Local Log-Euclidean Covariance Matrix (L2ECM) for Image Representation and Its Applications

摘要: This paper presents Local Log-Euclidean Covariance Matrix (L2ECM) to represent neighboring image properties by capturing correlation of various cues. Our work is inspired the structure tensor which computes second-order moment gradients for representing local properties, and Diffusion Tensor Imaging produces tensor-valued characterizing tissue structure. approach begins with extraction raw features consisting multiple For each pixel we compute a covariance matrix in its region, producing image. The matrices are symmetric positive-definite (SPD) forms Riemannian manifold. In framework, SPD form Lie group equipped Euclidean space structure, enables common operations logarithm domain. Hence, logarithm, obtaining pixel-wise matrix. After half-vectorization obtain vector-valued L2ECM image, can be flexibly handled while preserving geometric matrices. used diverse or vision tasks. We demonstrate some applications statistical modeling simple central achieve promising performance.