Riemannian level-set methods for tensor-valued data

TL;DR

This paper introduces a new PDE-based method for processing tensor-valued data using Riemannian geometry on the manifold of Symmetric Positive Definite Matrices, enabling curvature-driven flows.

Contribution

It develops a novel framework for PDE modeling of matrix-valued data leveraging Riemannian geometry, which was not previously applied in this context.

Findings

Provides a new PDE modeling approach for tensor data

Utilizes Riemannian geometry on Pos(n) manifold

Enables curvature-driven flows for matrix-valued data

Abstract

We present a novel approach for the derivation of PDE modeling curvature-driven flows for matrix-valued data. This approach is based on the Riemannian geometry of the manifold of Symmetric Positive Definite Matrices Pos(n).