A Riemannian Framework for Analysis of Human Body Surface

TL;DR

This paper introduces a Riemannian geometric framework for comparing 3D human body shapes that accounts for shape and pose variations, enabling more accurate shape analysis and retrieval.

Contribution

It develops a novel Riemannian approach mapping human surfaces to a metric space with invariant properties, facilitating shape and pose comparison.

Findings

Effective differentiation of shape and pose changes.

Efficient computation of geodesic paths between shapes.

Improved accuracy in human body shape retrieval.

Abstract

We propose a novel framework for comparing 3D human shapes under the change of shape and pose. This problem is challenging since 3D human shapes vary significantly across subjects and body postures. We solve this problem by using a Riemannian approach. Our core contribution is the mapping of the human body surface to the space of metrics and normals. We equip this space with a family of Riemannian metrics, called Ebin (or DeWitt) metrics. We treat a human body surface as a point in a "shape space" equipped with a family of Riemannian metrics. The family of metrics is invariant under rigid motions and reparametrizations; hence it induces a metric on the "shape space" of surfaces. Using the alignment of human bodies with a given template, we show that this family of metrics allows us to distinguish the changes in shape and pose. The proposed framework has several advantages. First, we define a family of metrics with desired invariance properties for the comparison of human shape. Second, we present an efficient framework to compute geodesic paths between human shape given the chosen metric. Third, this framework provides some basic tools for statistical shape analysis of human body surfaces. Finally, we demonstrate the utility of the proposed framework in pose and shape retrieval of human body.