Deformetrica is a software for the statistical analysis of 2D and 3D shape data. It essentially computes deformations of the 2D or 3D ambient space, which, in turn, warp any object embedded in this space, whether this object is a curve, a surface, a structured or unstructured set of points, an image, or any combination of them.

Deformetrica comes with three main applications:

  • registration : estimates the best possible deformation between two sets of objects;
  • atlas construction : estimates an average object configuration from a collection of object sets, and the deformations from this average to each sample in the collection;
  • geodesic regression : estimates an object time-series constrained to match as closely as possible a set of observations indexed by time.

Deformetrica has very little requirements about the data it can deal with.
In particular, it does not require point correspondence between objects!


  • Requirements: Anaconda 3, Linux or Mac OS X distributions
  • Best practice: “conda create -n deformetrica python=3.8 numpy && source activate deformetrica
  • Pip install: “pip install deformetrica
  • Run an example:
    • deformetrica estimate model.xml data_set.xml -p optimization_parameters.xml
    • deformetrica compute model.xml -p optimization_parameters.xml
  • Try the GUI (alpha version): “deformetrica gui
  • Documentation: wiki


Deformetrica relies on a control-points-based instance of the Large Deformation Diffeomorphic Metric Mapping framework, introduced in [Durrleman et al. 2014]. Are fully described in this article the shootingregistration, and deterministic atlas applications. Equipped with those fundamental building blocks, additional applications have been successively developed:

[Bône et al. 2018b] provides a concise reference summarizing those functionalities, with unified notations.





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  • [Bône et al. 2020], Learning the spatiotemporal variability in longitudinal shape data sets, International Journal of Computer Vision
  • [Bône et al. 2019], Hierarchical modeling of Alzheimer’s disease progression from a large longitudinal MRI data set, Organization for Human Brain Mapping Annual Meeting
  • [Bône et al. 2018b]Deformetrica 4: an open-source software for statistical shape analysis, International Workshop on Shape in Medical Imaging
  • [Bône et al. 2018a]Learning distributions of shape trajectories from longitudinal datasets: a hierarchical model on a manifold of diffeomorphisms, International Conference on Computer Vision and Pattern Recognition
  • [Biffi et al. 2017]Investigating Cardiac Motion Patterns Using Synthetic High-Resolution 3D Cardiovascular Magnetic Resonance Images and Statistical Shape Analysis, Frontiers in Pediatrics
  • [Bône et al. 2017]Prediction of the Progression of Subcortical Brain Structures in Alzheimer’s Disease from Baseline, MICCAI Workshop on Mathematical Foundations of Computational Anatomy
  • [Bruse et al. 2017]Detecting Clinically Meaningful Shape Clusters in Medical Image Data: Metrics Analysis for Hierarchical Clustering Applied to Healthy and Pathological Aortic Arches, IEEE Transactions on Biomedical Engineering
  • [Bruse et al. 2017], How successful is successful? Aortic arch shape after successful aortic coarctation repair correlates with left ventricular function, The Journal of Thoracic and Cardiovascular Surgery
  • [Fishbaugh et al. 2017], A Geodesic shape regression with multiple geometries and sparse parameters, Medical Image Analysis
  • [Gori et al. 2017], A Bayesian Framework for Joint Morphometry of Surface and Curve meshes in Multi-Object Complexes, Medical Image Analysis
  • [Louis et al. 2017], Parallel transport in shape analysis: a scalable numerical scheme, Geometric Science of Information
  • [Bruse et al. 2016], Looks Do Matter! Aortic Arch Shape After Hypoplastic Left Heart Syndrome Palliation Correlates With Cavopulmonary Outcomes, Annual Meeting of The Society of Thoracic Surgeons
  • [Tenhagen et al. 2016], Three-Dimensional Handheld Scanning to Quantify Head-Shape Changes in Spring-Assisted Surgery for Sagittal Craniosynostosis, Journal of Craniofacial Surgery
  • [Bruse et al. 2016], A statistical shape modelling framework to extract 3D shape biomarkers from medical imaging data: assessing arch morphology of repaired coarctation of the aorta, BMC Medical Imaging
  • [Bron et al. 2015], Standardized evaluation of algorithms for computer-aided diagnosis of dementia based on structural MRI: the CADDementia challenge, Neuroimage
  • [Bruse et al. 2015], CMR-based 3D statistical shape modelling reveals left ventricular morphological differences between healthy controls and arterial switch operation survivors, J Cardiovasc Magn Reson
  • [Bruse et al. 2015], A Non-parametric Statistical Shape Model for Assessment of the Surgically Repaired Aortic Arch in Coarctation of the Aorta: How Normal is Abnormal?, Statistical Atlases and Computational Modeling of the Heart
  • [Gori et al. 2015]Joint Morphometry of Fiber Tracts and Gray Matter Structures Using Double Diffeomorphisms, IPMI
  • [Fouquier et al. 2014], Iconic-Geometric Nonlinear Registration of a Basal Ganglia Atlas for Deep Brain Stimulation Planning, In Proc. of MICCAI Workshop on Deep Brain Stimulation Methodological Challenges (DBSMC’14)
  • [Routier et al. 2014], Evaluation of morphometric descriptors of deep brain structures for the automatic classification of patients with Alzheimer’s disease, mild cognitive impairment and elderly controls, In MICCAI challenge on Computer-Aided Diagnosis of Dementia based on structural MRI data (CADDementia)