Riemannian level-set methods for tensor-valued data

We present a novel approach for the derivation of PDEs modeling curvaturedriven flows for matrix-valued data. This approach is based on the Riemannian geometry of the manifold of Symmetric Positive Definite Matrices P(n). The differential geometric attributes of P(n) −such as the bi-invariant metric, the covariant derivative and the Christoffel symbols− allow us to extend scalar-valued mean curvature and snakes methods to the tensor data setting. Since the data live on P(n), these methods have the natural property of preserving positive definiteness of the initial data. Experiments on three-dimensional real DT-MRI data show that the proposed methods are highly robust.