<title>Affine-invariant recognition of gray-scale objects by Fourier descriptors</title>

Abstract

The affine invariant recognition of two-dimensional objects which have the same shape but a different gray level function is a difficult problem in computer vision. A possible solution to the problem is based on the method of affine invariant moments. However, the moments have a badly conditioned dynamic range and they turn out to be very sensitive to noise. This paper presents a new method which is based on affine invariant Fourier descriptors for planar curves. It suggests a weighted parameterization for the boundary of an object based on its gray level function. The parameter of a boundary point is defined as the sum of gray levels of the area covered by a line from the center of mass to a starting point of the boundary moving along the boundary. The parameterization is an affine mapping with respect to the transformed object and to an arbitrary starting point of the contour finder. This parameterization enables the development of affine invariant Fourier descriptors. The Fourier descriptors consider two features, the contour and the gray level function of the object. The set of Fourier descriptors which characterizes the image pattern is not complete but their capabilities for pattern separation is very good. The method is less vulnerable to noise than the method of affine invariant moments. Application tests under real conditions demonstrate the practicability of the proposed algorithm. The complexity of the algorithm for a pattern with N pixels is 0(N).