Deformetrica 4: an open- source software for statistical shape analysis · 2020-06-08 · 2 =1 𝑛...
Transcript of Deformetrica 4: an open- source software for statistical shape analysis · 2020-06-08 · 2 =1 𝑛...
ShapeMI workshop
MICCAI conference
20 September 2018
Granada, Spain
Alexandre Bône, Maxime Louis, Benoît Martin, Stanley Durrleman
Deformetrica 4: an open-source software for statistical shape analysis
I. Registration
II. Atlas
III.Regression
Deformetrica 4: an open-source software for statistical shape analysis
demo
Registration
𝚽𝒄,𝜶𝝈
𝑆 𝑇
Registration
𝚽𝒄,𝜶𝝈
𝑆 𝑇
Registration
cost
functionregularization
cost
attachment
cost
𝐸 𝑐, 𝛼 =1
𝜎𝜀2 Φ𝑐,𝛼
𝜎 ⋆ 𝑆 − 𝑇ℰ
2+𝑅(𝑐, 𝛼)
𝚽𝒄,𝜶𝝈
𝑆 𝑇
Registration
𝐸 𝑐, 𝛼 =1
𝜎𝜀2 Φ𝑐,𝛼
𝜎 ⋆ 𝑆 − 𝑇ℰ
2+𝑅(𝑐, 𝛼)
𝚽𝒄,𝜶𝝈
𝑆 𝑇
inputs
Registration
𝐸 𝑐, 𝛼 =1
𝜎𝜀2 Φ𝑐,𝛼
𝜎 ⋆ 𝑆 − 𝑇ℰ
2+𝑅(𝑐, 𝛼)
𝚽𝒄,𝜶𝝈
𝑆 𝑇
outputsinputs
Registration
𝐸 𝑐, 𝛼 =1
𝜎𝜀2 Φ𝑐,𝛼
𝜎 ⋆ 𝑆 − 𝑇ℰ
2+𝑅(𝑐, 𝛼)
𝑆 𝑇
Hyper-
parametersoutputsinputs
𝚽𝒄,𝜶𝝈
Registration
𝐸 𝑐, 𝛼 =1
𝜎𝜀2 Φ𝑐,𝛼
𝜎 ⋆ 𝑆 − 𝑇ℰ
2+𝑅(𝑐, 𝛼)
𝑆 𝑇
Hyper-
parametersoutputsinputs
𝚽𝒄,𝜶𝝈
133
190
Registration
𝐸 𝑐, 𝛼 =1
𝜎𝜀2 Φ𝑐,𝛼
𝜎 ⋆ 𝑆 − 𝑇ℰ
2+𝑅(𝑐, 𝛼)
𝑆 𝑇
Hyper-
parametersoutputsinputs
𝚽𝒄,𝜶𝝈
133
190
Registration
𝐸 𝑐, 𝛼 =1
𝜎𝜀2 Φ𝑐,𝛼
𝜎 ⋆ 𝑆 − 𝑇ℰ
2+𝑅(𝑐, 𝛼)
Hyper-
parametersoutputsinputs
Registration
𝐸 𝑐, 𝛼 =1
𝜎𝜀2 Φ𝑐,𝛼
𝜎 ⋆ 𝑆 − 𝑇ℰ
2+𝑅(𝑐, 𝛼)
Hyper-
parametersoutputsinputs
Registration
𝑇 𝑆
Registration
𝑇 𝑆
Registration
𝑇 𝑆
Registration
𝑇 𝑆
Registration
𝑇 𝑆
>> deformetrica estimate
model.xml data_set.xml –p
optimization_parameters.xml
Registration
𝑇 𝑆
I. Registration
II. Atlas
III.Regression
Deformetrica 4: an open-source software for statistical shape analysis
demo
Deterministic atlas
Deterministic atlas
Deterministic atlas
𝐸 𝑆, 𝑐, (𝛼𝑖)𝑖 =1
𝜎𝜀2
𝑖=1
𝑛
Φ𝑐,𝛼𝑖𝜎 ⋆ 𝑆 − 𝑇𝑖 ℰ
2+ 𝑅(𝑐, 𝛼𝑖)
Hyper-
parametersoutputsinputs
𝐸 𝑆, 𝑐, (𝛼𝑖)𝑖 =1
𝜎𝜀2
𝑖=1
𝑛
Φ𝑐,𝛼𝑖𝜎 ⋆ 𝑆 − 𝑇𝑖 ℰ
2+ 𝑅(𝑐, 𝛼𝑖)
Deterministic atlas
Hyper-
parametersoutputsinputs
𝐸 𝑆, 𝑐, (𝛼𝑖)𝑖 =1
𝜎𝜀2
𝑖=1
𝑛
Φ𝑐,𝛼𝑖𝜎 ⋆ 𝑆 − 𝑇𝑖 ℰ
2+ 𝑅(𝑐, 𝛼𝑖)
Deterministic atlas
Hyper-
parametersoutputsinputs
𝐸 𝑆, 𝑐, (𝛼𝑖)𝑖 =1
𝜎𝜀2
𝑖=1
𝑛
Φ𝑐,𝛼𝑖𝜎 ⋆ 𝑆 − 𝑇𝑖 ℰ
2+ 𝑅(𝑐, 𝛼𝑖)
Deterministic atlas
Hyper-
parametersoutputsinputs
𝐸 𝑆, 𝑐, (𝛼𝑖)𝑖 =1
𝜎𝜀2
𝑖=1
𝑛
Φ𝑐,𝛼𝑖𝜎 ⋆ 𝑆 − 𝑇𝑖 ℰ
2+ 𝑅(𝑐, 𝛼𝑖)
Deterministic atlas
Hyper-
parametersoutputsinputs
>> deformetrica estimate
model.xml data_set.xml –p
optimization_parameters.xml
Deterministic atlas
Deterministic atlas
Deterministic atlas
I. Registration
II. Atlas
III.Regression
Deformetrica 4: an open-source software for statistical shape analysis
demo
Geodesic regression
𝑡1 = 5 𝑡2 = 15 𝑡3 = 25 𝑡4 = 35Yin et al. 2008, “A High- Resolution 3D Dynamic Facial Expression Database”
Geodesic regression
𝐸 𝑆, 𝑐, 𝛼 =1
𝜎𝜀2
𝑗=1
𝑝
Φ𝑐,𝑡𝑗∙𝛼𝜎 ⋆ 𝑆 − 𝑇𝑗
ℰ
2+ 𝑅(𝑐, 𝛼)
Hyper-
parametersoutputsinputs
𝑡1 = 5 𝑡2 = 15 𝑡3 = 25 𝑡4 = 35Yin et al. 2008, “A High- Resolution 3D Dynamic Facial Expression Database”
𝑡1 = 5 𝑡2 = 15 𝑡3 = 25 𝑡4 = 35Yin et al. 2008, “A High- Resolution 3D Dynamic Facial Expression Database”
Geodesic regression
