Introduction

Multiview analysis of scenes is an active area in Computer Vision today. The structure of points and lines as seen in two views attracted the attention of computer vision researchers in the eighties and early nineties [5,1,3]. Similar studies on the underlying constraints in three views followed [6,2]. The structure of greater than three views has also been studied [7,8]. Two excellent textbooks have recently appeared focusing on multiview geometry for Computer Vision[1,3]. The mathematical structure underlying multiple views has been studied with respect to projective, affine, and Euclidean frameworks of the world with amazing results. Multiview studies have focussed on how geometric primitives such as points, lines and planes are related across views. Specifically, the algebraic constraints satisfied by the projection of such primitives in different views have been the focus of intense studies. The multilinear relationships that were discovered have been found to be useful for a number of tasks, such as view transfer, geometric reconstruction and self calibration. The richness of the information present among the geometric primitives in a collection of them has not attracted a lot of attention. Such properties are difficult to capture in the spatial domain but can be extracted with relative ease in a transform domain. The analysis of boundary shapes in multiple views using Fourier domain descriptors can provide structure not explicit in the geometric space and provide interesting handles for solving problems like object recognition and view transfer. The properties of collections of primitives in multiple views are studied in this paper. Specifically, we look at the situation of viewing a planar shape from different viewpoints. Recognizing objects from diverse viewpoints is essential to interpreting the structure and meaning of a scene. We use a Fourier domain representation for the boundary of the object and derive recognition constraints the projections of the object must satisfy in multiple views. These constraints are in the form of the rank of the matrix of the descriptor coefficient values. We present the basic problem formulation in the next section. Numerical results to validate the theoretical claims are presented in Section 3, along with some discussions on the underlying issues. Section 4 presents a few concluding remarks.