deformetrica 4: an open- source software for statistical shape analysisย ยท 2020-06-08ย ยท 2 =1 ๐...
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![Page 1: Deformetrica 4: an open- source software for statistical shape analysisย ยท 2020-06-08ย ยท 2 =1 ๐ ฮฆ๐ โ โ โฐ 2 + (๐ ,๐๐2) Gives a statistical interpretation of](https://reader033.vdocuments.us/reader033/viewer/2022043022/5f3ddc22d0a91608cb413b2d/html5/thumbnails/1.jpg)
ShapeMI workshop
MICCAI conference
20 September 2018
Granada, Spain
Alexandre Bรดne, Maxime Louis, Benoรฎt Martin, Stanley Durrleman
Deformetrica 4: an open-source software for statistical shape analysis
![Page 2: Deformetrica 4: an open- source software for statistical shape analysisย ยท 2020-06-08ย ยท 2 =1 ๐ ฮฆ๐ โ โ โฐ 2 + (๐ ,๐๐2) Gives a statistical interpretation of](https://reader033.vdocuments.us/reader033/viewer/2022043022/5f3ddc22d0a91608cb413b2d/html5/thumbnails/2.jpg)
I. Registration
II. Atlas
III.Regression
Deformetrica 4: an open-source software for statistical shape analysis
demo
![Page 3: Deformetrica 4: an open- source software for statistical shape analysisย ยท 2020-06-08ย ยท 2 =1 ๐ ฮฆ๐ โ โ โฐ 2 + (๐ ,๐๐2) Gives a statistical interpretation of](https://reader033.vdocuments.us/reader033/viewer/2022043022/5f3ddc22d0a91608cb413b2d/html5/thumbnails/3.jpg)
Registration
๐ฝ๐,๐ถ๐
๐ ๐
![Page 4: Deformetrica 4: an open- source software for statistical shape analysisย ยท 2020-06-08ย ยท 2 =1 ๐ ฮฆ๐ โ โ โฐ 2 + (๐ ,๐๐2) Gives a statistical interpretation of](https://reader033.vdocuments.us/reader033/viewer/2022043022/5f3ddc22d0a91608cb413b2d/html5/thumbnails/4.jpg)
Registration
๐ฝ๐,๐ถ๐
๐ ๐
![Page 5: Deformetrica 4: an open- source software for statistical shape analysisย ยท 2020-06-08ย ยท 2 =1 ๐ ฮฆ๐ โ โ โฐ 2 + (๐ ,๐๐2) Gives a statistical interpretation of](https://reader033.vdocuments.us/reader033/viewer/2022043022/5f3ddc22d0a91608cb413b2d/html5/thumbnails/5.jpg)
Registration
cost
functionregularization
cost
attachment
cost
๐ธ ๐, ๐ผ =1
๐๐2 ฮฆ๐,๐ผ
๐ โ ๐ โ ๐โฐ
2+๐ (๐, ๐ผ)
๐ฝ๐,๐ถ๐
๐ ๐
![Page 6: Deformetrica 4: an open- source software for statistical shape analysisย ยท 2020-06-08ย ยท 2 =1 ๐ ฮฆ๐ โ โ โฐ 2 + (๐ ,๐๐2) Gives a statistical interpretation of](https://reader033.vdocuments.us/reader033/viewer/2022043022/5f3ddc22d0a91608cb413b2d/html5/thumbnails/6.jpg)
Registration
๐ธ ๐, ๐ผ =1
๐๐2 ฮฆ๐,๐ผ
๐ โ ๐ โ ๐โฐ
2+๐ (๐, ๐ผ)
๐ฝ๐,๐ถ๐
๐ ๐
inputs
![Page 7: Deformetrica 4: an open- source software for statistical shape analysisย ยท 2020-06-08ย ยท 2 =1 ๐ ฮฆ๐ โ โ โฐ 2 + (๐ ,๐๐2) Gives a statistical interpretation of](https://reader033.vdocuments.us/reader033/viewer/2022043022/5f3ddc22d0a91608cb413b2d/html5/thumbnails/7.jpg)
Registration
