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Convex Solutions to SfT and NRSfM under Algebraic Deformation Models

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  • We present nonlinear formulations to Shape-from-Template (SfT) and Non-Rigid Structure-from-Motion (NRSfM) faithfully exploiting the isometric, conformal and equiareal deformation models. Existing work uses relaxations such as inextensibility or requires knowing the optic flow field around the correspondences, an impractical assumption. In contrast, the proposed formulations only require point correspondences and resolve all ambiguities using the notions of maximal depth and maximal isometry heuristics. We propose solution methods using Semi-Definite Programming (SDP) for all formulations. We show that straightforward SDP models conflict with the usual maximal depth heuristic and propose an adapted opposite-depth parameterisation demonstrating a lesser relaxation gap. Experimental results on many real-world benchmark datasets demonstrate superior accuracy over existing methods.

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Metadaten
Author:Agniva SenguptaORCiD, Adrien BartoliORCiD
Document Type:Article
Parent Title (English):IEEE Transactions on Pattern Analysis and Machine Intelligence
Year of first publication:2025
DOI:https://doi.org/10.1109/TPAMI.2025.3635039
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