Repairing Inconsistent Curve Networks on Non-parallel Cross-sections

Computer Graphics Forum (Proc. Eurographics 2018)
Zhiyang Huang*, Michelle Holloway*, Nathan Carr^, Tao Ju*
*Washington University in St. Louis,  ^Adobe


Result (bottom) of repairing an inconsistent 7-labelled mouse brain set (top), showing the labeling on three planes (p1,p2,p3) and labeling on other planes along the intersection lines. A few inconsistencies are highlighted in black boxes. The pictures at the right show the labeling on each plane as well as the labeling from the other plane on intersection lines.
(Mouse brain: 6 planes, 7 labels, total process time 421s)


Gallery: Results of repairing inconsistency on different complex examples
(a) Liver 1: 6 planes, 4 labels, total process time 90s, (b) Liver 2: 5 planes, 4 labels, total process time 25s, (c) Ferret brain: 10 planes, 2 labels, total process time 66s.


In this work we present the first algorithm for restoring consistency between curve networks on non-parallel cross-sections. Our method addresses a critical but overlooked challenge in the reconstruction process from cross-sections that stems from the fact that cross-sectional slices are often generated independently of one another, such as in interactive volume segmentation. As a result, the curve networks on two non-parallel slices may disagree where the slices intersect, which makes these cross- sections an invalid input for surfacing. We propose a method that takes as input an arbitrary number of non-parallel slices, each partitioned into two or more labels by a curve network, and outputs a modified set of curve networks on these slices that are guaranteed to be consistent. We formulate the task of restoring consistency while preserving the shape of input curves as a constrained optimization problem, and we propose an effective solution framework. We demonstrate our method on a data-set of complex multi-labeled input cross-sections. Our technique efficiently produces consistent curve networks even in the presence of large errors.


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