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This paper addresses the problem of distributed coding of images whose correlation is driven by the motion of objects or the camera positioning. It concentrates on the problem where images are encoded with compressed linear measurements. We propose a geometry-based correlation model that describes the common information in pairs of images. We assume that the constitutive components of natural images can be captured by visual features that undergo local transformations (e.g., translation) in different images. We first identify prominent visual features by computing a sparse approximation of a reference image with a dictionary of geometric basis functions. We then pose a regularized optimization problem in order to estimate the corresponding features in correlated images that are given by quantized linear measurements. The correlation model is thus given by the relative geometric transformations between corresponding features. We then propose an efficient joint decoding algorithm that reconstructs the compressed images such that they are consistent with both the quantized measurements and the correlation model. Experimental results show that the proposed algorithm effectively estimates the correlation between images in multiview data sets. In addition, the proposed algorithm provides effective decoding performance that advantageously compares to independent coding solutions and state-of-the-art distributed coding schemes based on disparity learning.