1 Introduction
2 Datasets
2.1 Real Dataset
2.2 Synthetic Dataset
2.3 FAUST Dataset
3 Retrieval Task and Evaluation
-
Given a query model, return a list of all models, ordered by decreasing shape similarity to the query.
Author | Method | Simplification | Watertight (FAUST) |
---|---|---|---|
Giachetti | APT | No | Used |
APT-trained | No | Used | |
Lai | HKS | 10,000 faces | Used |
WKS | 10,000 faces | Used | |
SA | 10,000 faces | Used | |
Multi-feature | 10,000 faces | Used | |
B. Li | Curvature | No | Used |
Geodesic | 1000 vertices | Used | |
Hybrid | 1000 vertices | Used | |
MDS-R | 1000 vertices | Used | |
MDS-ZFDR | 1000 vertices | Used | |
C. Li | Spectral Geom. | No | Used |
Litman | supDL | 4500 vertices | Used |
UnSup32 | 4500 vertices | Used | |
softVQ48 | 4500 vertices | Used | |
Pickup | Surface area | No | Used |
Compactness | No | Used | |
Canonical | No | Used | |
Bu | 3DDL | No | Used |
Tatsuma | BoF-APFH | No | Not used |
MR-BoF-APFH | No | Not used | |
Ye | R-BiHDM | No | Used |
R-BiHDM-s | No | Used | |
Tam | MRG | No | Used |
TPR | No | Used |
Author | Timings | Language | ||||||
---|---|---|---|---|---|---|---|---|
Method | Real | Synthetic | FAUST | |||||
Preprocessing (s) | Model descriptor (s) | Preprocessing (s) | Model descriptor (s) | Preprocessing (s) | Model descriptor (s) | |||
Giachetti | APT | – | 38 | – | 25 | – | 40 | C++ |
APT-trained | 3810 | 38 | 1135 | 25 | 4010 | 40 | C++ | |
Lai | HKS | – | 15 | – | 17 | – | 15 | Matlab |
WKS | – | 12 | – | 13 | – | 12 | Matlab | |
SA | – |
\(<\)1 | – |
\(<\)1 | – |
\(<\)1 | Matlab | |
Multi-feature | 2708 | 27 | 1356 | 29 | 2709 | 27 | Matlab | |
B. Li | Curvature | – | 14 | – | 57 | – | 4 | C++ |
Geodesic | – | 51 | – | 54 | – | – | Matlab, C++ | |
Hybrid | 48,200 | 119 | 54,884 | 178 | – | – | Matlab, C++ | |
MDS-R | – | 54 | – | 67 | – | – | Matlab, C++ | |
MDS-ZFDR | – | 54 | – | 67 | – | – | Matlab, C++ | |
C. Li | Spectral Geom. | 2700 | 8 | 2700 | 37 | 2700 | 96 | Matlab |
Litman | supDL | 18,000 | 3 | 18,000 | 3 | 18,000 | 3 | Matlab, C++ |
UnSup32 | 900 | 3 | 900 | 3 | 900 | 3 | Matlab, C++ | |
softVQ48 | 3600 | 3 | 3600 | 3 | 3600 | 3 | Matlab, C++ | |
Pickup | Surface area | – |
\(<\)1 | – |
\(<\)1 | – |
\(<\)1 | Matlab |
Compactness | – |
\(<\)1 | – | 2 | – | 3 | Matlab | |
Canonical | – | 20 | – | 106 | – | 510 | Matlab, C++ | |
