Perception of local shape from shading

Theoretically, metric solid shape is not determined uniquely by shading. Consequently, human vision has difficulty in categorizing shape when shading is the only cue. In the present research, subjects were required to categorize shaded quadric surfaces. We found that they were rather poor at this task; they confused hyperbolic and elliptic (both convex and concave) shapes easily. When a cast shadow visually indicated the direction of the illuminant, they were able to notice the concavity or convexity of elliptic shapes. However, they still confused elliptic and hyperbolic ones. Finally, when an animated sequence of eight intensity patterns belonging to one quadric shape had been displayed, the subjects were able to categorize the quadrics. However, the results are still quite moderate. Our experiments indicate that local shading structure is only a weak shape cue when presented in the absence of other visual cues

Pre-Symmetry Sets of 3D shapes

The investigation of 3D euclidean symmetry sets (SS) and medial axis is an important area, due in particular to their various important applications. The pre-symmetry set of a surface M in 3-space (resp. smooth closed curve in 2D) is the set of pairs of points which contribute to the symmetry set, that is, the closure of the set of pairs of distinct points p and q in M, for which there exists a sphere (resp. a circle) tangent to M at p and at q. The aim of this paper is to address problems related to the smoothness and the singularities of the pre-symmetry sets of 3D shapes. We show that the pre-symmetry set of a smooth surface in 3-space has locally the structure of the graph of a function from R^2 to R^2, in many cases of interest.Comment: ACM-class: I.2; I.5; I.4; J.2. Latex, 3 grouped figures. The final version will appear in the proceedings of the First International Workshop on Deep Structure, Singularities and Computer Vision, Maastricht June 200

Pictorial surface attitude and local depth comparisons

We measured local surface attitude for monocular pictorial relief and performed pairwise depth-comparison judgments on the same picture. Both measurements were subject to internal consistency checks. We found that both measurements were consistent with a relief (continuous pictorial surface) interpretation within the session-to-session scatter. We reconstructed the pictorial relief from both measurements separately, and found results that differed in detail but were quite similar in their basic structures. Formally, one expects certain geometrical identities that relate range and attitude data. Because we have independent measurements of both, we can attempt an empirical verification of such geometrical identities. Moreover, we can check whether the statistical scatter in the data indicates that, for example, the surface attitudes are derivable from a depth map or vice versa. We estimate that pairwise depth comparisons are an order of magnitude less precise than might be expected from the attitude data. Thus, the surface attitudes cannot be derived from a depth map as operationally defined by our methods, although the reverse is a possibility

Shape from stereo : a systematic approach using quadratic surfaces

We used quadratic shapes in several psychophysical shape-from-stereo tasks. The shapes were elegantly represented in a 2-D parameter space by the scale-independent shape index and the scale-dependent curvedness. Using random-dot stereograms to depict the surfaces, we found that the shape of hyperbolic surfaces is slightly more difficult to recognize than the shape of elliptic surfaces. We found that curvedness (and indirectly, scale) has little or no influence on shape recognition

Geometry of isophote curves

In this paper, we consider the intensity surface of a 2D image, we study the evolution of the symmetry sets (and medial axes) of 1-parameter families of iso-intensity curves. This extends the investigation done on 1-parameter families of smooth plane curves (Bruce and Giblin, Giblin and Kimia, etc.) to the general case when the family of curves includes a singular member, as will happen if the curves are obtained by taking plane sections of a smooth surface, at the moment when the plane becomes tangent to the surface. Looking at those surface sections as isophote curves, of the pixel values of an image embedded in the real plane, this allows us to propose to combine object representation using a skeleton or symmetry set representation and the appearance modelling by representing image information as a collection of medial representations for the level-sets of an image.Comment: 15 pages, 7 figure

On Image Contours of Projective Shapes

International audienceThis paper revisits classical properties of the outlines of solid shapes bounded by smooth surfaces, and shows that they can be established in a purely projective setting, without appealing to Euclidean measurements such as normals or curvatures. In particular, we give new synthetic proofs of Koenderink's famous theorem on convexities and concavities of the image contour, and of the fact that the rim turns in the same direction as the viewpoint in the tangent plane at a convex point, and in the opposite direction at a hyperbolic point. This suggests that projective geometry should not be viewed merely as an analytical device for linearizing calculations (its main role in structure from motion), but as the proper framework for studying the relation between solid shape and its perspective projections. Unlike previous work in this area, the proposed approach does not require an oriented setting, nor does it rely on any choice of coordinate system or analytical considerations