Graph kernels between point clouds

TL;DR

This paper extends graph kernel methods to point clouds, enabling shape recognition and analysis in computer vision by leveraging covariance-based kernels and efficient dynamic programming algorithms.

Contribution

It introduces novel graph kernels tailored for point clouds, incorporating covariance matrix kernels and efficient recursive computations for practical shape recognition.

Findings

Effective recognition of handwritten digits with few examples

Application to Chinese character recognition

Polynomial time algorithms for kernel computation

Abstract

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, we present extensions of graph kernels for point clouds, which allow to use kernel methods for such ob jects 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, we use kernels between covariance matrices and their factorizations on graphical models. We derive polynomial time dynamic programming recursions and present applications to recognition of handwritten digits and Chinese characters from few training examples.