The recognition of objects from imagery in a manner that is independent of scale, posi-tion, and orientation may be achieved by characterizing an object with a set of extracted invariant features. Several different recognition techniques have been demonstrated that utilize moments to generate such invariant features. These techniques are derived from general moment theory that is widely used throughout statistics and mechanics. In this paper, basic Cartesian moment theory is reviewed and its application to object recognition and image analysis is presented. The geometric properties of low-order moments are discussed along with the definition of several moment-space linear geometric transforms. Finally, significant research in moment-based object recognition is reviewed. 1.

. Moments of images are widely used in pattern recognition, because in suitable form they can be made invariant to variations in translation, rotation and size. However the computation of discrete moments by their definition requires many multiplications which limits the speed of computation. In this paper we express the moments as a linear combination of higher order prefix sums, obtained by iterating the prefix sum computation on previous prefix sums, starting with the original function values. Thus the p 0 th moment m p = P N x=1 x p f(x) can be computed by O(N \Deltap) additions followed by p multiplyadds. The prefix summations can be realized in time O(N) using p + 1 simple adders, and in time O(p\DeltalogN ) using parallel prefix computation and O(N) adders. The prefix sums can also be used in the computation of two-dimensional moments for any intensity function f(x; y). Using a simple bit-serial addition architecture, it is sufficient with 13 full adders and some shift re...

Green's theorem evaluates a double integral over the region of an object by a simple integration along the boundary of the object. It has been used in moment computation since the shape of a binary object is totally determined by its boundary. By using a discrete analogue of Green's theorem, we present a new algorithm for fast computation of geometric moments. The algorithm is faster than previous methods, and gives exact results. The importance of exact computation is discussed by examining the invariance of Hu's moments. A fast method for computing moments of regions in grey level image, using discrete Green's theorem, is also presented. 1 Introduction Moments have been widely used in shape analysis and pattern recognition [1][9]. The (p + q)'th order moment of an image is deøned as m pq = Z y Z x g(x; y)x p y q dxdy (1) where g(x; y) is the intensity as a function of spatial position. The double integral is often replaced by a double summation in discrete images m pq = ...