39-Issue 6

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https://diglib.eg.org/handle/10.2312/2632940

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Browsing 39-Issue 6 by Subject "deformation"

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    Adaptive Block Coordinate Descent for Distortion Optimization
    (© 2020 Eurographics ‐ The European Association for Computer Graphics and John Wiley & Sons Ltd, 2020) Naitsat, Alexander; Zhu, Yufeng; Zeevi, Yehoshua Y.; Benes, Bedrich and Hauser, Helwig
    We present a new algorithm for optimizing geometric energies and computing positively oriented simplicial mappings. Our major improvements over the state‐of‐the‐art are: (i) introduction of new energies for repairing inverted and collapsed simplices; (ii) adaptive partitioning of vertices into coordinate blocks with the blended local‐global strategy for more efficient optimization and (iii) introduction of the displacement norm for improving convergence criteria and for controlling block partitioning. Together these improvements form the basis for the Adaptive Block Coordinate Descent (ABCD) algorithm aimed at robust geometric optimization. ABCD achieves state‐of‐the‐art results in distortion minimization, even under hard positional constraints and highly distorted invalid initializations that contain thousands of collapsed and inverted elements. Starting with an invalid non‐injective initial map, ABCD behaves as a modified block coordinate descent up to the point where the current mapping is cleared of invalid simplices. Then, the algorithm converges rapidly into the chosen iterative solver. Our method is very general, fast‐converging and easily parallelizable. We show over a wide range of 2D and 3D problems that our algorithm is more robust than existing techniques for locally injective mapping.
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    Hyperspectral Inverse Skinning
    (© 2020 Eurographics ‐ The European Association for Computer Graphics and John Wiley & Sons Ltd, 2020) Liu, Songrun; Tan, Jianchao; Deng, Zhigang; Gingold, Yotam; Benes, Bedrich and Hauser, Helwig
    In example‐based inverse linear blend skinning (LBS), a collection of poses (e.g. animation frames) are given, and the goal is finding skinning weights and transformation matrices that closely reproduce the input. These poses may come from physical simulation, direct mesh editing, motion capture or another deformation rig. We provide a re‐formulation of inverse skinning as a problem in high‐dimensional Euclidean space. The transformation matrices applied to a vertex across all poses can be thought of as a point in high dimensions. We cast the inverse LBS problem as one of finding a tight‐fitting simplex around these points (a well‐studied problem in hyperspectral imaging). Although we do not observe transformation matrices directly, the 3D position of a vertex across all of its poses defines an affine subspace, or flat. We solve a ‘closest flat’ optimization problem to find points on these flats, and then compute a minimum‐volume enclosing simplex whose vertices are the transformation matrices and whose barycentric coordinates are the skinning weights. We are able to create LBS rigs with state‐of‐the‐art reconstruction error and state‐of‐the‐art compression ratios for mesh animation sequences. Our solution does not consider weight sparsity or the rigidity of recovered transformations. We include observations and insights into the closest flat problem. Its ideal solution and optimal LBS reconstruction error remain an open problem.