Fast and robust Hausdorff distance computation from triangle mesh to quad mesh in near-zero cases

Kang, Yunku; Kyung, Min-Ho; Yoon, Seung‐Hyun; Kim, Myung-Soo

doi:10.1016/j.cagd.2018.03.017

Cited by 9 publications

(4 citation statements)

References 19 publications

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“…Hausdorff distance is the maximum distance of a set to the nearest point in the other set. More formally, Hausdorff distance from set A to set B is a minimum function, defined as: h(A, B) = maxmind(a, b) where a and b are points of sets A and B, respectively, and d(a,b) is any metric between these points [36]. For simplicity, we will take d(a,b) as the Euclidean distance between a and b.…”

Section: Hausdorff Distance Measurementmentioning

confidence: 99%

A Comparative Study between Scanning Devices for 3D Printing of Personalized Ostomy Patches

Zahia

Garcia-Zapirain

Anakabe

et al. 2022

Sensors

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This papers presents a comparative study of three different 3D scanning modalities to acquire 3D meshes of stoma barrier rings from ostomized patients. Computerized Tomography and Structured light scanning methods were the digitization technologies studied in this research. Among the Structured Light systems, the Go!Scan 20 and the Structure Sensor were chosen as the handheld 3D scanners. Nineteen ostomized patients took part in this study, starting from the 3D scans acquisition until the printed ostomy patches validation. 3D mesh processing, mesh generation and 3D mesh comparison was carried out using commercial softwares. The results of the presented study show that the Structure Sensor, which is the low cost structured light 3D sensor, has a great potential for such applications. This study also discusses the benefits and reliability of low-cost structured light systems.

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Section: Hausdorff Distance Measurementmentioning

confidence: 99%

A Comparative Study between Scanning Devices for 3D Printing of Personalized Ostomy Patches

Zahia

Garcia-Zapirain

Anakabe

et al. 2022

Sensors

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“…The reduction phase comes after the traverse phase, which takes advantage of the triangle heap to reduce the gap between the lower bound and the upper bound. The heap

H

is a max heap ordered by the upper bound Hausdorff distance from triangle to

B

, which is also used in [KYKK19] and [KKYK18]. The detailed algorithm is put in Appendix Algorithm 3.…”

Section: Preliminary and Overviewmentioning

confidence: 99%

“…When the two models are highly overlapping, the Hausdorff distance is usually very close to zero, and only a few triangles can be culled which reduces the overall performance of the algorithm. By utilizing a uniform grid with an appropriate size, [KKYK18] and [KYKK19] get rid of an unnecessary traverse on the BVH tree and improve the performance significantly. This method is suitable for the ‘near zero’ cases, but not universally applicable.…”

Section: Background and Related Workmentioning

confidence: 99%

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Economic Upper Bound Estimation in Hausdorff Distance Computation for Triangle Meshes

Zheng

Sun

Liu

et al. 2021

Computer Graphics Forum

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The Hausdorff distance is one of the most fundamental metrics for comparing 3D shapes. To compute the Hausdorff distance efficiently from a triangular mesh A$A$ to another triangular mesh B$B$, one needs to cull the unnecessary triangles on A$A$ quickly. These triangles have no chance to improve the Hausdorff distance estimation, that is the parts with local upper bound smaller than the global lower bound. The local upper bound estimation should be tight, use fast distance computation, and involve a small number of triangles in B$B$ during the reduction phase for efficiency. In this paper, we propose to use point‐triangle distance, and only involve at most four triangles in B$B$ in the reduction phase. Comparing with the state‐of‐the‐art proposed by Tang et al. in 2009, which uses more costly triangle‐triangle distance and may involve a large number of triangles in reduction phase, our local upper bound estimation is faster, and with only a small impact on the tightness of the bound on error estimation. Such a more economic strategy boosts the overall performance significantly. Experiments on the Thingi10K dataset show that our method can achieve several (even over 20) times speedup on average. On a few models with different placements and resolutions, we show that close placement and large difference in resolution bring big challenges to Hausdorff distance computation, and explain why our method can achieve more significant speedup on challenging cases.

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NC machining verification algorithm based on the STL model

Miao

Song

Wang

et al. 2020

Int J Adv Manuf Technol

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Fast and robust Hausdorff distance computation from triangle mesh to quad mesh in near-zero cases

Cited by 9 publications

References 19 publications

A Comparative Study between Scanning Devices for 3D Printing of Personalized Ostomy Patches

A Comparative Study between Scanning Devices for 3D Printing of Personalized Ostomy Patches

Economic Upper Bound Estimation in Hausdorff Distance Computation for Triangle Meshes

NC machining verification algorithm based on the STL model

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