๐ธ ๐, ๐ผ =1
๐๐2 ฮฆ๐,๐ผ
๐ โ ๐ โ ๐โฐ
2+๐ (๐, ๐ผ)
๐ฝ๐,๐ถ๐
๐ ๐
outputsinputs
![Page 8: Deformetrica 4: an open- source software for statistical shape analysisย ยท 2020-06-08ย ยท 2 =1 ๐ ฮฆ๐ โ โ โฐ 2 + (๐ ,๐๐2) Gives a statistical interpretation of](https://reader033.vdocuments.us/reader033/viewer/2022043022/5f3ddc22d0a91608cb413b2d/html5/thumbnails/8.jpg)
Registration
๐ธ ๐, ๐ผ =1
๐๐2 ฮฆ๐,๐ผ
๐ โ ๐ โ ๐โฐ
2+๐ (๐, ๐ผ)
๐ ๐
Hyper-
parametersoutputsinputs
๐ฝ๐,๐ถ๐
![Page 9: Deformetrica 4: an open- source software for statistical shape analysisย ยท 2020-06-08ย ยท 2 =1 ๐ ฮฆ๐ โ โ โฐ 2 + (๐ ,๐๐2) Gives a statistical interpretation of](https://reader033.vdocuments.us/reader033/viewer/2022043022/5f3ddc22d0a91608cb413b2d/html5/thumbnails/9.jpg)
Registration
๐ธ ๐, ๐ผ =1
๐๐2 ฮฆ๐,๐ผ
๐ โ ๐ โ ๐โฐ
2+๐ (๐, ๐ผ)
๐ ๐
Hyper-
parametersoutputsinputs
๐ฝ๐,๐ถ๐
133
190
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Registration
๐ธ ๐, ๐ผ =1
๐๐2 ฮฆ๐,๐ผ
๐ โ ๐ โ ๐โฐ
2+๐ (๐, ๐ผ)
๐ ๐
Hyper-
parametersoutputsinputs
๐ฝ๐,๐ถ๐
133
190
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Registration
๐ธ ๐, ๐ผ =1
๐๐2 ฮฆ๐,๐ผ
๐ โ ๐ โ ๐โฐ
2+๐ (๐, ๐ผ)
Hyper-
parametersoutputsinputs
![Page 12: Deformetrica 4: an open- source software for statistical shape analysisย ยท 2020-06-08ย ยท 2 =1 ๐ ฮฆ๐ โ โ โฐ 2 + (๐ ,๐๐2) Gives a statistical interpretation of](https://reader033.vdocuments.us/reader033/viewer/2022043022/5f3ddc22d0a91608cb413b2d/html5/thumbnails/12.jpg)
Registration
๐ธ ๐, ๐ผ =1
๐๐2 ฮฆ๐,๐ผ
๐ โ ๐ โ ๐โฐ
2+๐ (๐, ๐ผ)
Hyper-
parametersoutputsinputs
![Page 13: Deformetrica 4: an open- source software for statistical shape analysisย ยท 2020-06-08ย ยท 2 =1 ๐ ฮฆ๐ โ โ โฐ 2 + (๐ ,๐๐2) Gives a statistical interpretation of](https://reader033.vdocuments.us/reader033/viewer/2022043022/5f3ddc22d0a91608cb413b2d/html5/thumbnails/13.jpg)
Registration
๐ ๐
![Page 14: Deformetrica 4: an open- source software for statistical shape analysisย ยท 2020-06-08ย ยท 2 =1 ๐ ฮฆ๐ โ โ โฐ 2 + (๐ ,๐๐2) Gives a statistical interpretation of](https://reader033.vdocuments.us/reader033/viewer/2022043022/5f3ddc22d0a91608cb413b2d/html5/thumbnails/14.jpg)
Registration
๐ ๐
![Page 15: Deformetrica 4: an open- source software for statistical shape analysisย ยท 2020-06-08ย ยท 2 =1 ๐ ฮฆ๐ โ โ โฐ 2 + (๐ ,๐๐2) Gives a statistical interpretation of](https://reader033.vdocuments.us/reader033/viewer/2022043022/5f3ddc22d0a91608cb413b2d/html5/thumbnails/15.jpg)
Registration
๐ ๐
![Page 16: Deformetrica 4: an open- source software for statistical shape analysisย ยท 2020-06-08ย ยท 2 =1 ๐ ฮฆ๐ โ โ โฐ 2 + (๐ ,๐๐2) Gives a statistical interpretation of](https://reader033.vdocuments.us/reader033/viewer/2022043022/5f3ddc22d0a91608cb413b2d/html5/thumbnails/16.jpg)