Bu | 3DDL | 3600 | 10 | 3600 | 10 | 3600 | 10 | Matlab, C++ |
Tatsuma | BoF-APFH | 74 | 3 | 82 | 3 | 78 | 4 | Python, C++ |
MR-BoF-APFH | 74 | 3 | 82 | 3 | 78 | 4 | Python, C++ | |
Ye | R-BiHDM | – | 10 | – | 40 | – | 55 | C++ |
R-BiHDM-s | – | 30 | – | 120 | – | 160 | C++ | |
Tam | MRG | – | 51 | – | 834 | – | – | C++ |
TPR | – | 11 | – | 225 | – | 1126 | C++ |
4 Methods
4.1 Simple Shape Measures, and Skeleton Driven Canonical Forms
4.1.1 Simple Shape Measures
4.1.2 Skeleton Driven Canonical Forms
4.2 Hybrid Shape Descriptor and Meta Similarity Generation for Non-rigid 3D Model Retrieval
4.2.1 Curvature-based local feature vector: \(V_C\)
4.2.2 Geodesic Distance-Based Global Feature Vector: \(V_G\)
4.2.3 MDS-Based ZFDR Global Feature Vector: \(V_Z\)
4.2.4 Retrieval Algorithm
4.3 Histograms of Area Projection Transform
4.3.1 Trained Approach
4.4 R-BiHDM
4.5 Multi-feature Descriptor
4.6 High-Level Feature Learning for 3D Shapes
4.7 Bag-of-Features approach with Augmented Point Feature Histograms
Author | Method | NN | 1-T | 2-T | E-M | DCG |
---|---|---|---|---|---|---|
Giachetti | APT |
0.830
| 0.572 | 0.761 | 0.396 |
0.826
|
APT-trained |
0.910
|
0.673
|
0.848
|
0.414
|
0.874
| |
Lai | HKS | 0.245 | 0.259 | 0.461 | 0.314 | 0.548 |
WKS | 0.326 | 0.322 | 0.559 | 0.347 | 0.605 | |
SA | 0.288 | 0.298 | 0.491 | 0.300 | 0.563 | |
Multi-feature | 0.510 | 0.470 | 0.691 | 0.382 | 0.708 | |
B. Li | Curvature | 0.083 | 0.076 | 0.138 | 0.099 | 0.347 |
Geodesic | 0.070 | 0.078 | 0.158 | 0.113 | 0.355 | |
Hybrid | 0.063 | 0.091 | 0.171 | 0.120 | 0.363 | |
MDS-R | 0.035 | 0.066 | 0.129 | 0.090 | 0.330 | |
MDS-ZFDR | 0.030 | 0.040 | 0.091 | 0.075 | 0.310 | |
C. Li | Spectral Geom. | 0.313 | 0.206 | 0.323 | 0.192 | 0.488 |
Litman | supDL |
0.775
|
0.663
|
0.859
|
0.421
|
0.857
|
UnSup32 | 0.583 | 0.451 | 0.659 | 0.354 | 0.712 | |
softVQ48 | 0.598 | 0.472 | 0.657 | 0.356 | 0.717 | |
Pickup | Surface area | 0.263 | 0.289 | 0.509 | 0.326 | 0.571 |
Compactness | 0.275 | 0.221 | 0.384 | 0.255 | 0.519 | |
Canonical | 0.010 | 0.012 | 0.040 | 0.043 | 0.279 | |
Bu | 3DDL | 0.225 | 0.193 | 0.374 | 0.262 | 0.504 |
Tatsuma | BoF-APFH | 0.040 | 0.111 | 0.236 | 0.163 | 0.388 |
MR-BoF-APFH | 0.063 | 0.072 | 0.138 | 0.084 | 0.330 | |
Ye | R-BiHDM | 0.275 | 0.201 | 0.334 | 0.217 | 0.492 |
R-BiHDM-s | 0.720 |
0.616
|
0.793
|
0.399
| 0.819 | |
Tam | MRG | 0.018 | 0.023 | 0.051 | 0.037 | 0.280 |
