A Bayesian framework for joint morphometry of surface and curve meshes in multi-object complexes

• Published in: Medical image analysis Vol. 35; pp. 458 - 474
• Main Authors: Gori, Pietro, Colliot, Olivier, Marrakchi-Kacem, Linda, Worbe, Yulia, Poupon, Cyril, Hartmann, Andreas, Ayache, Nicholas, Durrleman, Stanley
• Format: Journal Article
• Language: English
• Published: Netherlands Elsevier B.V 01.01.2017; Elsevier BV; Elsevier
• Subjects: Algorithms; Bayes Theorem; Bayesian; Bayesian analysis; Case-Control Studies; Complex; Computer graphics; Computer Science; Conditioning; Cortex; Covariance matrix; Deformation; Fiber bundle; Humans; Mathematical models; Medical Imaging; Morphometry; Multi-object; Normal Distribution; Parameter estimation; Physical characteristics; Probability density functions; Shape; Software; Software packages; Substantia alba; Tourette Syndrome - diagnostic imaging; Tourette Syndrome - pathology; Varifolds; White Matter - diagnostic imaging; White Matter - pathology; Atlas; Shape; Varifolds; Multi-object; Bayesian; Fiber bundle; Morphometry; Complex; varifolds; multi - object; shape; atlas; complex; fiber bundle; morphometry
• ISSN: 1361-8415; 1361-8423; 1361-8423
• DOI: 10.1016/j.media.2016.08.011

•Bayesian framework to embed atlas constructions of multi-object shape complexes.•Trade-off parameters between data-terms and regularity are automatically estimated.•Well-conditioned covariance matrix of the deformation parameters.•Shape complexes composed of curves and surfaces modeled as Gaussian random varifolds.•Extension to a multi-population atlas construction. [Display omitted] We present a Bayesian framework for atlas construction of multi-object shape complexes comprised of both surface and curve meshes. It is general and can be applied to any parametric deformation framework and to all shape models with which it is possible to define probability density functions (PDF). Here, both curve and surface meshes are modelled as Gaussian random varifolds, using a finite-dimensional approximation space on which PDFs can be defined. Using this framework, we can automatically estimate the parameters balancing data-terms and deformation regularity, which previously required user tuning. Moreover, it is also possible to estimate a well-conditioned covariance matrix of the deformation parameters. We also extend the proposed framework to data-sets with multiple group labels. Groups share the same template and their deformation parameters are modelled with different distributions. We can statistically compare the groups’distributions since they are defined on the same space. We test our algorithm on 20 Gilles de la Tourette patients and 20 control subjects, using three sub-cortical regions and their incident white matter fiber bundles. We compare their morphological characteristics and variations using a single diffeomorphism in the ambient space. The proposed method will be integrated with the Deformetrica software package, publicly available at www.deformetrica.org.