Registration
๐ ๐
![Page 17: Deformetrica 4: an open- source software for statistical shape analysisย ยท 2020-06-08ย ยท 2 =1 ๐ ฮฆ๐ โ โ โฐ 2 + (๐ ,๐๐2) Gives a statistical interpretation of](https://reader033.vdocuments.us/reader033/viewer/2022043022/5f3ddc22d0a91608cb413b2d/html5/thumbnails/17.jpg)
Registration
๐ ๐
>> deformetrica estimate
model.xml data_set.xml โp
optimization_parameters.xml
![Page 18: Deformetrica 4: an open- source software for statistical shape analysisย ยท 2020-06-08ย ยท 2 =1 ๐ ฮฆ๐ โ โ โฐ 2 + (๐ ,๐๐2) Gives a statistical interpretation of](https://reader033.vdocuments.us/reader033/viewer/2022043022/5f3ddc22d0a91608cb413b2d/html5/thumbnails/18.jpg)
Registration
๐ ๐
![Page 19: Deformetrica 4: an open- source software for statistical shape analysisย ยท 2020-06-08ย ยท 2 =1 ๐ ฮฆ๐ โ โ โฐ 2 + (๐ ,๐๐2) Gives a statistical interpretation of](https://reader033.vdocuments.us/reader033/viewer/2022043022/5f3ddc22d0a91608cb413b2d/html5/thumbnails/19.jpg)
I. Registration
II. Atlas
III.Regression
Deformetrica 4: an open-source software for statistical shape analysis
demo
![Page 20: Deformetrica 4: an open- source software for statistical shape analysisย ยท 2020-06-08ย ยท 2 =1 ๐ ฮฆ๐ โ โ โฐ 2 + (๐ ,๐๐2) Gives a statistical interpretation of](https://reader033.vdocuments.us/reader033/viewer/2022043022/5f3ddc22d0a91608cb413b2d/html5/thumbnails/20.jpg)
Deterministic atlas
![Page 21: Deformetrica 4: an open- source software for statistical shape analysisย ยท 2020-06-08ย ยท 2 =1 ๐ ฮฆ๐ โ โ โฐ 2 + (๐ ,๐๐2) Gives a statistical interpretation of](https://reader033.vdocuments.us/reader033/viewer/2022043022/5f3ddc22d0a91608cb413b2d/html5/thumbnails/21.jpg)
Deterministic atlas
![Page 22: Deformetrica 4: an open- source software for statistical shape analysisย ยท 2020-06-08ย ยท 2 =1 ๐ ฮฆ๐ โ โ โฐ 2 + (๐ ,๐๐2) Gives a statistical interpretation of](https://reader033.vdocuments.us/reader033/viewer/2022043022/5f3ddc22d0a91608cb413b2d/html5/thumbnails/22.jpg)
Deterministic atlas
๐ธ ๐, ๐, (๐ผ๐)๐ =1
๐๐2
๐=1
๐
ฮฆ๐,๐ผ๐๐ โ ๐ โ ๐๐ โฐ
2+ ๐ (๐, ๐ผ๐)
Hyper-
parametersoutputsinputs
![Page 23: Deformetrica 4: an open- source software for statistical shape analysisย ยท 2020-06-08ย ยท 2 =1 ๐ ฮฆ๐ โ โ โฐ 2 + (๐ ,๐๐2) Gives a statistical interpretation of](https://reader033.vdocuments.us/reader033/viewer/2022043022/5f3ddc22d0a91608cb413b2d/html5/thumbnails/23.jpg)
๐ธ ๐, ๐, (๐ผ๐)๐ =1
๐๐2
๐=1
๐
ฮฆ๐,๐ผ๐๐ โ ๐ โ ๐๐ โฐ
2+ ๐ (๐, ๐ผ๐)
Deterministic atlas
Hyper-
parametersoutputsinputs
![Page 24: Deformetrica 4: an open- source software for statistical shape analysisย ยท 2020-06-08ย ยท 2 =1 ๐ ฮฆ๐ โ โ โฐ 2 + (๐ ,๐๐2) Gives a statistical interpretation of](https://reader033.vdocuments.us/reader033/viewer/2022043022/5f3ddc22d0a91608cb413b2d/html5/thumbnails/24.jpg)