TPR | 0.015 | 0.024 | 0.057 | 0.050 | 0.288 |
Author | Method | NN | 1-T | 2-T | E-M | DCG |
---|---|---|---|---|---|---|
Giachetti | APT |
0.970
| 0.710 | 0.951 | 0.655 | 0.935 |
APT-trained |
0.967
|
0.805
|
0.982
|
0.692
|
0.958
| |
Lai | HKS | 0.467 | 0.476 | 0.743 | 0.504 | 0.729 |
WKS | 0.810 | 0.726 | 0.939 | 0.667 | 0.886 | |
SA | 0.720 | 0.682 | 0.973 | 0.670 | 0.862 | |
Multi-feature | 0.867 | 0.714 |
0.981
| 0.682 | 0.906 | |
B. Li | Curvature | 0.620 | 0.485 | 0.710 | 0.488 | 0.774 |
Geodesic | 0.540 | 0.362 | 0.529 | 0.363 | 0.674 | |
Hybrid | 0.430 | 0.509 | 0.751 | 0.520 | 0.768 | |
MDS-R | 0.267 | 0.284 | 0.470 | 0.314 | 0.594 | |
MDS-ZFDR | 0.207 | 0.228 | 0.407 | 0.265 | 0.559 | |
C. Li | Spectral Geom. |
0.993
|
0.832
| 0.971 |
0.706
|
0.971
|
Litman | supDL | 0.963 |
0.871
| 0.974 |
0.704
|
0.974
|
UnSup32 | 0.893 | 0.754 | 0.918 | 0.657 | 0.938 | |
softVQ48 | 0.910 | 0.729 | 0.949 | 0.659 | 0.927 | |
Pickup | Surface area | 0.807 | 0.764 |
0.987
| 0.691 | 0.901 |
Compactness | 0.603 | 0.544 | 0.769 | 0.527 | 0.773 | |
Canonical | 0.113 | 0.182 | 0.333 | 0.217 | 0.507 | |
Bu | 3DDL | 0.923 | 0.760 | 0.911 | 0.641 | 0.921 |
Tatsuma | BoF-APFH | 0.550 | 0.550 | 0.722 | 0.513 | 0.796 |
MR-BoF-APFH | 0.790 | 0.576 | 0.821 | 0.563 | 0.836 | |
Ye | R-BiHDM | 0.737 | 0.496 | 0.673 | 0.467 | 0.778 |
R-BiHDM-s | 0.787 | 0.571 | 0.811 | 0.551 | 0.833 | |
Tam | MRG | 0.070 | 0.165 | 0.283 | 0.187 | 0.478 |
TPR | 0.107 | 0.188 | 0.333 | 0.216 | 0.506 |
Author | Method | NN | 1-T | 2-T | E-M | DCG |
---|---|---|---|---|---|---|
Giachetti | APT |
0.960
|
0.865
|
0.962
|
0.700
|
0.966
|
APT-trained |
0.990
|
0.891
|
0.984
|
0.711
|
0.979
| |
Lai | HKS | 0.170 | 0.205 | 0.382 | 0.244 | 0.546 |
WKS | 0.195 | 0.181 | 0.354 | 0.222 | 0.525 | |
SA | 0.230 | 0.223 | 0.406 | 0.262 | 0.560 | |
Multi-feature | 0.350 | 0.226 | 0.379 | 0.246 | 0.573 | |
B. Li | Curvature | 0.805 | 0.644 | 0.777 | 0.558 | 0.853 |
Geodesic | – | – | – | – | – | |
Hybrid | – | – | – | – | – | |
MDS-R | – | – | – | – | – | |
MDS-ZFDR | – | – | – | – | – | |
C. Li | Spectral Geom. | 0.555 | 0.255 | 0.369 | 0.252 | 0.611 |
Litman | supDL | 0.835 | 0.635 | 0.783 | 0.558 | 0.872 |
UnSup32 | 0.770 | 0.523 | 0.670 | 0.477 | 0.812 | |
softVQ48 | 0.730 | 0.426 | 0.551 | 0.387 | 0.748 | |
Pickup | Surface area | 0.545 | 0.509 | 0.818 | 0.544 | 0.763 |
