Perception-Based 2D Shape Modeling by Curvature Shaping

2D curve representations usually take algebraic forms in ways not related to visual perception. This poses great difficulties in connecting curve representation with object recognition where information computed from raw images must be manipulated in a perceptually meaningful way and compared to the representation. In this paper we show that 2D curves can be represented compactly by imposing shaping constraints in curvature space, which can be readily computed directly from input images. The inverse problem of reconstructing a 2D curve from the shaping constraints is solved by a method using curvature shaping, in which the 2D image space is used in conjunction with its curvature space to generate the curve dynamically. The solution allows curve length to be determined and used subsequently for curve modeling using polynomial basis functions. Polynomial basis functions of high orders are shown to be necessary to incorporate perceptual information commonly available at the biological visual front-end.