๐ธ ๐, ๐, (๐ผ๐)๐ =1
๐๐2
๐=1
๐
ฮฆ๐,๐ผ๐๐ โ ๐ โ ๐๐ โฐ
2+ ๐ (๐, ๐ผ๐)
Deterministic atlas
Hyper-
parametersoutputsinputs
![Page 25: Deformetrica 4: an open- source software for statistical shape analysisย ยท 2020-06-08ย ยท 2 =1 ๐ ฮฆ๐ โ โ โฐ 2 + (๐ ,๐๐2) Gives a statistical interpretation of](https://reader033.vdocuments.us/reader033/viewer/2022043022/5f3ddc22d0a91608cb413b2d/html5/thumbnails/25.jpg)
๐ธ ๐, ๐, (๐ผ๐)๐ =1
๐๐2
๐=1
๐
ฮฆ๐,๐ผ๐๐ โ ๐ โ ๐๐ โฐ
2+ ๐ (๐, ๐ผ๐)
Deterministic atlas
Hyper-
parametersoutputsinputs
![Page 26: Deformetrica 4: an open- source software for statistical shape analysisย ยท 2020-06-08ย ยท 2 =1 ๐ ฮฆ๐ โ โ โฐ 2 + (๐ ,๐๐2) Gives a statistical interpretation of](https://reader033.vdocuments.us/reader033/viewer/2022043022/5f3ddc22d0a91608cb413b2d/html5/thumbnails/26.jpg)
๐ธ ๐, ๐, (๐ผ๐)๐ =1
๐๐2
๐=1
๐
ฮฆ๐,๐ผ๐๐ โ ๐ โ ๐๐ โฐ
2+ ๐ (๐, ๐ผ๐)
Deterministic atlas
Hyper-
parametersoutputsinputs
>> deformetrica estimate
model.xml data_set.xml โp
optimization_parameters.xml
![Page 27: Deformetrica 4: an open- source software for statistical shape analysisย ยท 2020-06-08ย ยท 2 =1 ๐ ฮฆ๐ โ โ โฐ 2 + (๐ ,๐๐2) Gives a statistical interpretation of](https://reader033.vdocuments.us/reader033/viewer/2022043022/5f3ddc22d0a91608cb413b2d/html5/thumbnails/27.jpg)
Deterministic atlas
![Page 28: Deformetrica 4: an open- source software for statistical shape analysisย ยท 2020-06-08ย ยท 2 =1 ๐ ฮฆ๐ โ โ โฐ 2 + (๐ ,๐๐2) Gives a statistical interpretation of](https://reader033.vdocuments.us/reader033/viewer/2022043022/5f3ddc22d0a91608cb413b2d/html5/thumbnails/28.jpg)
Deterministic atlas
![Page 29: Deformetrica 4: an open- source software for statistical shape analysisย ยท 2020-06-08ย ยท 2 =1 ๐ ฮฆ๐ โ โ โฐ 2 + (๐ ,๐๐2) Gives a statistical interpretation of](https://reader033.vdocuments.us/reader033/viewer/2022043022/5f3ddc22d0a91608cb413b2d/html5/thumbnails/29.jpg)
Deterministic atlas
![Page 30: Deformetrica 4: an open- source software for statistical shape analysisย ยท 2020-06-08ย ยท 2 =1 ๐ ฮฆ๐ โ โ โฐ 2 + (๐ ,๐๐2) Gives a statistical interpretation of](https://reader033.vdocuments.us/reader033/viewer/2022043022/5f3ddc22d0a91608cb413b2d/html5/thumbnails/30.jpg)
I. Registration
II. Atlas
III.Regression
Deformetrica 4: an open-source software for statistical shape analysis
demo
![Page 31: Deformetrica 4: an open- source software for statistical shape analysisย ยท 2020-06-08ย ยท 2 =1 ๐ ฮฆ๐ โ โ โฐ 2 + (๐ ,๐๐2) Gives a statistical interpretation of](https://reader033.vdocuments.us/reader033/viewer/2022043022/5f3ddc22d0a91608cb413b2d/html5/thumbnails/31.jpg)
Geodesic regression