Compactness | 0.405 | 0.377 | 0.653 | 0.429 | 0.679 | |
Canonical | 0.245 | 0.159 | 0.286 | 0.186 | 0.507 | |
Bu | 3DDL | 0.415 | 0.281 | 0.492 | 0.321 | 0.619 |
Tatsuma | BoF-APFH | 0.890 | 0.652 | 0.785 | 0.559 | 0.886 |
MR-BoF-APFH |
0.900
|
0.815
|
0.901
|
0.645
|
0.938
| |
Ye | R-BiHDM | 0.645 | 0.368 | 0.533 | 0.370 | 0.698 |
R-BiHDM-s | 0.870 | 0.555 | 0.720 | 0.501 | 0.846 | |
Tam | MRG | – | – | – | – | – |
TPR | 0.285 | 0.169 | 0.279 | 0.184 | 0.521 |
4.8 BoF and SI-HKS
4.9 Spectral Geometry
4.9.1 Spectral Graph Wavelet Signature
4.9.2 Intrinsic Spatial Pyramid Matching
4.10 Topological Matching
4.10.1 Topological Matching with Multi-resolution Reeb Graphs
4.10.2 Topological Point Rings and Geometric Signatures
5 Results
5.1 Experimental Results
5.2 Discussion
Author | Method |
Real
|
Synthetic
|
FAUST
|
---|---|---|---|---|
Giachetti | APT | 0.676 | 0.000 | 0.000 |
APT-trained | 0.611 | 0.300 | 0.000 | |
Lai | HKS | 0.109 | 0.025 | 0.060 |
WKS | 0.175 | 0.000 | 0.062 | |
SA | 0.105 | 0.036 | 0.104 | |
Multi-feature | 0.276 | 0.000 | 0.169 | |
B. Li | Curvature | 0.681 | 0.702 | 0.333 |
Geodesic | 0.909 | 0.768 | – | |
Hybrid | 0.924 | 0.944 | – | |
MDS-R | 0.969 | 0.927 | – | |
MDS-ZFDR | 0.905 | 0.861 | – | |
C. Li | Spectral Geom. | 0.807 | 0.000 | 0.371 |
Litman | supDL | 0.778 | 1.000 | 0.848 |
UnSup32 | 0.886 | 0.969 | 0.826 | |
softVQ48 | 0.758 | 1.000 | 0.685 | |
Pickup | Surface area | 0.112 | 0.017 | 0.154 |
Compactness | 0.093 | 0.092 | 0.059 | |
Canonical | 0.995 | 0.987 | 0.338 | |
Bu | 3DDL | 0.561 | 0.087 | 0.325 |
Tatsuma | BoF-APFH | 1.000 | 0.993 | 0.909 |
MR-BoF-APFH | 0.965 | 0.587 | 0.750 | |
Ye | R-BiHDM | 0.903 | 0.506 | 0.634 |
R-BiHDM-s | 0.732 | 0.625 | 0.692 | |
Tam | MRG | 0.947 | 0.953 | – |
TPR | 0.967 | 0.892 | 0.594 |
Real
|
Synthetic
|
FAUST
|
---|---|---|
\(-0.25\)
|
\(-0.50\)
| 0.46 |
Author | Method | NN | 1-T | 2-T | E-M | DCG |
---|---|---|---|---|---|---|
Giachetti | APT |
0.955
| 0.672 | 0.939 | 0.644 | 0.920 |
APT-trained |
0.955
|
0.783
|
0.988
|
0.688
|
0.950
| |
Lai | HKS | 0.390 | 0.401 | 0.659 | 0.444 | 0.681 |
WKS | 0.730 | 0.626 | 0.912 | 0.635 | 0.838 | |
SA | 0.610 | 0.591 | 0.961 | 0.644 | 0.816 | |
Multi-feature | 0.815 | 0.645 |
0.973
| 0.661 | 0.873 | |
B. Li | Curvature | 0.520 | 0.451 | 0.733 | 0.487 | 0.748 |
Geodesic | 0.440 | 0.336 | 0.519 | 0.351 | 0.654 | |
