Learning affine transformations of the plane for model-based object recognition

We consider the problem of learning the mapping between the image coordinates of unknown affine views of an object and the parameters of the affine transformation that can align a known view of the same object with them. A single layer neural network (SL-NN) is used to learn the mapping. Although the proposed approach is conceptually similar to other approaches in the literature, its practical advantages are more profound. The views used to train the SL-NN are not obtained by taking different pictures of the object but by sampling the space of its affine transformed views. This space is constructed by estimating the range of values that the parameters of affine transformation can assume using a single view and a methodology based on singular value decomposition and interval arithmetic. The proposed scheme is as accurate as traditional least-squares approaches but faster. A front-end stage to the SL-NN, based on principal components analysis increases its noise tolerance dramatically and guides us in deciding how many training views are necessary in order for it to learn a good mapping.