Geodesic Distance Propagation Across Open Boundaries
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Date
2024
Journal Title
Journal ISSN
Volume Title
Publisher
The Eurographics Association
Abstract
The computation of geodesic distances on curved surfaces stands as a fundamental operation in digital geometry processing. Throughout distance propagation, each surface point assumes the dual role of a receiver and transmitter. Despite substantial research on watertight triangle meshes, algorithms designed for broken surfaces-those afflicted with open-boundary defects-remain scarce. Current algorithms primarily focus on bridging holes and gaps in the embedding space to facilitate distance propagation across boundaries but fall short in addressing large open-boundary defects in highly curved regions. In this paper, we delve into the prospect of inferring defect-tolerant geodesics exclusively within the intrinsic space. Our observation reveals that open-boundary defects can give rise to a ''shadow'' region, where the shortest path touches open boundaries. Based o n such an observation, we have made three key adaptations to the fast marching method (FMM). Firstly, boundary points now exclusively function as distance receivers, impeding any further distance propagation. Secondly, bidirectional distance propagation is permitted, allowing the prediction of geodesic distances in the shadow region based on those in the visible region (even if the visual region is a little more distant from the source). Lastly, we have redefined priorities to harmonize distance propagation between the shadow and visible regions. Notably intrinsic, our algorithm distinguishes itself from existing counterparts. Experimental results showcase its exceptional performance and accuracy, even in the presence of large and irregular open boundaries.
Description
CCS Concepts: Computing methodologies → Mesh models; Mesh geometry models
@inproceedings{10.2312:pg.20241284,
booktitle = {Pacific Graphics Conference Papers and Posters},
editor = {Chen, Renjie and Ritschel, Tobias and Whiting, Emily},
title = {{Geodesic Distance Propagation Across Open Boundaries}},
author = {Chen, Shuangmin and Yue, Zijia and Wang, Wensong and Xin, Shiqing and Tu, Changhe},
year = {2024},
publisher = {The Eurographics Association},
ISBN = {978-3-03868-250-9},
DOI = {10.2312/pg.20241284}
}