Convex Relaxations for Isometric and Equiareal NRSfM

TL;DR

This paper introduces convex relaxation techniques for non-rigid structure from motion (NRSfM) that incorporate isometric and equiareal deformation models, enabling better handling of extensible objects with physically plausible assumptions.

Contribution

It proposes novel convex relaxations for isometric and equiareal models, addressing ambiguities and nonconvex constraints in NRSfM of extensible objects.

Findings

Effective on real and synthetic datasets

Outperforms existing methods in benchmark tests

Handles ambiguous and highly nonconvex constraints

Abstract

Extensible objects form a challenging case for NRSfM, owing to the lack of a sufficiently constrained extensible model of the point-cloud. We tackle the challenge by proposing 1) convex relaxations of the isometric model up to quasi-isometry, and 2) convex relaxations involving the equiareal deformation model, which preserves local area and has not been used in NRSfM. The equiareal model is appealing because it is physically plausible and widely applicable. However, it has two main difficulties: first, when used on its own, it is ambiguous, and second, it involves quartic, hence highly nonconvex, constraints. Our approach handles the first difficulty by mixing the equiareal with the isometric model and the second difficulty by new convex relaxations. We validate our methods on multiple real and synthetic data, including well-known benchmarks.