Shape description and recognition by implicit Chebyshev moments

Abstract

Chebyshev Moments(CMs) have been applied to representation and recognition of 2D object shapes in image processing and computer vision. However they still suffer from poor representation power and difficulty in computing invariants for shapes. In this work, we present Implicit Chebyshev Moments (ICMs) to overcome these issues. Firstly, we use Euclid distance transformation to generate a series of level sets based on a given shape. Secondly, we fit an implicit Chebyshev polynomial to the data set consisting of the obtained level sets together with all the boundary points on the original shape and call the obtained coefficients of the fitted implicit Chebyshev polynomial ICMs. Finally, we propose a new approach to derive geometric invariants based on ICMs. In addition, we also develop an algorithm for the determination of a suitable degree for implicit Chebyshev polynomials before representing a given shape. Experimental results show the ICMs are more efficient for representing complex shapes than CMs.