Categorical Local-Shape Perception

Abstract

How well do observers perceive the local shape of an object from its shaded image? We address this complex problem by rst deriving a potential representation of local solid shape, and by presenting the results of a simple psychophysical experiment. Our descriptor of local solid shape, called shape characteristic, provides a viewpoint independent continuum between hyperbolic saddle-shaped and elliptic egg-shaped points. We then study the ability of human observers to make categorical judgments of local solid shape. We investigated this question using a smooth croissant", a simple object made of two connected regions of elliptic and hyperbolic points. Observers decided whether the surface was locally elliptic or hyperbolic at various points on the object. The task was natural, and the observers could reliably partition the shaded image of the object into one elliptic and one hyperbolic region. The ability of observers to perform this partition shows that they can, at least implicitly, localize the parabolic curves on a surface. This ability to locate the parabolic curve can in turn beexploited for other purposes, in particular to segment an object into its parts.Categorical Local Shape Perception 1 A central issue in object perception is how the shape of an object is represented by the visual system. Shape may be represented in a variety of ways that depend on the visual task and the stages of processing in a given task. However, several factors might be common to all these representations. In particular, we take as a fundamental property of any shape representation that it should be viewpoint invariant. This property alone precludes traditional representations in terms of depth values or local surface orientation Marr, 1982. We suggest here that a natural local representation of solid shape is given by the dichotomy b e t ween hyperbolic and elliptic patches.Hyperbolic points are the points on the surface where the shape can locally be described as a saddle, while elliptic points correspond to egg-shaped regions. The boundaries between hyperbolic and elliptic regions are the parabolic curves, at which loci the surface is locally cylindrical. Parabolic curves are associated with important events occuring on a surface, such as the formation of a new occluding contour segment, a new shadow o r a n e w s p e c u l a r point Koenderink, 1990;Mamassian, 1995;Longuet-Higgins, 1960.In this paper, we take the rst steps towards characterizing human ability to categorize local solid shape in terms of view-independent descriptions. In the rst section, we derive a local representation of solid shape based on the hyperbolic-elliptic dichotomy. We then describe a psychophysical experiment whose purpose was to see how reliably human observers could partition a simple surface into hyperbolic and elliptic regions. Encouraged by the results of the experiment, we discuss the advantages to have a local solid shape representation such as the one built from our viewpoint i n variant descriptor. Local Solid Shape SpaceIn this se...

Illumination, Shading and the Perception of Local Orientation

“…These studies demonstratedthat such a task could be repeatedwith little variability, but unfortunately the error in terms of slant and tilt was not reported. Thirdly, perceived local solid shape has been estimated from its two components, which describe how the surface is curved and how much it is curved (Koenderink, 1990;Mamassian et al, 1996). Regarding the first component, one finds a bias to perceive small quadratic shapes as elliptic convex (Erens et al, 1993); regarding the second component, a shaded cylinder appears flatter than it actually is (Todd & Mingolla, 1983), although a relatively small Weber fraction was found in a curvature discrimination task (Johnston & Passmore, 1994a).…”

Shape, Illumination, and Reflectance from Shading

“…The occluding contour of a shape (the contour that surrounds the silhouette of a shape) is a powerful cue for shape interpretation [56] which often dominates shading cues [57], and algorithms have been presented for coarsely estimating shape given contour information [58]. At the occluding contour of an object, the surface is tangent to all rays from the vantage point.…”

Categorical perception of familiar objects

“…It has also been reported that other types of local shape changes are also categorically perceived (Mamassian, Kersten, & Knill, 1996). In their study, Mamassian et al asked participants to classify a specified local shape on an object surface as either hyperbolic or elliptical.…”