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

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