3D Mesh Pre-Processing Method Based on Feature Point Classification and Anisotropic Vertex Denoising Considering Scene Structure Characteristics
Abstract
:1. Introduction
2. Literature Review
2.1. Isotropic Mesh Filtering
2.2. Anisotropic Mesh Filtering
2.3. Conclusions of the Literature Review
3. Methodology
3.1. Facet Normal Filtering
3.1.1. Guidance Normal Considering Corner Features
3.1.2. Joint Bilateral Normal Filtering
3.2. Feature Point Classification
3.2.1. Feature Vertex Detection
3.2.2. Weak Feature Recognition and False Feature Elimination
3.3. Anisotropic Vertex Update
3.3.1. Non-Feature Vertex Update
3.3.2. Feature Vertex Update
4. Results
4.1. Parameter Tuning
4.2. Qualitative Assessment Experiments
4.2.1. Qualitative Comparison of the Feature Vertex Classification Results
4.2.2. Qualitative Comparison of the Mesh Denoising Results
4.3. Quantitative Evaluation Experiments
4.3.1. Quantitative Comparison of the Normal Difference
4.3.2. Quantitative Comparison Of Distance
4.3.3. Quantitative Comparison of Running Time
4.4. Discussion
5. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Acknowledgments
Conflicts of Interest
Abbreviations
NVT | Normal voting tensor |
BM | The bilateral mesh denoising method [3] |
NoIter | The noniterative, feature-preserving mesh smoothing method [27] |
Fast | Fast and effective feature-preserving mesh denoising [28] |
BNF | The local scheme of bilateral normal filtering method [4] |
L0 | Mesh denoising via L0 minimization [23] |
GMNF | Guided mesh normal filtering [5] |
RoFi | Robust and high fidelity mesh denoising [32] |
CPD | Constraint-based point set denoising [9] |
ENVT | Mesh denoising based on normal voting tensor and binary optimization [45] |
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Symbols | Glossary |
---|---|
Face i, | |
Area of face i | |
Centroid of face i | |
Vertex i | |
New coordinate of vertex i in the iteration | |
Normal vector for face i | |
Filtered normal of face i for the first time in each iteration | |
Filtered normal of face i for the second time in each iteration | |
Guidedance normal vector for face i | |
The patch of the face | |
Dual weight function | |
Set of neighboring faces of face i | |
Set of neighboring faces of vertex i | |
Set of isotropic neighbor faces of vertex i | |
Tensor voting matrix based on the normals at vertex i | |
Normal voting component of the face | |
Eigenvalue of , | |
Unit eigenvector of , | |
Feature classification threshold | |
Set of non-feature vertices | |
Set of shape edge vertices | |
Set of corner vertices | |
Normal angle threshold | |
The supported neighborhood of feature point , | |
The supported plane of feature point | |
Set of supported planes of feature point | |
Dihedral angle constraint threshold, | |
Coefficients of the constraint terms, , | |
The spatial kernel | |
The range kernel | |
Variance parameter of | |
Variance parameter of | |
Average facet normal difference between the denoised mesh and the ground-truth mesh | |
Maximum distance from the resulting mesh vertices to the ground-truth mesh surface | |
Average distance from the resulting mesh vertices to the ground-truth mesh surface | |
Number of iteration filtering facet normals, total number of iterations | |
Number of times the vertices are updated in each iteration |