๐ก1 = 5 ๐ก2 = 15 ๐ก3 = 25 ๐ก4 = 35Yin et al. 2008, โA High- Resolution 3D Dynamic Facial Expression Databaseโ
![Page 32: Deformetrica 4: an open- source software for statistical shape analysisย ยท 2020-06-08ย ยท 2 =1 ๐ ฮฆ๐ โ โ โฐ 2 + (๐ ,๐๐2) Gives a statistical interpretation of](https://reader033.vdocuments.us/reader033/viewer/2022043022/5f3ddc22d0a91608cb413b2d/html5/thumbnails/32.jpg)
Geodesic regression
๐ธ ๐, ๐, ๐ผ =1
๐๐2
๐=1
๐
ฮฆ๐,๐ก๐โ๐ผ๐ โ ๐ โ ๐๐
โฐ
2+ ๐ (๐, ๐ผ)
Hyper-
parametersoutputsinputs
๐ก1 = 5 ๐ก2 = 15 ๐ก3 = 25 ๐ก4 = 35Yin et al. 2008, โA High- Resolution 3D Dynamic Facial Expression Databaseโ
![Page 33: Deformetrica 4: an open- source software for statistical shape analysisย ยท 2020-06-08ย ยท 2 =1 ๐ ฮฆ๐ โ โ โฐ 2 + (๐ ,๐๐2) Gives a statistical interpretation of](https://reader033.vdocuments.us/reader033/viewer/2022043022/5f3ddc22d0a91608cb413b2d/html5/thumbnails/33.jpg)
๐ก1 = 5 ๐ก2 = 15 ๐ก3 = 25 ๐ก4 = 35Yin et al. 2008, โA High- Resolution 3D Dynamic Facial Expression Databaseโ
Geodesic regression
![Page 34: Deformetrica 4: an open- source software for statistical shape analysisย ยท 2020-06-08ย ยท 2 =1 ๐ ฮฆ๐ โ โ โฐ 2 + (๐ ,๐๐2) Gives a statistical interpretation of](https://reader033.vdocuments.us/reader033/viewer/2022043022/5f3ddc22d0a91608cb413b2d/html5/thumbnails/34.jpg)
๐ก1 = 5 ๐ก2 = 15 ๐ก3 = 25 ๐ก4 = 35Yin et al. 2008, โA High- Resolution 3D Dynamic Facial Expression Databaseโ
Geodesic regression
![Page 35: Deformetrica 4: an open- source software for statistical shape analysisย ยท 2020-06-08ย ยท 2 =1 ๐ ฮฆ๐ โ โ โฐ 2 + (๐ ,๐๐2) Gives a statistical interpretation of](https://reader033.vdocuments.us/reader033/viewer/2022043022/5f3ddc22d0a91608cb413b2d/html5/thumbnails/35.jpg)
Geodesic regression
>> deformetrica estimate
model.xml data_set.xml
๐ก1 = 5 ๐ก2 = 15 ๐ก3 = 25 ๐ก4 = 35Yin et al. 2008, โA High- Resolution 3D Dynamic Facial Expression Databaseโ
![Page 36: Deformetrica 4: an open- source software for statistical shape analysisย ยท 2020-06-08ย ยท 2 =1 ๐ ฮฆ๐ โ โ โฐ 2 + (๐ ,๐๐2) Gives a statistical interpretation of](https://reader033.vdocuments.us/reader033/viewer/2022043022/5f3ddc22d0a91608cb413b2d/html5/thumbnails/36.jpg)
๐ก1 = 5 ๐ก2 = 15 ๐ก3 = 25 ๐ก4 = 35Yin et al. 2008, โA High- Resolution 3D Dynamic Facial Expression Databaseโ
Geodesic regression
![Page 37: Deformetrica 4: an open- source software for statistical shape analysisย ยท 2020-06-08ย ยท 2 =1 ๐ ฮฆ๐ โ โ โฐ 2 + (๐ ,๐๐2) Gives a statistical interpretation of](https://reader033.vdocuments.us/reader033/viewer/2022043022/5f3ddc22d0a91608cb413b2d/html5/thumbnails/37.jpg)
Parallel transport
Transfer a reference temporal evolution towards a new target geometry
Data courtesy of Paolo Piras, Sapienza Universitร di Roma, Italy