𝑡1 = 5 𝑡2 = 15 𝑡3 = 25 𝑡4 = 35Yin et al. 2008, “A High- Resolution 3D Dynamic Facial Expression Database”
Geodesic regression
Geodesic regression
>> deformetrica estimate
model.xml data_set.xml
𝑡1 = 5 𝑡2 = 15 𝑡3 = 25 𝑡4 = 35Yin et al. 2008, “A High- Resolution 3D Dynamic Facial Expression Database”
𝑡1 = 5 𝑡2 = 15 𝑡3 = 25 𝑡4 = 35Yin et al. 2008, “A High- Resolution 3D Dynamic Facial Expression Database”
Geodesic regression
Parallel transport
Transfer a reference temporal evolution towards a new target geometry
Data courtesy of Paolo Piras, Sapienza Università di Roma, Italy
MR image registration performance
Registration of full-resolution MR images (7 millions voxels) in 2-3 minutes, with low GPU memory usage
Teaser: graphical user interface alpha
Teaser: python API beta
PyTorch
• Auto-differentiation, without memory
overflows
• Seamless CUDA code
PyTorch + PyKeops
• Auto-differentiation, without memory
overflows
• Seamless CUDA code
Thanks to Benjamin Charlier, Jean Feydy & Joan Glaunès
Conclusion
Implements many statistical shape analysis tasks ...
• Registration
• Deterministic atlas
• Bayesian atlas
• Geodesic regression
• Parallel transport
• Longitudinal atlas
• Principal geodesic
analysis
beta
alpha
Conclusion
Implements many statistical shape analysis tasks ...
• Registration
• Deterministic atlas
• Bayesian atlas
• Geodesic regression
• Parallel transport
• Longitudinal atlas
• Principal geodesic
analysis
beta
alpha
... with very few requirements about the data
• Image
• Meshes
• No required point
correspondence
• Multi-object
• Cross-sectional or
longitudinal datasets
• Linux or Mac
• 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!
Future work
Grow the pool of users
• Graphical user
interface (GUI)
• Python API
• Windows platform
Add functionalities
• Longitudinal atlas
• Principal geodesic
analysis
• MCMC-SAEM
estimation algorithm
Improve performance
• Achieve massive parallelization on large clusters
• Emphasis on GPU-specific optimizations
A decade of development
Deformetrica 1 C++
Deformetrica 3 C++
Deformetrica 4 PythonDeformetrica 2
C++
2011 2013 2017 2018
Deterministic atlas: landmark/2d/skulls
Deterministic atlas: landmark/2d/skulls
Deterministic atlas: landmark/2d/skulls
A note on the Bayesian atlas
𝐶 𝑇, (𝜇𝑖)𝑖, 𝜎𝜀2 =
1
𝜎𝜀2
𝑖=1
𝑛
Φ𝜇𝑖 ⋆ 𝑇 − 𝑆𝑖 ℰ
2+𝑅(𝜇𝑖 , 𝜎𝜀
2)
cost
functionregularization
cost
attachment
cost
A note on the Bayesian atlas
𝐶 𝑇, (𝜇𝑖)𝑖, 𝜎𝜀2 =
1
𝜎𝜀2
𝑖=1
𝑛
Φ𝜇𝑖 ⋆ 𝑇 − 𝑆𝑖 ℰ
2+𝑅(𝜇𝑖 , 𝜎𝜀
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 𝝈𝜺𝟐 anymore!
The optimal tradeoff between attachment and
regularity terms is estimated from the data
Bayesian atlas
𝐶 𝑇, (𝜇𝑖)𝑖, 𝜎𝜀2 =
1
𝜎𝜀2
𝑖=1
𝑛
Φ𝜇𝑖 ⋆ 𝑇 − 𝑆𝑖 ℰ
2+𝑅(𝜇𝑖 , 𝜎𝜀
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 𝝈𝜺𝟐 anymore!
Bayesian atlas
Registration
𝑇 𝑆
Registration
𝑇 𝑆
Registration
𝑇 𝑆
Registration
𝑇 𝑆
Registration
𝑇 𝑆
>> deformetrica estimate model.xml
data_set.xml –p
optimization_parameters.xml