Learning orthographic transformations for object recognition

In this paper, we consider the problem of learning to predict the correct pose of a 3D object, assuming orthographic projection and 3D linear transformations. A neural network is trained to learn the desired mapping. First, we consider the problem of predicting all possible views that an object can produce. This is performed by representing the object with a small number of reference views and using algebraic functions of views to construct the space of all possible views that the object can produce. Fundamental to this procedure is a methodology based on Singular Value Decomposition and interval Arithmetic for estimating of the ranges of values that the parameters of algebraic functions can assume. Then, a neural network is trained using a number of views (training views) which are generated by sampling the space of views of the object. During learning, a training view is presented to the inputs of the network which is required to respond at its outputs with the parameters of the algebraic functions used to generate the view from the reference views. Compared to similar approaches in the literature, the proposed approach has the advantage that it does not require the 3D models of the objects or a large number of views, it is extendible to other types of projections, and it is more practical for object recognition.