Robust atlas generation via angle-based segmentation

We present a robust method to generate atlases with low isometric distortion and high packing efficiency. Given a surface that has been cut to disk topology, the algorithm contains four steps: (1) computing a bijective parameterization with low isometric distortion; (2) partitioning the input parameterized charts into a set of rectangle-like patches; (3) mapping rectangle-like patches onto rectangles that are packed into a rectangular domain; and (4) reducing parameterization distortion while maintaining high packing efficiency and bijection. Since there have been elegant and robust solutions for the first, third, and fourth steps, we focus on the second step. Central to the second step is a novel and robust segmentation technique. To improve the robustness of the segmentation, we first deform the parameterized charts to straighten their boundaries while aligning with the axes as much as possible, bounding the deformation distortion, and not introducing intersecting boundaries. Since rectangle-like patches are preferred for the third and fourth steps, we segment the deformed charts by decomposing concave interior angles into several interior angles close to pi/2 or pi. To this end, we develop four types of operations: (i) bridging operation, (ii) extension operation, (iii) vertical line operation, and (iv) bisector operation. The pre-deformation process makes our heuristic segmentation very simple and effective. We demonstrate the efficacy of our method on various complex models. Compared to other state-of-the-art methods, our method achieves higher robustness. (C) 2020 Elsevier B.V. All rights reserved.