OptCuts: Joint Optimization of Surface Cuts and Parameterization

Minchen Li  -  University of British Columbia & Adobe Research
Danny M. Kaufman  -  Adobe Research
Vladimir G. Kim  -  Adobe Research
Justin Solomon  -  Massachusetts Institute of Technology
Alla Sheffer  -  University of British Columbia
ACM Transactions on Graphics (SIGGRAPH Asia), 2018
Starting from an initial embedding (left), we show the iteration process of our OptCuts algorithm jointly optimizing surface cuts and mapping distortion while enforcing global bijectivity. OptCuts iteratively updates continuous changes in the embedding vertices and discrete topological changes in the UV mesh by propagating simple and local topology splitting and merging operations. In this example a distortion bound of 4.1 is enforced, measured by the symmetric Dirichlet distortion energy [Smith and Schaefer 2015]; we report total inner iterations at each rendered frame.

Low-distortion mapping of three-dimensional surfaces to the plane is a critical problem in geometry processing. The intrinsic distortion introduced by these UV mappings is highly dependent on the choice of surface cuts that form seamlines which break mapping continuity. Parameterization applications typically require UV maps with an application-specific upper bound on distortion to avoid mapping artifacts; at the same time they seek to reduce cut lengths to minimize discontinuity artifacts. We propose OptCuts, an algorithm that jointly optimizes the parameterization and cutting of a three-dimensional mesh. OptCuts starts from an arbitrary initial embedding and a user-requested distortion bound. It requires no parameter setting and automatically seeks to minimize seam lengths subject to satisfying the distortion bound of the mapping computed using these seams. OptCuts alternates between topology and geometry update steps that consistently decrease distortion and seam length, producing a UV map with compact boundaries that strictly satisfies the distortion bound. OptCuts automatically produces high-quality, globally bijective UV maps without user intervention. While OptCuts can thus be a highly effective tool to create new mappings from scratch, we also show how it can be employed to improve pre-existing embeddings. Additionally, when semantic or other priors on seam placement are desired, OptCuts can be extended to respect these user preferences as constraints during optimization of the parameterization. We demonstrate the scalable performance of OptCuts on a wide range of challenging benchmark parameterization examples, as well as in comparisons with state-of-the-art UV methods and commercial tools.

Source Code and Data
Here are the results of all experiments presented in our paper, together with an experiment on the current optimized version of OptCuts which results in 3x speedup in average. For each expriment linked below we present results as a table, where row corresponds to a different benchmark shape and each column demonstrates output using different variants of our method or alternative approaches. For each output we render UV embedding, 3D mesh with checkerboard pattern, report distortion (Dirichlet and stretch), seam length, and execution time, and provide a link to the resulting parameterized mesh.

NOTE: most tables have many columns so, please, scroll to the right.
  author  = {Minchen Li and Danny M. Kaufman and Vladimir G. Kim and Justin Solomon and Alla Sheffer},
  title   = {OptCuts: Joint Optimization of Surface Cuts and Parameterization},
  journal = {ACM Transactions on Graphics},
  year    = {2018},
  volume = {37},
  number = {6},
  doi = {http://dx.doi.org/10.1145/3272127.3275042},
  publisher = {ACM},
  address = {New York, NY, USA}
Supplemental Document

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