As-rigid-as-possible volume tracking for time-varying surfaces

Surfaces evolving through time are hard to analyze without prior knowledge of the represented de-forming shape. Topological noise introduced by inaccuracies during surface capture and reconstruction renders the estimation of time-consistent correspondence an ill-posed problem. It has previously been shown that this problem may be mitigated by tracking the volume within the surface rather than the surface itself. Assuming that the captured phenomenon does not involve sudden appearance or disappearance of volume, it is possible to establish a bijective correspondence of volume elements, which in turn may be used for various purposes, such as extracting a canonical shape and guiding the computation of surface correspondence. In this paper, we discuss an improved volume tracking methodology that provides better results by modifying the energy formulation and by incorporating a notion of volume element affinity, combined with an improved optimization strategy. We also discuss two metrics that, when combined, quantify the quality of the tracking results. (c) 2021 Elsevier Ltd. All rights reserved.