The Shape Manifold and Its Hilbert Space Embedding

Sadeep Jayasumana (NICTA)

COMPUTER VISION AND ROBOTICS SERIES

DATE: 2013-09-05
TIME: 16:00:00 - 17:00:00
LOCATION: NICTA - 7 London Circuit
CONTACT: JavaScript must be enabled to display this email address.

ABSTRACT:
In this presentation, I will talk about our recent work on shape manifolds, which has been accepted for publication in ICCV 2013.More specifically, I will talk about Kendall's shape manifold formed by 2D shapes, different Procrustes distances defined on it, and positive definite kernels that permits us to embed the shape manifold in a Hilbert space. Utilizing usual Computer Vision and Machine Learning techniques on the shape manifold is challenging due to its Riemannian geometry. Therefore, most existing shape classification algorithms resort to nearest neighbor methods and to learning distances on shape spaces. We propose to map shapes on Kendall's shape manifold to a high dimensional Hilbert space where Euclidean geometry applies. To this end, we introduce a provably positive definite kernel on this manifold that permits such a mapping. This kernel lets us extend kernel-based algorithms developed for Euclidean spaces such as SVM, MKL and kernel PCA, to the shape manifold. We demonstrate the benefits of our approach over the state-of-the-art methods on shape classification, clustering and retrieval.