Perceptual Compression Of Space Through Position Integration

Perceptual Compression of Space through Position Integration

When moving figures are occluded and revealed piecemeal as they move across a narrow slit, observers may perceive them as integrated but distorted. They may also perceive much more of the figure as simultaneously visible than is actually presented at any moment. We obtained quantitative measures of both the perceived distortion and perceived simultaneity under free viewing conditions and related these phenomena to spontaneous pursuit eye movements, the retinal painting produced by this pursuit, and the occurrence of saccades. We found both shape compressions and expansions, depending on figure velocity. We also obtained quantitative evidence that observers perceived slices of the moving figures far wider than the slit through which they were presented. Eye-motion records and retinal stabilization revealed that spontaneous pursuit and the spatially extended images that could have been painted out by this pursuit played no role in the perceived global shape distortions and made only a small contribution to the perceived simultaneity. Therefore, under free viewing conditions, both the distortions and simultaneity of these “anorthoscopic” figure percepts must be the consequence of a post retinal process that integrates the figures over space and time independent of eye motions.

Under natural viewing conditions, occluded objects are often revealed in a piecemeal fashion as they move past apertures. Objects revealed in this way are often not only recognized by inference but also perceived as integrated wholes. Even when the aperture is a strait slit that reveals only a narrow slice of a moving object at any moment in time, observers often report seeing the complete object moving across the slit rather than a sequence of local features (Anstis & Atkinson, 1967; Parks, 1965; ZÐ"¶llner, 1862). These slit-viewed percepts share many of the attributes of simultaneously viewed objects. They can, for example, elicit visual illusions such as the MÐ"јllerвЂ"Lyer illusion (Day & Duffy, 1988; Morgan, Findlay, & Watt, 1982). However, they can also differ from simultaneously viewed objects insofar as they often appear spatially distorted (compressed or elongated). ZÐ"¶llner (1862) designated these percepts “anorthoscopic”. He adopted this term from Plateau (1836), who had previously developed a device he termed an “anorthoscope”, which allowed distorted images on a rotating disc to be viewed through a sequence of slits rotating in opposite direction in a manner that allowed them to be seen as undistorted and stationary. It is plausible that Plateau derived the name from the Greek prefixes “ana” and “ortho” to indicate “restoration” of the figures by the viewing device. Whatever Plateau's intent, following ZÐ"¶llner, we will use the term anorthoscopic to specifically refer to the integrated percepts formed when an object moves behind a stationary slit.

The visual system must integrate spatial information over time along the motion trajectory of the partially occluded object to form such anorthoscopic object percepts. Observers typically perceive the moving objects compressed along the axis of motion when their velocities are sufficiently high and elongated on the axis of motion when their velocities are sufficiently low (Anstis & Atkinson, 1967; Helmholtz, 1867; Morgan et al., 1982; Rotschild, 1922; von Vierordt, 1868; ZÐ"¶llner, 1862). In addition, there is a tendency for observers to substantially overestimate the amount of figure simultaneously visible in the aperture at any moment (Morgan et al., 1982; Parks, 1965; ZÐ"¶llner, 1862). A review of the early research on anorthoscopic perception can be found in Anstis and Atkinson (1967) and Morgan et al. (1982); a review of contemporary research can be found in Fendrich, Rieger, and Heinze (2005).

Theories seeking to explain the formation of anorthoscopic percepts have sometimes linked their formation, their character, or both to eye movements (Anstis & Atkinson, 1967; Hafed & Krauzlis, 2006; Helmholtz, 1867; Rock, 1981). Alternatively, eye movements observed when observers view anorthoscopic displays (Fendrich et al., 2005; Mack, Fendrich, & Wong, 1982; Morgan et al., 1982) might be contingent on the perception of the motion of the integrated figure.

An eye-motion-based explanation that can, in principle, account for both the formation and properties of anorthoscopic figure percepts is the “retinal painting” hypothesis, which was first formulated by Helmholtz (1867) and continues to be debated (e.g., Anstis, 2005). This hypothesis assumes that observers tend to track the trajectory of a moving object with their eyes as it crosses the narrow aperture, causing a (persisting) image of its successively visible parts to be painted onto adjacent positions on the retina. The resulting spatially extended retinal image is taken to be the basis of the integrated percept of the object. Pursuit that is slower than the actual object velocity will result in a compressed painted image, which could account for the perceived compression of objects that move rapidly. Similarly, pursuit faster than the actual rate of object motion would result in an elongation of the painted image and percept. Finally, the formation of a spatially extended retinal image can account for the apparent increase in the amount of figure that appears to be simultaneously visible. It should be noted, however, that this account of perceived simultaneity depends on both the retinal painting produced by pursuit and the persistence of the spatially extended painted image, either at the level of the retina itself or in some subsequent retinotopic store. To acknowledge this, we will henceforward refer to the retinal painting/retinotopic storage hypothesis.

The retinal painting/retinotopic storage hypothesis has an appealing simplicity and has received some empirical support. Specifically, when a continuously visible tracking target is used to guide pursuit eye motions, the image painted by the figure moving behind the slit can be highly predictive of the shape that is perceived (Anstis & Atkinson, 1967; Morgan et al., 1982). Anstis and Atkinson (1967), for example, found that, during the tracking of external targets, the perceived width of a series of ellipses was independent of their actual shape but closely matched their painted shape. Morgan et al. (1982) found that during the tracking of an external target, when figure velocities were high (10 deg/s) or a very narrow slit was employed (4.5 arcmin), the width of anorthoscopic percepts was reduced proportional to a reduction in retinal painting