Defining a geometric probability measure in correspondence problems for branched structures

Correspondence Problems in the case of branched structures are a challenging and interesting sub-case of general Correspondence Problems. Many usual assumptions do not hold in this framework. Therefore, we seek to define a probability measure for the correspondence that takes into account only the geometrical properties of the structure which are known to be always true and some possible observed features. In the present paper we first define what should be meant as solution to Correspondence Problems in the case of branched structures. Then, we propose a probability measure defined only on the epipolar constraint and observable variables. We state that, in this way, we can generalize some general assumptions, e.g. the ordering constraint. Finally, we test the goodness of our definition of probability measure using a simplified framework, i.e. the images show the entire scene. We apply our probability to find correspondences in simulated examples and propose further developments for a correspondence method.