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The problem of matching two images of the same objects but after movements or slight deformations arises in medical imaging, but also in the microscopic analysis of physical or biological structures. We present a new matching strategy consisting of two steps. We consider the grey level function (modulo a normalization) as a probability density function. First, we apply a density based clustering method in order to obtain a tree which classifies the points on which the grey level function is defined. Secondly, we use the identification of the hierarchical representations of the two images to guide the image matching or to define a distance between the images for object recognition. The transformation invariance properties of the representations allow to extract invariant image points. Using the identification of the trees, they allow, in addition, to find the correspondence between invariant points even if these have moved locally. Then, we obtain the transformation function as the thin plate interpolation of the corresponding point pairs. On the other hand, if we use tree identification, this enables us to propose several criterias to distinguish between real deformations and noise effects. In practice, we treat, for instance, first coarse trees (with few leaves) and pass to ever refining trees, after. The method's results on real images will be discussed.

Tree Representation for Image Matching and Object Recognition