Level set segmentation using image second order statistics

This paper proposes a novel level set based image segmentation method by use of image second statistics and logarithmic Euclidean metric. Different from previous tensor based image segmentation approaches, the proposed method adopts covariance feature as region-level descriptor rather than pixel-level one. On the basis of feature image, we utilize second order statistics of image feature, i.e., covariance matrix, to model image region representation, which is of low dimension, invariant to uniform illumination change, insensitive to noise, and more importantly provide a natural mechanism of incorporating different types of image features by modeling their correlations. We model image segmentation problem as one finding the optimal segmentation that maximizes the covariance distance between foreground region and background region. Typically, covariance matrices do not lie on Euclidean space. Our solution to this is to exploit logarithmic Euclidean distance as a metric to compute the similarity between two matrices. The experimental results show that covariance matrix as region descriptor do form an effective representation for image segmentation problems, and the proposed image energy can be used to segment images and extract object boundaries reliably and accurately.