A Novel Approach To The Approximation Of Conformal Mappings And Emerging Applications To Shape Recognition Of Planar-Domain

There have been significant advances in computer graphics and computer vision for description and recognition of rigid shapes and objects. However, the problem of description and recognition of non-rigid shapes and objects is still an open problem. In an earlier study [10], we proposed a geodesic field space-based approach to describe and analyze non-rigid shapes from a point correspondence perspective. In this current study, we describe a canonical set of shapes, very much like a dictionary with mathematical structures that are inherently relevant to the shape classification task. We propose a novel method of representing 2D shapes where every planar shape will be assigned a unique fingerprint, which is a conformal map of the shape to a canonical shape in the plan. We believe that the study presented in this paper can be extended to describe and recognize both, rigid and non-rigid shapes and objects. The main focus of this paper is to provide an insight into the mathematical and geometrical fundamentals. We will restrict our attention to the case of doubly-connected planar domains.