Fractional Order Derivatives as an Optimization Tool for Object Detection and Tracking Algorithms

Abstract

Optimization techniques are nowadays one of the most important branches of computer science due to the limitations of the computing power availability especially in cases of mobile platforms. Algorithms which can be used on such units have to be optimized for memory and computing power. In the paper we focused on optimization techniques for image analysis algorithms by limiting the number of necessary operations. The optimized algorithm has been designed to detect and follow a specified marker, known a priori, and is based on the correlation coefficient match between the acquired template and the current image. The acquired template is taken from the previous processed frame. The match operation is based on Pearson's correlation coefficient, so the whole mechanism is therefore highly demanding in terms of computing power. Optimization is performed mainly using the Region of Interest (ROI) to exclude irrelevant parts of the image. The algorithm is optimized using Grünvald - Letnikov fractional - order backward difference to estimate the position of the marker in a sequence of images. This limits the number of operations required to maintain the precision of the algorithm. Based on the position of the object in previous frames, a fractional order mathematical tool is able to estimate at relatively low cost and with high accuracy the probable position of the object in the incoming image. Here, we explain the workflow of the template detection and following algorithm, as well as the mathematical basis of the fractional order derivative optimization tool. The processor load connected to the optimized algorithm was reduced by over 35%.