Fourier domain representation of planar curves for recognition in multiple views

Recognition of planar shapes is an important problem in computer vision and pattern recognition. The same planar object contour imaged from different cameras or from different viewpoints looks different and their recognition is non-trivial. Traditional shape recognition deals with views of the shapes that differ only by simple rotations, translations, and scaling. However, shapes suffer more serious deformation between two general views and hence recognition approaches designed to handle translations, rotations, and/or scaling would prove to be insufficient. Many algebraic relations between matching primitives in multiple views have been identified recently. In this paper, we explore how shape properties and multiview relations can be combined to recognize planar shapes across multiple views. We propose novel recognition constraints that a planar shape boundary must satisfy in multiple views. The constraints are on the rank of a Fourier-domain measurement matrix computed from the points on the shape boundary. Our method can additionally compute the correspondence between the curve points after a match is established. We demonstrate the applications of these constraints experimentally on a number of synthetic and real images.