Abstract: The relationship between simulated and judged depth separations for pairs of probe dots on planar surface patches was examined in a series of 6 experiments. The simulated slant of the patches was varied without varying the simulated depth separation of the probe dots by varying the depth gradient orthogonal to the direction determined by the probe dots on the image plane. Judged depth separation varied with mean slant for constant simulated depth separations. When observers judged depth separations along a closed path, the integral of the signed depths did not sum to zero, as would be required in Euclidean geometry. These results are inconsistent with the view that the mapping between simulated and perceived 3-D structure is alfme and indicate that, in general, the perceived structure cannot be represented in either a Euclidean space or an affine space. Moreover, these results are consistent with a first-order temporal analysis of the optic flow.

Abstract: The paper deals with the structure-motion problem for uncalibrated cameras, in the case that subsidiary information is available, consisting e.g. in known coplanarities or parallelities among points in the scene, or known positions of some focal points (hand-eye calibration). Despite unknown camera calibrations, it is shown that in many instances the subsidiary information makes affine or even Euclidean reconstruction possible. A parametrization by affine shape and depth is used, providing a simple framework for the incorporation of apriori knowledge, and enabling the development of iterative, rapidly converging algorithms. Any number of points in any number of images are used in a uniform way, with equal priority, and independently of coordinate representations. Moreover, occlusions are allowed.

Abstract: We introduce a unified framework for developing matching constraints of multiple affine views and rederive 2-view (affine epipolar geometry) and 3-view (affine image transfer) constraints within this framework. We then describe a new linear method for Euclidean motion and structure from 3 calibrated affine images, based on insight into the particular structure of these multiple-view constraints. Compared with the existing linear method of Huang and Lee (1989), the new method uses different and more appropriate constraints. It has no failure mode of the Euclidean factorisation method of Tomasi and Kanade (1992). We demonstrate the method on real image sequences.

Abstract: This paper addresses the recovery of structure and motion from uncalibrated images of a scene under full perspective or under affine projection. Particular emphasis is placed on the configuration of two views, while the extension to $N$ views is given in Appendix. A unified expression of the fundamental matrix is derived which is valid for any projection model without lens distortion (including full perspective and affine camera). Affine reconstruction is considered as a special projective reconstruction. The theory is elaborated in a way such that everyone having knowledge of linear algebra can understand the discussion without difficulty. A new technique for affine reconstruction is developed, which consists in first estimating the affine epipolar geometry and then performing a triangulation for each point match with respect to an implicit common affine basis.

Abstract: We introduce a unified framework for developing matching constraints of multiple affine views and rederive 2-view (affine epipolar geometry) and 3-view (affine image transfer) constraints within this framwork. With the insight into the particular structure of these multiple-view constraints, we first describe a new linear method for Euclidean motion and structure from 3 calibrated affine images. Compared with the existing linear method of Huang and Lee [6], the new method uses different and more appropriate constraints. It has no failure mode of the Euclidean factorisation method of Tomasi and Kanade [20]. We then describe how to integrate points and lines and establish some minimal point/line configurations for structure recovery. The method is demonstrated on real image sequences.

Abstract: We establish a one-one affine parametrization of all completely positive maps on a matrix algebra that map the identity matrix to a given positive matrix. The parametrization is applied to the analysis of quantum binary channels.

Abstract: In this paper, we present an area-based affine invariant representation of shapes and a point-correspondence algorithm which supports multi-scale similarity matching for shape-based retrieval. This method is affine invariant and stable against noise and shape deformations. Since the area-based representation scheme simultaneously captures both local and global affine invariant features of shapes, it makes the solution to the correspondence problem very robust.

Abstract: The algebra consisting of those linear transformations of a complex inner product space that have a formal adjoint is shown to possess a special involution. Two earlier results concerning special involutions are then generalized.