A robust intrinsic feature of images derived from the tensor manifold

As an important feature of images, the structure tensor (ST) provides properties of the local image intensities. However, it is a challenging task to analyse images directly using STs since STs are 2nd-order symmetric positive semi-definite matrices. In this paper, we define a robust intrinsic feature of images using ST. In addition, using our feature, we propose an improved image similarity measure. By converting the ST into a symmetric positive definite (called tensor) matrix, we define our feature using the extended of tensors calculated in a Riemannian manifold. Our feature shows the essential natural properties of ST and images as tensors are analysed on the tensor manifold. Moreover, defined by the global embedded geometry of the structure tensor, our feature provides a stable intrinsic property of images. The experiments show that our feature performs well in representing the essential attributes of images, especially the edges and important structures. It also shows that our image similarity measure can accurately detect similar images or patches.