Abstract
Implicit polynomials (IPs) are applied to represent 2D object shapes in image processing and computer vision. However, it is difficult for IPs to represent complex object shapes due to high computational cost and high instability. In this work, we present a new representation model based on IPs, which is called fractional implicit polynomial (FIP). Firstly, the general formula for FIP and a definition of base are given; secondly, we investigate the properties of FIPs and conclude that the FIP representation exhibits higher stability and higher power than IP representation due to the presence of the base. Thirdly, we develop an algorithm for determination of a moderate degree for an FIP to represent a given shape, which can be obtained by only computing the number of stationary points on the shapes. We compare FIPs with IPs by test on various object shapes and the results show that the FIP is indeed sufficiently powerful to represent the complex object shapes.
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