Search for identical regions in images using invariant moments

Abstract

One of the ways to describe objects on images is to identify some of their characteristic points or points of attention. Areas of neighborhoods of attention points are described by descriptors (lots of signs) in such way that they can be identified and compared. These signs are used to search for identical points in other images. The article investigates and establishes the possibility of searching for arbitrary local image regions by descriptors constructed with using invariant moments. A feature of the proposed method is that the calculation of the invariant moments of local areas is carried out with using the integral representation of the geometric moments of the image. Integral representation is a matrix with the same size as the image. The elements of the matrix is the sums of the geometric moments of individual pixels, which are located above and to the left with respect to the coordinates of this element. The number of matrices depends on the order of the geometric moments. For moments up to the second order (inclusively), there will be six such matrices. Calculation of one of six geometric moments of an arbitrary rectangular area of the image comes down up to 3 operations such as summation or subtraction of elements of the corresponding matrix located in the corners of this area. The invariant moments are calculated on base of six geometric moments. The search is performed by scanning the image coordinate grid with a window of a given size. In this case, the invariant moments and additional parameters are calculated and compared with similar parameters of the neighborhoods of the reference point of different size (taking into account the possible change in the image scale). The best option is selected according to a given condition. Almost all mass operations of the procedures for calculating the parameters of standards and searching of identical points make it possible explicitly perform parallel computations in the SIMD mode. As a result, the integral representation of geometric moments and the possibility of using parallel computations at all stages will significantly speed up the calculations and allow you to get good indicators of the search efficiency for identical points and the speed of work