Real-Time Texture Detection Using the LU-Transform

This paper introduces a fast texture descriptor, the LU-transform. It is inspired by previous methods, the SVD-transform and Eigen-transform, which yield measures of image roughness by considering the singular values or eigenvalues of matrices formed by copying greyvalues from a square patch around a pixel directly into a matrix of the same size. The SVD and Eigen-transforms therefore capture the degree to which linear dependencies are present in the image patch. In this paper we demonstrate that similar information can be recovered by examining the properties of the LU factorization of the matrix, and in particular the diagonal part of the U matrix. While the LU-transform yields an output qualitatively similar to the those of the SVD and Eigen-transforms, it can be computed about an order of magnitude faster. It is a much simpler algorithm and well-suited to implementation on parallel architectures. We capitalise on these properties in an implementation of the algorithm on a Graphics Processor Unit (GPU) which makes it even faster than a CPU implementation, and frees the CPU for other computations.