratory curiosities—are recognized as profound evolutionary adaptations. They represent the brain’s solution to the constraints of biological neural latency and sensory fragmentation. By internalizing the kinematic laws of Newtonian mechanics and the continuous spatial structure of the ecological world, the visual system ensures that human conscious experience remains synchronized with an unforgiving, rapidly evolving physical reality. As cognitive neuroscience, computational artificial intelligence, and neuroengineering progress, the foundational insights of Freyd and Intraub will remain central to our understanding of how the brain constructs the seamless, dynamic experience of conscious awareness.

References

• Bartlett, F. C. (1932). Remembering: An experimental and social study. Cambridge: Cambridge University Press.
• Finke, R. A., & Freyd, J. J. (1985). Transformations of mental representations in visual memory. Science, 228(4707), 1541-1542. https://doi.org/10.1126/science.4012304
• Freyd, J. J. (1983). The mental representation of movement when static stimuli are used. Perception & Psychophysics, 33(6), 575-581. https://doi.org/10.3758/BF03202940
• Freyd, J. J. (1987). Dynamic representations. Psychological Review, 94(4), 427-438. https://doi.org/10.1037/0033-295X.94.4.427
• Freyd, J. J., & Finke, R. A. (1984). Representational momentum. Journal of Experimental Psychology: Learning, Memory, and Cognition, 10(1), 126-132. https://doi.org/10.1037/0278-7393.10.1.126
• Freyd, J. J., & Finke, R. A. (1985). A velocity effect for representational momentum. Bulletin of the Psychonomic Society, 23(6), 443-446. https://doi.org/10.3758/BF03329851
• Friston, K. (2005). A theory of cortical responses. Philosophical Transactions of the Royal Society B: Biological Sciences, 360(1456), 815-836. https://doi.org/10.1098/rstb.2005.1622
• Gibson, J. J. (1979). The ecological approach to visual perception. Boston: Houghton Mifflin.
• Goodale, M. A., & Milner, A. D. (1992). Separate visual pathways for perception and action. Trends in Neurosciences, 15(1), 20-25. https://doi.org/10.1016/0166-2236(92)90344-8
• Hubbard, T. L. (2005). Representational momentum: Mentally following the consequences of dynamic principles. Psychonomic Bulletin & Review, 12(5), 822-851. https://doi.org/10.3758/BF03196775
• Intraub, H. (1997). The representation of visual scenes: A fresh look at boundary extension. Cognitive Psychology, 34(3), 260-286. https://doi.org/10.1006/cogp.1997.0669
• Intraub, H. (2010). Rethinking scene perception: A multisource model. Psychology of Learning and Motivation, 52, 231-264. https://doi.org/10.1016/S0079-7421(10)52006-2
• Intraub, H., & Dickinson, C. A. (2008). Boundary extension occurs in toddlers and infants: Evidence for an innate spatial schema. Infancy, 13(4), 302-322. https://doi.org/10.1080/15250000802188719
• Intraub, H., Gottesman, C. V., & Bills, K. V. (1998). Effects of visual context on memory for objects: Boundary extension versus boundary restriction. Journal of Experimental Psychology: Learning, Memory, and Cognition, 24(4), 1014-1024. https://doi.org/10.1037/0278-7393.24.4.1014
• Intraub, H., Morelli, F., & Lopez, A. (2010). Haptic boundary extension in sighted and blind observers. Perception, 39(8), 1081-1094. https://doi.org/10.1068/p6700
• Intraub, H., & Richardson, M. (1989). Wide-angle memories of close-up scenes: A boundary extension effect in picture memory. Journal of Experimental Psychology: Learning, Memory, and Cognition, 15(2), 179-187. https://doi.org/10.1037/0278-7393.15.2.179
• Kourtzi, Z., & Kanwisher, N. (2000). Activation in human MT/MST by static images with implied motion. Nature Neuroscience, 3(4), 393-396. https://doi.org/10.1038/73962
• Park, S., Intraub, H., Yi, D. J., Widders, D., & Chun, M. M. (2007). Beyond the edges of a view: Boundary extension in human ventral visual cortex. Neuron, 54(2), 335-342. https://doi.org/10.1016/j.neuron.2007.04.006
• Rao, R. P., & Ballard, D. H. (1999). Predictive coding in the visual cortex: A functional interpretation of some extra-classical receptive-field effects. Nature Neuroscience, 2(1), 79-87. https://doi.org/10.1038/4580
• Senior, C., Barnes, J., Giampietro, V., Simmons, A., Bullmore, E. T., Brammer, M., & David, A. S. (2000). The functional neuroanatomy of implicit-motion perception or ‘representational momentum’. Current Biology, 10(1), 16-22. https://doi.org/10.1016/S0960-9822(99)00259-6