Extracting Fourier descriptors from compressive measurements

Fourier descriptors (FDs) are shape-based features for the recognition of two-dimensional connected shapes. We propose a method that can extract FDs of an object directly from compressive measurements without reconstructing the image. Our method entails estimating the edges via discrete horizontal and vertical image gradients from compressive measurements. Fourier descriptors are then extracted from the thresholded edges. One of the main advantages of the proposed method is that it requires fewer number of compressive measurements to estimate FDs than required to estimate the original image. Various numerical experiments on synthetic and real data demonstrate the effectiveness of the proposed method.