Comparison of image patches using local moment invariants

We propose a new set of moment invariants based on Krawtchouk polynomials for comparison of local patches in 2D images. Being computed from discrete functions, these moments do not carry the error due to discretization. Unlike many orthogonal moments, which usually capture global features, Krawtchouk moments can be used to compute local descriptors from a region-of-interest in an image. This can be achieved by changing two parameters, and hence shifting the center of interest region horizontally or vertically or both. This property enables comparison of two arbitrary local regions. We show that Krawtchouk moments can be written as a linear combination of geometric moments, so easily converted to rotation, size, and position independent invariants. We also construct local Hu-based invariants using Hu invariants and utilizing them on images localized by the weight function given in the definition of Krawtchouk polynomials. We give the formulation of local Krawtchouk-based and Hu-based invariants, and evaluate their discriminative performance on local comparison of artificially generated test images.