Fast Calculation of Covariance Matrices for Arbitrary Size Cuboids

We propose a fast calculation method to extract feature covariance matrix of cuboid of arbitrary size and arbitrary location within a given video. Every pixel in a video has several features, such as coordinates, color, gray value, gradients and orientation. Feature covariance matrix can be used to describe a video cuboid. By taking advantage of the spatio-temporal arrangement of pixels using integral video, any cuboid sum can be computed in constant time. We follow a similar idea for fast calculation of cuboid's covariance matrices. We construct integral videos for all separate features as well as integral videos of the multiplication of any two feature combinations. Using this set of integral videos we can expedite the search process more than hundreds of times in comparison to the existing conventional approach.