![Page 38: Deformetrica 4: an open- source software for statistical shape analysisย ยท 2020-06-08ย ยท 2 =1 ๐ ฮฆ๐ โ โ โฐ 2 + (๐ ,๐๐2) Gives a statistical interpretation of](https://reader033.vdocuments.us/reader033/viewer/2022043022/5f3ddc22d0a91608cb413b2d/html5/thumbnails/38.jpg)
MR image registration performance
Registration of full-resolution MR images (7 millions voxels) in 2-3 minutes, with low GPU memory usage
![Page 39: Deformetrica 4: an open- source software for statistical shape analysisย ยท 2020-06-08ย ยท 2 =1 ๐ ฮฆ๐ โ โ โฐ 2 + (๐ ,๐๐2) Gives a statistical interpretation of](https://reader033.vdocuments.us/reader033/viewer/2022043022/5f3ddc22d0a91608cb413b2d/html5/thumbnails/39.jpg)
Teaser: graphical user interface alpha
![Page 40: Deformetrica 4: an open- source software for statistical shape analysisย ยท 2020-06-08ย ยท 2 =1 ๐ ฮฆ๐ โ โ โฐ 2 + (๐ ,๐๐2) Gives a statistical interpretation of](https://reader033.vdocuments.us/reader033/viewer/2022043022/5f3ddc22d0a91608cb413b2d/html5/thumbnails/40.jpg)
Teaser: python API beta
![Page 41: Deformetrica 4: an open- source software for statistical shape analysisย ยท 2020-06-08ย ยท 2 =1 ๐ ฮฆ๐ โ โ โฐ 2 + (๐ ,๐๐2) Gives a statistical interpretation of](https://reader033.vdocuments.us/reader033/viewer/2022043022/5f3ddc22d0a91608cb413b2d/html5/thumbnails/41.jpg)
PyTorch
โข Auto-differentiation, without memory
overflows
โข Seamless CUDA code
![Page 42: Deformetrica 4: an open- source software for statistical shape analysisย ยท 2020-06-08ย ยท 2 =1 ๐ ฮฆ๐ โ โ โฐ 2 + (๐ ,๐๐2) Gives a statistical interpretation of](https://reader033.vdocuments.us/reader033/viewer/2022043022/5f3ddc22d0a91608cb413b2d/html5/thumbnails/42.jpg)
PyTorch + PyKeops
โข Auto-differentiation, without memory
overflows
โข Seamless CUDA code
Thanks to Benjamin Charlier, Jean Feydy & Joan Glaunรจs
![Page 43: Deformetrica 4: an open- source software for statistical shape analysisย ยท 2020-06-08ย ยท 2 =1 ๐ ฮฆ๐ โ โ โฐ 2 + (๐ ,๐๐2) Gives a statistical interpretation of](https://reader033.vdocuments.us/reader033/viewer/2022043022/5f3ddc22d0a91608cb413b2d/html5/thumbnails/43.jpg)
Conclusion
Implements many statistical shape analysis tasks ...
โข Registration
โข Deterministic atlas
โข Bayesian atlas
โข Geodesic regression
โข Parallel transport
โข Longitudinal atlas
โข Principal geodesic
analysis
beta
alpha
![Page 44: Deformetrica 4: an open- source software for statistical shape analysisย ยท 2020-06-08ย ยท 2 =1 ๐ ฮฆ๐ โ โ โฐ 2 + (๐ ,๐๐2) Gives a statistical interpretation of](https://reader033.vdocuments.us/reader033/viewer/2022043022/5f3ddc22d0a91608cb413b2d/html5/thumbnails/44.jpg)
Conclusion
Implements many statistical shape analysis tasks ...
