This paper presents a novel algorithm for computing the relative motion between images from compressed linear measurements. We propose a geometry based correlation model that describes the relative motion between images by translational motion of visual features. We focus on the problem of estimating the motion field from a reference image and a highly compressed image given by means of random projections, which are further quantized and entropy coded. We capture the most prominent visual features in the reference image using geometric basis functions. Then, we propose a regularized optimization problem for estimating the corresponding features in the compressed image, and eventually the dense motion field is generated from the local transform of the geometric features. Experimental results show that the proposed scheme defines an accurate motion field. In addition, when the motion field is used for image prediction, the resulting rate-distortion (RD) performance becomes better than the independent coding solution based on JPEG-2000, which demonstrates the potential of the proposed scheme for distributed coding algorithms.