This paper proposes a methodology to estimate the correlation model between a pair of images that are given under the form of linear measurements. We consider an image pair whose common objects are relatively displaced due to the positioning of vision sensors. In such scenarios the correlation model that relates the displacement between the objects is effectively represented by a disparity image. We consider a framework where each image is directly acquired and compressed by projecting onto a random basis of lower dimension. Given the linear measurements computed from the images we propose to estimate the underlying correlation model directly in the compressed domain without reconstructing the images that is usually a costly solution. We first show that the correlated images can be efficiently related using a linear operator. Using this linear relationship between the images we derive the relationship between the corresponding measurements in the compressed domain. The underlying correlation model is then built by solving a regularized energy minimization problem. Experimental results show that the proposed scheme estimates an accurate correlation model between the images. Also we show by experiments that the proposed scheme performs competitively with the scheme that estimates the correlation model from the reconstructed images.