This paper proposes a novel method called micro-deformation analysis to analyze and describe local image structures. This method is a general analytic tool and can be applied to any high-dimensional scalar or vector functions. We derive the tensor matrix from this method as the descriptor to represent the information within local image patches. Our experimental results suggest that we can design low-dimensional local tensor descriptors with performance comparable to the popular SIFT descriptor, which is the state-of-the-art feature descriptor used for object recognition and categorization.