Matrix-valued kernels for shape deformation analysis

Matrix-valued Kernels for Shape Deformation Analysis

The main purpose of this paper is providing a systematic study and classification of non-scalar kernels for Reproducing Kernel Hilbert Spaces (RKHS), to be used in the analysis of deformation in shape spaces endowed with metrics induced by the action of groups of diffeomorphisms. After providing an introduction to matrix-valued kernels and their relevant differential properties, we explore exte...

Learning Equivariant Functions with Matrix Valued Kernels

This paper presents a new class of matrix valued kernels that are ideally suited to learn vector valued equivariant functions. Matrix valued kernels are a natural generalization of the common notion of a kernel. We set the theoretical foundations of so called equivariant matrix valued kernels. We work out several properties of equivariant kernels, we give an interpretation of their behavior and...

Rotation Invariant Object Detection with Matrix-Valued Kernels

This article presents a rotation invariant object detection system. We propose two main contributions. On the one hand we fuse two different approaches, the ’Parts and Structure’-model and the generalized Hough Transform. Local image patches cast votes for the locations of the parts of the searched object. Then, an explicit model is fitted to the estimated density functions for the different pa...

Learning Equivariant Functions with Matrix Valued Kernels - Theory and Applications

This paper presents a new class of matrix valued kernels, which are ideally suited to learn vector valued equivariant functions. Matrix valued kernels are a natural generalization of the common notion of a kernel. We set the theoretical foundations of so called equivariant matrix valued kernels. We work out several properties of equivariant kernels, we give an interpretation of their behavior a...

Deformation analysis for shape and image processing