Correspondence and Affine Shape from Two Orthographic Views: Motion and Recognition

The paper presents a simple model for recovering affine shape and correspondence from two orthographic views of a 3D object. It is shown that four corresponding points along two orthographic views, taken under similar illumination conditions, determine affine shape and correspondence for all other points. The scheme is useful for purposes of visual recognition by generating novel views of an object given two model views. It is also shown that the scheme can handle objects with smooth boundaries, to a good approximation, without introducing any modifications or additional model views

c ○ 2003 Kluwer Academic Publishers. Manufactured in The Netherlands. Understanding the Behavior of SFM Algorithms: A Geometric Approach

Abstract. We put forth in this paper a geometrically motivated motion error analysis which is capable of supporting investigation of global effect such as inherent ambiguities. This is in contrast with the usual statistical kinds of motion error analyses which can only deal with local effect such as noise perturbations, and where much of the results regarding global ambiguities are empirical in nature. The error expression that we derive allows us to predict the exact conditions likely to cause ambiguities and how these ambiguities vary with motion types such as lateral or forward motion. Given the erroneous 3-D motion estimates caused by the inherent ambiguities, it is also important to study the behavior of the resultant distortion in depth recovered under different motion-scene configurations. Such an investigation may alert us to the occurrence of ambiguities under different conditions and be more careful in picking the solution. Our formulation, though geometrically motivated, was also put to use in modeling the effect of noise and in revealing the strong influence of feature distribution. Experiments on both synthetic and real image sequences were conducted to verify the various theoretical predictions. Keywords: structure from motion, error analysis, epipolar constraint, inherent ambiguity, depth distortio

Geometry and Photometry in 3D Visual Recognition

The report addresses the problem of visual recognition under two sources of variability: geometric and photometric. The geometric deals with the relation between 3D objects and their views under orthographic and perspective projection. The photometric deals with the relation between 3D matte objects and their images under changing illumination conditions. Taken together, an alignment-based method is presented for recognizing objects viewed from arbitrary viewing positions and illuminated by arbitrary settings of light sources