Abstract:

We present a novel, integral image based algorithm to compute feature covariance matrices within all arbitrary size rectangular regions in an image. This technique significantly improves the computational load of covariance matrix extraction process by taking advantage of the spatial arrangement of points. Covariance is an essential measure of how much the deviation of two or more variables or processes match. In our case, these variables correspond to point features such as coordinate, color, gradient, orientation, and filter responses. Integral images are intermediate image representations used for calculation of region sums. Each point of the integral image is a summation of all the points inside the rectangle bounded by the upper left corner of the image and the point of interest. Using this representation, any rectangular region sum can be computed in constant time. We follow a similar idea for fast calculation of region covariance. We construct integral images for all separate features as well as integral images of the multiplication of any two feature combinations. Using these set of integral images and region corner point coordinates, we directly extract the covariance matrix coefficients. We show that the proposed integral image based method decreases the computational load to quadratic time.