Graph Kernels Between Point Clouds
Point clouds are sets of points in two or three dimensions. Most kernel methods for learning on sets of points have not yet dealt with the specific geometrical invariances and practical constraints associated with point clouds in computer vision and graphics. In this paper, the authors present extensions of graph kernels for point clouds, which allow to use kernel methods for such objects as shapes, line drawings, or any three-dimensional point clouds. In order to design rich and numerically efficient kernels with as few free parameters as possible, they use kernels between covariance matrices and their factorizations on graphical models. They derive polynomial time dynamic programming recursions and present applications to recognition of handwritten digits and Chinese characters from few training examples.