This paper introduces a novel method for reconstructing closed curves on Riemannian manifolds from sparse, unordered samples. The key contributions are:
Extending state-of-the-art theory and techniques for 2D curve reconstruction to manifold domains, addressing the challenges of working in non-Euclidean spaces.
Relaxing the sampling conditions required for curve reconstruction on manifolds compared to previous work, allowing for sparser and non-uniform sampling.
Generalizing the SIGDT proximity graph to manifold domains (SIGDV) and proving that it contains the correct curve reconstruction under the new sampling conditions.
Developing an algorithm that leverages the properties of the SIGDV graph to efficiently reconstruct closed curves on manifolds, even when the sampling conditions are not fully met.
The authors demonstrate the robustness and versatility of their method through qualitative experiments on various real-world applications, including motion tracking, virtual cultural heritage processing, contour matching, and sparse data visualization. The proposed solution outperforms the previous state-of-the-art approach, which fails in many cases due to its stricter sampling requirements.
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by Diana Marin,... kl. arxiv.org 04-16-2024
https://arxiv.org/pdf/2404.09661.pdfDybere Forespørgsler