Fast and robust computation of the Hausdorff distance between triangle mesh and quad mesh for near-zero cases

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

doi:10.1016/j.cag.2019.03.014

Cited by 8 publications

(11 citation statements)

References 8 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…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%

“…The BVH (bounding volume hierarchy) is a widely applied [TLK09] spatial data structure here. Though the uniform grid shows excellent performance for ‘near‐zero’ cases [KKYK18, KYKK19], its performance strongly depends on how close the models are to each other, and whether the user properly chooses the grid density.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Economic Upper Bound Estimation in Hausdorff Distance Computation for Triangle Meshes

Zheng

Sun

Liu

et al. 2021

Computer Graphics Forum

View full text Add to dashboard Cite

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.

show abstract

“…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%

Section: Background and Related Workmentioning

confidence: 99%

See 1 more Smart Citation

Economic Upper Bound Estimation in Hausdorff Distance Computation for Triangle Meshes

Zheng

Sun

Liu

et al. 2021

Computer Graphics Forum

View full text Add to dashboard Cite

show abstract

“…, where the objective function is defined as Hausdorff distance function for image matching [34][35][36][37], which is expressed as follows: , otherwise return to Step2. Soft tissue deformation can be simulated more realistically by using the optimal spring stiffness and damping coefficients which determined by the above simulated annealing algorithm.…”

Section: Simulated Annealing Algorithm For Parameter Optimizationmentioning

confidence: 99%

An Optimized Model for the Local Compression Deformation of Soft Tissue

Zhang¹,

Yu²,

Sun³

et al. 2020

KSII TIIS

View full text Add to dashboard Cite

Due to the long training time and high training cost of traditional surgical training methods, the emerging virtual surgical training method has gradually replaced it as the mainstream. However, the virtual surgical system suffers from poor authenticity and high computational cost problems. For overcoming the deficiency of these problems, we propose an optimized model for the local compression deformation of soft tissue. This model uses a simulated annealing algorithm to optimize the parameters of the soft tissue model to improve the authenticity of the simulation. Meanwhile, although the soft tissue deformation is divided into local deformation region and non-deformation region, our proposed model only needs to calculate and update the deformation region, which can improve the simulation real-time performance. Besides, we define a compensation strategy for the "superelastic" effect which often occurs with the mass-spring model. To verify the validity of the model, we carry out a compression simulation experiment of abdomen and human foot and compare it with other models. The experimental results indicate the proposed model is realistic and effective in soft tissue compression simulation, and it outperforms other models in accuracy and real-time performance.

show abstract

“…Typical non-Euclidean distances are Manhattan [9,10], Chessboard [11], octagonal [12], quasi-Euclidean, and Hausdorff [13][14][15][16][17][18]. Our work is based on the Hausdorff distance (HD), which has captured a considerable attention of scholars over the past few decades [19][20][21][22][23][24]. Distance measures are widely applied in computer vision to determine the similarity between pairs of sets or images.…”

Section: Introductionmentioning

confidence: 99%

Hausdorff Distance with Outliers and Noise Resilience Capabilities

Maiseli

2021

SN COMPUT. SCI.

View full text Add to dashboard Cite

For years, the Hausdorff distance (HD) has been an indispensable tool to address computer vision and pattern recognition problems. Compared with other metrics, HD incorporates critical details of objects (position and shapes) to output reasonable distances between pairs of point sets. Despite its capabilities, HD is highly sensitive to outliers and noisy data. From previous studies, we discovered that the issues have been inadequately addressed. In the present work, a technique is proposed to empower HD under undesirable conditions of data. The technique uses diffusion-like stopping kernels that investigate regions of data and trim-off outliers and noise. We, additionally, have analyzed our formulation to show why it works. Extensive experimental results demonstrate the efficacy of our approach relative to previous methods.

show abstract

Fast and robust computation of the Hausdorff distance between triangle mesh and quad mesh for near-zero cases

Cited by 8 publications

References 8 publications

Economic Upper Bound Estimation in Hausdorff Distance Computation for Triangle Meshes

Economic Upper Bound Estimation in Hausdorff Distance Computation for Triangle Meshes

An Optimized Model for the Local Compression Deformation of Soft Tissue

Hausdorff Distance with Outliers and Noise Resilience Capabilities

Contact Info

Product

Resources

About