Riemannian Geometry, Sparse Representation, the Marriage

Mehrtash Harandi (NICTA)

COMPUTER VISION AND ROBOTICS SERIES

DATE: 2012-09-20
TIME: 16:00:00 - 17:00:00
LOCATION: NICTA - 7 London Circuit
CONTACT: JavaScript must be enabled to display this email address.

ABSTRACT:
Sparse-based representations have recently led to notable results in various visual recognition tasks.

In a separate line of research, recent advances suggest that a wide range of computer vision problems

can be addressed more appropriately by considering Riemannian geometry. This talk addresses the problem of sparse coding and dictionary learning

over the space of symmetric positive definite matrices, which form a Riemannian manifold.

With the aid of the recently introduced Stein kernel (related to a symmetric version of Bregman matrix divergence),

we propose to perform sparse coding by embedding Riemannian manifolds into reproducing kernel Hilbert spaces.

This leads to a convex and kernel version of the Lasso problem, which can be solved efficiently. We furthermore propose an algorithm

for learning a Riemannian dictionary (used for sparse coding), closely tied to the Stein kernel.

Experiments on several classification tasks (face recognition, texture classification, person re-identification)

show that the proposed sparse coding approach achieves notable improvements in discrimination accuracy,

in comparison to several state-of-the-art methods including tensor sparse coding, Riemannian locality preserving projection,

and symmetry-driven accumulation of local features.