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This paper describes a numerical method for surface parameterization, yielding maps that are locally injective and discretely conformal in an exact sense. Unlike previous methods for discrete conformal parameterization, the method is guaranteed to work for any manifold triangle mesh, with no restrictions on triangulatiothat each task can be formulated as a convex problem where the triangulation is allowed to change---we complete the picture by introducing the machinery needed to actually construct a discrete conformal map. In particular, we introduce a new scheme for tracking correspondence between triangulations based onnormal coordinates, and a new interpolation procedure based on layout in thelight cone.Stress tests involving difficult cone configurations and near-degenerate triangulations indicate that the method is extremely robust in practice, and provides high-quality interpolation even on meshes with poor elements.
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Automatic and Robust Skull Registration Based on Discrete Uniformization
Skull registration plays a fundamental role in forensic science and is crucial for craniofacial reconstruction. The complicated topology, lack of anatomical features, and low quality reconstructed mesh make skull registration challenging. In this work, we propose an automatic skull registration method based on the discrete uniformization theory, which can handle complicated topologies and is robust to low quality meshes. We apply dynamic Yamabe flow to realize discrete uniformization, which modifies the mesh combinatorial structure during the flow and conformally maps the multiply connected skull surface onto a planar disk with circular holes. The 3D surfaces can be registered by matching their planar images using harmonic maps. This method is rigorous with theoretic guarantee, automatic without user intervention, and robust to low mesh quality. Our experimental results demonstrate the efficiency and efficacy of the method.
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- PAR ID:
- 10185293
- Date Published:
- Journal Name:
- IEEE International Conference on Computer Vision workshops
- ISSN:
- 2473-9936
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Conference Paper:
- https://doi.org/10.1109/ICCV.2019.00052