โข Registration
โข Deterministic atlas
โข Bayesian atlas
โข Geodesic regression
โข Parallel transport
โข Longitudinal atlas
โข Principal geodesic
analysis
beta
alpha
... with very few requirements about the data
โข Image
โข Meshes
โข No required point
correspondence
โข Multi-object
โข Cross-sectional or
longitudinal datasets
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โข Linux or Mac
โข Anaconda 3
Requirements
Thanks!
Install
conda install -c pytorch -c conda-
forge
-c anaconda -c aramislab deformetrica
www.deformetrica.org
Come see us at the lunch & demo session!
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Future work
Grow the pool of users
โข Graphical user
interface (GUI)
โข Python API
โข Windows platform
Add functionalities
โข Longitudinal atlas
โข Principal geodesic
analysis
โข MCMC-SAEM
estimation algorithm
Improve performance
โข Achieve massive parallelization on large clusters
โข Emphasis on GPU-specific optimizations
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A decade of development
Deformetrica 1 C++
Deformetrica 3 C++
Deformetrica 4 PythonDeformetrica 2
C++
2011 2013 2017 2018
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Deterministic atlas: landmark/2d/skulls
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Deterministic atlas: landmark/2d/skulls
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Deterministic atlas: landmark/2d/skulls
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A note on the Bayesian atlas
๐ถ ๐, (๐๐)๐, ๐๐2 =
1
๐๐2
๐=1
๐
ฮฆ๐๐ โ ๐ โ ๐๐ โฐ
2+๐ (๐๐ , ๐๐
2)
cost
functionregularization
cost
attachment
cost
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A note on the Bayesian atlas
๐ถ ๐, (๐๐)๐, ๐๐2 =
1
๐๐2
๐=1
๐
ฮฆ๐๐ โ ๐ โ ๐๐ โฐ
2+๐ (๐๐ , ๐๐
2)
Gives a statistical interpretation of the regularization term, which arises from assumed underlying random
structures on the momenta and residuals
In practice, no need to specify ๐๐บ๐ anymore!
The optimal tradeoff between attachment and
regularity terms is estimated from the data
![Page 53: Deformetrica 4: an open- source software for statistical shape analysisย ยท 2020-06-08ย ยท 2 =1 ๐ ฮฆ๐ โ โ โฐ 2 + (๐ ,๐๐2) Gives a statistical interpretation of](https://reader033.vdocuments.us/reader033/viewer/2022043022/5f3ddc22d0a91608cb413b2d/html5/thumbnails/53.jpg)
Bayesian atlas
๐ถ ๐, (๐๐)๐, ๐๐2 =
1
๐๐2
๐=1
๐
ฮฆ๐๐ โ ๐ โ ๐๐ โฐ
2+๐ (๐๐ , ๐๐
2)
cost
functionregularization
cost
attachment
cost
Statistical interpretation of the regularization term, which arises from assumed underlying random structures on
the momenta and residuals
In practice, no need to specify ๐๐บ๐ anymore!
![Page 54: Deformetrica 4: an open- source software for statistical shape analysisย ยท 2020-06-08ย ยท 2 =1 ๐ ฮฆ๐ โ โ โฐ 2 + (๐ ,๐๐2) Gives a statistical interpretation of](https://reader033.vdocuments.us/reader033/viewer/2022043022/5f3ddc22d0a91608cb413b2d/html5/thumbnails/54.jpg)
Bayesian atlas
![Page 55: Deformetrica 4: an open- source software for statistical shape analysisย ยท 2020-06-08ย ยท 2 =1 ๐ ฮฆ๐ โ โ โฐ 2 + (๐ ,๐๐2) Gives a statistical interpretation of](https://reader033.vdocuments.us/reader033/viewer/2022043022/5f3ddc22d0a91608cb413b2d/html5/thumbnails/55.jpg)
Registration
๐ ๐
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Registration
๐ ๐
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Registration
๐ ๐
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Registration
๐ ๐
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Registration
๐ ๐
>> deformetrica estimate model.xml
data_set.xml โp
optimization_parameters.xml