Shape space estimation by higher-rank of SOM

The aim of this study is to develop an estimation method for a shape space. In this work, “shape space” means a nonlinear subspace formed by a class of visual shapes, in which the continuous change in shapes is naturally represented. By using the shape space, various operations dealing with shapes, such as identification, classification, recognition, and interpolation can be carried out in the shape space. This paper introduces an algorithm based on a generative model of shapes. A higher-rank of the self-organizing map (SOM²) is used to implement the shape space estimation method. We use this method to estimate the shape space of artificial contours. In addition, we present results from a simulation of omnidirectional camera images taken from mobile robots. Our technique accurately predicts changes in image properties as the robot’s attitude changes. Finally, we consider the addition of local features to our method. We show that the inclusion of local features solves the correspondence problem. These results suggest the potential of our technique in the future.