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 frame-work in pose and shape retrieval of human body.

This paper describes a novel framework for computing geodesic paths in shape spaces of spherical surfaces under an elastic Riemannian metric. The novelty lies in defining this Riemannian metric directly on the quotient (shape) space, rather than inheriting it from pre-shape space, and using it to formulate a path energy that measures only the normal components of velocities along the path. In other words, this paper defines and solves for geodesics directly on the shape space and avoids complications resulting from the quotient operation. This comprehensive framework is invariant to arbitrary parameterizations of surfaces along paths, a phenomenon termed as gauge invariance. Additionally, this paper makes a link between different elastic metrics used in the computer science literature on one hand, and the mathematical literature on the other hand, and provides a geometrical interpretation of the terms involved. Examples using real and simulated 3D objects are provided to help illustrate the main ideas.