Sigma Set: A Small Second Order Statistical Region Descriptor

Abstract

Given an image region of pixels, second order statistics can be used to construct a descriptor for object representation. One example is the covariance matrix descriptor, which shows high discriminative power and good robustness in many computer vision applications. However, operations for the covariance matrix on Riemannian manifolds are usually computationally demanding. This paper proposes a novel second order statistics based region descriptor, named "Sigma Set", in the form of a small set of vectors, which can be uniquely constructed through Cholesky decomposition on the covariance matrix. Sigma Set is of low dimension, powerful and robust. Moreover, compared with the covariance matrix, Sigma Set is not only more efficient in distance evaluation and average calculation, but also easier to be enriched with first order statistics. Experimental results in texture classification and object tracking verify the effectiveness and efficiency of this novel object descriptor.