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Shape perception is generally treated as a problem relevant to the ability to recognize objects. Alternatively, it is a problem that falls within the general domain of space perception and as such, the data from shape perception studies contributes to discussions about the geometry of visual space. This geometry is generally acknowledged not to be Euclidian, but instead, elliptical, hyperbolic or affine, which is to say, something that admits the distortions found in so many shape perception studies. In this article, I consider the repercussions of such understanding of perceived shape and the geometry of visual space in the context of visually guided action. Assuming that, then what does the need for information about surface shape to guide such actions imply about the current theory and results in the shape perception literature? Mainly, I compared two prominent approaches in perception and action, world model and control law approaches. Numerous shape perception (space perception) literatures have provided strong evidence that 3-D structures cannot be accurately perceived and there are only the non-Euclidean and ordinal relationships between physical and perceived space. The recovery of Euclidean structure cannot occur in the perception of structure from motion(e.g., Cornilleau-peres & Droulez, 1989; Norman & Lappin, 1992; Norman & Todd, 1993; Perotti, Todd, Lappin & Phillips, 1998; Todd & Bressan, 1990; Todd & Norman, 1991), the perception of structure from binocular stereopsis (e.g., Johnston, 1991; Tittle, Todd, Perotti & Norman, 1995), the perception of structure from combination of stereo and motion (e.g., Tittle & Braunstein, 1993; Tittle et al., 1995), and even under full cue conditions (e.g., Norman & Todd, 1996; Norman, Todd, & Phillips, 1995, Todd & Norman, 2003; Todd, Tittle & Norman, 1995). 1 Dankook University, Requests for reprints should be sent to Young-Lim Lee, Psychology department, Dankook University, 119 Dandae-ro, Dongnam-gu, Cheonan-si, Chungnam, South Korea. 66 Journal of Psychology and Behavioral Science, Vol. 2(3 & 4), December 2014 It is important to keep in mind that although there are many sources of optical information to perceive 3-D structure, neither a single individual source nor a combination of sources is enough for accurate perception of 3-D structure. However, it could be possible that the laboratory environment is constrained compared to our natural environment, thus other crucial sources of optical information are missed in the experiments. Borjesson & Lind (1996) found that there was no difference between parallel and polar projection for the perception of Euclidean structure, but they also examined the possibility of polar projection with large visual angles for the perception of Euclidean structure. To investigate the effect of large visual angle, they used a continuous dot surface simulating a sinusoidal protuberance directed toward the observer from polar-projected motion and two different visual angles (4.35° and 17.4°). Observers had to judge the height of the protuberance relative to its width at the base and to reproduce the height to width ratios on the response screen using the keyboard. There were two vertical lines on the response screen. The left line indicated the width of the protuberance, and the distance between left line and right line indicated the height of the protuberance. The observers had to move the right vertical line to reproduce the height to width ratios. At the small visual angle, the observers could not reproduce the height to width ratios at all. At the large visual angle, the observers consistently produced the height to width ratios relative to the simulated height to width ratios, although they underestimated the height to width ratios as the simulated height to width ratios increased. Thus, the observers perceived the depth dimension (i.e., height of the protuberance) more precisely at the large visual angle, but Euclidean structure was not recovered since the height was still underestimated even at the large visual angle. They concluded that the observers can use additional information from the polar project with the large visual angle, although the recovery of Euclidean structure was not yielded by the addition of polar information. Also, they suggested that the visual system might be limited when trying to perceive Euclidean structure because of the noise in the measurements of retinal velocities. Under small visual angles, a very small noise while measuring retinal velocities produces great errors. For instance, Koendreink and van Doorn (1987) have shown that if the visual angle is less than 15° and the measurement noise variance is 5%, it is nearly impossible to recover Euclidean structure.

Perception and Action: A Closer Look at Two Theories