Matching two clusters of points extracted from satellite images

Image matching is a stage one performs as soon as one has two images of the same scene, taken from two different points of view. Matching these images aims at finding the mathematical transformation that enables passing from any point of the first one to the corresponding point in the other. As this study is related to satellite images, we show that the geometrical transformation can be approximated by a homography. Furthermore we want to match two clusters of points with no information of radiometry. Therefore, we have to guess the right parameters for this homography, by minimizing an appropriate cost function we define here. Then, the topography of the cost function is our main concern for the minimisation process. If looking for the right mathematical parameters seems the most natural way, we show that in this case the cost function has ''chaotic'' variations, so we need a complex technique for the minimization. To avoid this, we suggest guessing the parameters determining the conditions of the snapshot. Thus, we give the expression of the homography from these ''physical parameters'' and show that the topography of the cost function gets smoother. Thus the minimization process gets simpler.