Hybrid | 0.290 | 0.461 | 0.737 | 0.498 | 0.732 | |
MDS-R | 0.205 | 0.249 | 0.422 | 0.281 | 0.567 | |
MDS-ZFDR | 0.185 | 0.204 | 0.367 | 0.235 | 0.541 | |
C. Li | Spectral Geom. |
0.990
|
0.808
| 0.962 |
0.698
|
0.963
|
Litman | supDL | 0.945 |
0.832
| 0.961 |
0.686
|
0.963
|
UnSup32 | 0.845 | 0.709 | 0.892 | 0.631 | 0.917 | |
softVQ48 | 0.870 | 0.657 | 0.926 | 0.630 | 0.900 | |
Pickup | Surface area | 0.710 | 0.651 |
0.981
| 0.664 | 0.853 |
Compactness | 0.750 | 0.637 | 0.914 | 0.629 | 0.842 | |
Canonical | 0.000 | 0.136 | 0.302 | 0.190 | 0.452 | |
Bu | 3DDL | 0.905 | 0.682 | 0.888 | 0.607 | 0.897 |
Tatsuma | BoF-APFH | 0.405 | 0.517 | 0.726 | 0.510 | 0.768 |
MR-BoF-APFH | 0.735 | 0.496 | 0.814 | 0.541 | 0.799 | |
Ye | R-BiHDM | 0.690 | 0.456 | 0.652 | 0.459 | 0.754 |
R-BiHDM-s | 0.730 | 0.508 | 0.791 | 0.537 | 0.800 | |
Tam | MRG | 0.060 | 0.151 | 0.270 | 0.176 | 0.474 |
TPR | 0.085 | 0.161 | 0.304 | 0.190 | 0.490 |
Author | Method | NN | 1-T | 2-T | E-M | DCG |
---|---|---|---|---|---|---|
Giachetti | APT |
0.945
| 0.813 |
0.951
|
0.437
|
0.943
|
APT-trained |
0.968
|
0.870
|
0.974
|
0.438
|
0.961
| |
Lai | HKS | 0.625 | 0.628 | 0.878 | 0.433 | 0.804 |
WKS | 0.714 | 0.680 | 0.899 | 0.433 | 0.839 | |
SA | 0.649 | 0.630 | 0.854 | 0.426 | 0.809 | |
Multi-feature | 0.825 | 0.775 | 0.948 |
0.437
| 0.900 | |
B. Li | Curvature | 0.281 | 0.232 | 0.391 | 0.253 | 0.528 |
Geodesic | 0.273 | 0.265 | 0.442 | 0.277 | 0.553 | |
Hybrid | 0.299 | 0.279 | 0.458 | 0.287 | 0.565 | |
MDS-R | 0.207 | 0.215 | 0.353 | 0.236 | 0.510 | |
MDS-ZFDR | 0.147 | 0.184 | 0.338 | 0.226 | 0.476 | |
C. Li | Spectral Geom. | 0.594 | 0.413 | 0.592 | 0.324 | 0.688 |
Litman | supDL |
0.931
|
0.878
|
0.980
|
0.439
|
0.958
|
UnSup32 | 0.831 | 0.720 | 0.902 | 0.429 | 0.890 | |
softVQ48 | 0.847 | 0.728 | 0.909 | 0.432 | 0.897 | |
Pickup | Surface area | 0.650 | 0.658 | 0.892 | 0.432 | 0.820 |
Compactness | 0.563 | 0.525 | 0.760 | 0.395 | 0.744 | |
Canonical | 0.006 | 0.041 | 0.191 | 0.161 | 0.367 | |
Bu | 3DDL | 0.582 | 0.540 | 0.794 | 0.414 | 0.759 |
Tatsuma | BoF-APFH | 0.247 | 0.358 | 0.575 | 0.326 | 0.608 |
MR-BoF-APFH | 0.182 | 0.205 | 0.335 | 0.224 | 0.500 | |
Ye | R-BiHDM | 0.614 | 0.458 | 0.682 | 0.377 | 0.730 |
R-BiHDM-s | 0.910 |
0.838
| 0.950 | 0.434 | 0.941 | |
Tam | MRG | 0.103 | 0.097 | 0.208 | 0.159 | 0.408 |
TPR | 0.100 | 0.129 | 0.265 | 0.197 | 0.431 |