Model | Noisy | BM [3] | NoIter [27] | Fast [28] | BNF [4] | L0 [23] | GMNF [5] | RoFi [32] | Ours |
---|---|---|---|---|---|---|---|---|---|
Block | 33.7185 | 14.4753 | 13.8501 | 14.4753 | 5.30624 | 4.97352 | 3.77320 | 5.22034 | 3.18393 |
Fandisk | 28.4211 | 11.1113 | 9.81795 | 4.04264 | 3.34944 | 5.52852 | 2.62181 | 2.44769 | 1.37350 |
SharpSphere | 33.0070 | 16.7373 | 17.3618 | 11.8920 | 6.70474 | 12.9565 | 9.53772 | 9.05684 | 8.43270 |
Julius | 23.9629 | 10.2910 | 7.63005 | 7.01017 | 6.00205 | 7.97741 | 6.50926 | 7.70099 | 6.42512 |
Cube | 21.0551 | 8.71710 | 7.48375 | 2.02613 | 1.38315 | 1.82864 | 0.69145 | 2.42332 | 0.593294 |
Pyramid | 19.2730 | 5.81730 | 4.66767 | 0.68221 | 0.84914 | 3.51391 | 0.51771 | 1.35993 | 0.504128 |
jointSharpEdges | 33.6741 | 13.7765 | 13.2518 | 10.5136 | 8.25214 | 2.13461 | 3.35048 | 2.47633 | 2.28357 |
Model | Noisy | BM [3] | NoIter [27] | Fast [28] | BNF [4] | L0 [23] | GMNF [5] | RoFi [32] | Ours |
---|---|---|---|---|---|---|---|---|---|
Block | 1.24700 | 0.86231 | 0.68534 | 0.60524 | 0.60328 | 0.60257 | 0.30105 | 0.60313 | 0.30061 |
Fandisk | 0.12625 | 0.08283 | 0.08349 | 0.05911 | 0.05895 | 0.08276 | 0.04153 | 0.04161 | 0.04150 |
SharpSphere | 0.45456 | 0.44946 | 0.33997 | 0.44865 | 0.22433 | 0.33649 | 0.33760 | 0.39257 | 0.33257 |
Julius | 0.00792 | 0.00790 | 0.00790 | 0.00789 | 0.00790 | 0.00790 | 0.00790 | 0.00789 | 0.00788 |
Cube | 0.08521 | 0.06631 | 0.04955 | 0.03227 | 0.01602 | 0.06350 | 0.02119 | 0.03186 | 0.01589 |
Pyramid | 0.03197 | 0.02104 | 0.02125 | 0.01587 | 0.01587 | 0.03156 | 0.01590 | 0.01578 | 0.01583 |
jointSharpEdges | 0.02117 | 0.01793 | 0.01194 | 0.01181 | 0.01181 | 0.01177 | 0.01181 | 0.00884 | 0.01179 |
Model | Noisy | BM [3] | NoIter [27] | Fast [28] | BNF [4] | L0 [23] | GMNF [5] | RoFi [32] | Ours |
---|---|---|---|---|---|---|---|---|---|
Block | 0.19502 | 0.08608 | 0.08632 | 0.05385 | 0.03436 | 0.13168 | 0.03559 | 0.11360 | 0.01988 |
Fandisk | 0.02151 | 0.00842 | 0.01017 | 0.00424 | 0.00321 | 0.01345 | 0.00457 | 0.00447 | 0.00118 |
SharpSphere | 0.06948 | 0.02864 | 0.03005 | 0.03235 | 0.00773 | 0.06397 | 0.01811 | 0.02110 | 0.01455 |
Julius | 0.00022 | 0.00004 | 0.00005 | 0.00002 | 0.00004 | 0.00004 | 0.00002 | 0.00003 | 0.00001 |
Cube | 0.01892 | 0.00954 | 0.01109 | 0.00437 | 0.00177 | 0.01029 | 0.00483 | 0.00605 | 0.00526 |
Pyramid | 0.00292 | 0.00104 | 0.00203 | 0.00015 | 0.00015 | 0.00102 | 0.00001 | 0.00010 | 0.00000 |
jointSharpEdges | 0.00338 | 0.00091 | 0.00112 | 0.00075 | 0.00078 | 0.00122 | 0.00085 | 0.00029 | 0.00028 |
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Liu, Y.; Guo, B.; Xiao, X.; Qiu, W. 3D Mesh Pre-Processing Method Based on Feature Point Classification and Anisotropic Vertex Denoising Considering Scene Structure Characteristics. Remote Sens. 2021, 13, 2145. https://doi.org/10.3390/rs13112145
Liu Y, Guo B, Xiao X, Qiu W. 3D Mesh Pre-Processing Method Based on Feature Point Classification and Anisotropic Vertex Denoising Considering Scene Structure Characteristics. Remote Sensing. 2021; 13(11):2145. https://doi.org/10.3390/rs13112145
Chicago/Turabian StyleLiu, Yawen, Bingxuan Guo, Xiongwu Xiao, and Wei Qiu. 2021. "3D Mesh Pre-Processing Method Based on Feature Point Classification and Anisotropic Vertex Denoising Considering Scene Structure Characteristics" Remote Sensing 13, no. 11: 2145. https://doi.org/10.3390/rs13112145