Description of solid shape and its inference from occluding contours

Beusmans, Jack M. H.; Hoffman, Donald D.; Bennett, Bruce M.

doi:10.1364/josaa.4.001155

Cited by 45 publications

(33 citation statements)

References 21 publications

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“…It does not give part cuts that segment the shape, however, which are needed to determine part structure. For example, if a shape has more than two negative minima, they may be joined in more than one way to give part cuts (see Figures 16A and 16B; Beusmans, Hoffman, & Bennett, 1987;Siddiqi & Kimia, 1995). In addition, even if a shape has precisely two negative minima, joining them may not always give a natural parsing of the shape (see Figures 16C and 16D; Singh et al, 1999).…”

Section: Discussionmentioning

confidence: 99%

Early computation of part structure: Evidence from visual search

Singh

2002

Perception & Psychophysics

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The visual system represents object shapes in terms of intermediate-level parts. The minima rule proposes that the visual system uses negative minima of curvature to define boundaries between parts. We used visual search to test whether part structures consistent with the minima rule are computed preattentively-or at least, rapidly and early in visual processing. The results of Experiments 1 and 2 showed that whereas the search for a non-minima-segmentedshape is fast and efficient among minimasegmented shapes, the reverse search is slow and inefficient. This asymmetry is expected if parsing at negative minima occurs obligatorily. The results of Experiments 3 and 4 showed that although both minima-and non-minima-segmentedshapes pop out among unsegmented shapes, the search for minimasegmented shapes is significantly slower. Together, these results demonstrate that the visual system segments shapes into parts, using negative minima of curvature, and that it does so rapidly in early stages of visual processing.

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Section: Discussionmentioning

confidence: 99%

Early computation of part structure: Evidence from visual search

Singh

2002

Perception & Psychophysics

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“…As we have seen, for a 2D shape these part boundaries are points of negative minima of curvature on the outline of the shape. The minima rule does not, however, define part cuts: It does not tell how to pair negative minima of curvature to create cuts that parse the shape into parts (Beusmans et al, 1987;Siddiqi & Kimia, 1995). For example, for the cross on the left in Figure 20, the minima rule gives the four negative minima as part boundaries, but is silent on how to join these to give cuts.…”

Section: From Part Boundaries To Part Cutsmentioning

confidence: 99%

Part-Based Representations of Visual Shape and Implications for Visual Cognition

Singh

Hoffman

2001

From Fragments to Objects - Segmentation and Grouping in Vision

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Human vision organizes object shapes in terms of parts and their spatial relationships.Converging experimental evidence suggests that parts are computed rapidly and early in visual processing. We review theories of how human vision parses shapes. In particular, we discuss the minima rule for finding part boundaries on shapes, geometric factors for creating part cuts, and a theory of part salience. We review empirical evidence that human vision parses shapes into parts, and show that parts-based representations explain various aspects of our visual cognition, including figure-ground assignment, judgments of shape similarity, memory for shapes, visual search for shapes, the perception of transparency, and the allocation of visual attention to objects. From Fragments to Objects: Segmentation and Grouping in Vision2

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“…Speci cally, estimates of local shape may beextracted early on in the visual system to facilitate the parsing of complex objects into parts. It has been suggested that a smooth object could be partitioned, either along the contours of negative minima of a principal curvature Ho man and Richards, 1984;Beusmans, Ho man and Bennett, 1987, or along the parabolic curves which separate hyperbolic from elliptic regions Koenderink and van Doorn, 1982; Brady, P once, Yuille and Asada, 1985;Vaina and Zlaveta, 1990. The results of our experiment suggests that such a segmentation of an object along its parabolic curves is a reasonable possibility.…”

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confidence: 59%

Categorical Local-Shape Perception

1996

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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...

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Description of solid shape and its inference from occluding contours

Cited by 45 publications

References 21 publications

Early computation of part structure: Evidence from visual search

Early computation of part structure: Evidence from visual search

Part-Based Representations of Visual Shape and Implications for Visual Cognition

Categorical Local-Shape Perception

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