Anatomical Image Series Analysis in the Computational Anatomy Random Orbit Model

Serially acquired medical imagery plays an important role in the computational study of human anatomy. In this work, we describe the development of novel algorithms set in the large deformation diffeomorphic metric mapping framework for analyzing serially acquired imagery of two general types: spatial image series and temporal image series. In the former case, a critical step in the analysis of neural connectivity from serially-sectioned brain histology data is the reconstruction of spatially distorted image volumes and registration into a common coordinate space. In the latter case, computational methods are required for building low dimensional representations of the infinite dimensional shape space standard to computational anatomy. Here, we review the vast body of work related to volume reconstruction and atlas-mapping of serially-sectioned data as well as diffeomorphic methods for longitudinal data and we position our work relative to these in the context of the computational anatomy random orbit model. We show how these two problems are embedded as extensions to the classic random orbit model and use it to both enforce diffeomorphic conditions and analyze the distance metric associated to diffeomorphisms. We apply our new algorithms to histology and MRI datasets to study the structure, connectivity, and pathological degeneration of the brain

Proceedings of the Fourth International Workshop on Mathematical Foundations of Computational Anatomy - Geometrical and Statistical Methods for Biological Shape Variability Modeling (MFCA 2013), Nagoya, Japan

International audienceComputational anatomy is an emerging discipline at the interface of geometry, statistics and image analysis which aims at modeling and analyzing the biological shape of tissues and organs. The goal is to estimate representative organ anatomies across diseases, populations, species or ages, to model the organ development across time (growth or aging), to establish their variability, and to correlate this variability information with other functional, genetic or structural information. The Mathematical Foundations of Computational Anatomy (MFCA) workshop aims at fostering the interactions between the mathematical community around shapes and the MICCAI community in view of computational anatomy applications. It targets more particularly researchers investigating the combination of statistical and geometrical aspects in the modeling of the variability of biological shapes. The workshop is a forum for the exchange of the theoretical ideas and aims at being a source of inspiration for new methodological developments in computational anatomy. A special emphasis is put on theoretical developments, applications and results being welcomed as illustrations. Following the first edition of this workshop in 2006, second edition in New-York in 2008, the third edition in Toronto in 2011, the forth edition was held in Nagoya Japan on September 22 2013

Combining Shape and Learning for Medical Image Analysis

Automatic methods with the ability to make accurate, fast and robust assessments of medical images are highly requested in medical research and clinical care. Excellent automatic algorithms are characterized by speed, allowing for scalability, and an accuracy comparable to an expert radiologist. They should produce morphologically and physiologically plausible results while generalizing well to unseen and rare anatomies. Still, there are few, if any, applications where today\u27s automatic methods succeed to meet these requirements.\ua0The focus of this thesis is two tasks essential for enabling automatic medical image assessment, medical image segmentation and medical image registration. Medical image registration, i.e. aligning two separate medical images, is used as an important sub-routine in many image analysis tools as well as in image fusion, disease progress tracking and population statistics. Medical image segmentation, i.e. delineating anatomically or physiologically meaningful boundaries, is used for both diagnostic and visualization purposes in a wide range of applications, e.g. in computer-aided diagnosis and surgery.The thesis comprises five papers addressing medical image registration and/or segmentation for a diverse set of applications and modalities, i.e. pericardium segmentation in cardiac CTA, brain region parcellation in MRI, multi-organ segmentation in CT, heart ventricle segmentation in cardiac ultrasound and tau PET registration. The five papers propose competitive registration and segmentation methods enabled by machine learning techniques, e.g. random decision forests and convolutional neural networks, as well as by shape modelling, e.g. multi-atlas segmentation and conditional random fields

On variational solutions for whole brain serial-section histology using a Sobolev prior in the computational anatomy random orbit model

This paper presents a variational framework for dense diffeomorphic atlas-mapping onto high-throughput histology stacks at the 20 mum meso-scale. The observed sections are modelled as Gaussian random fields conditioned on a sequence of unknown section by section rigid motions and unknown diffeomorphic transformation of a three-dimensional atlas. To regularize over the high-dimensionality of our parameter space (which is a product space of the rigid motion dimensions and the diffeomorphism dimensions), the histology stacks are modelled as arising from a first order Sobolev space smoothness prior. We show that the joint maximum a-posteriori, penalized-likelihood estimator of our high dimensional parameter space emerges as a joint optimization interleaving rigid motion estimation for histology restacking and large deformation diffeomorphic metric mapping to atlas coordinates. We show that joint optimization in this parameter space solves the classical curvature non-identifiability of the histology stacking problem. The algorithms are demonstrated on a collection of whole-brain histological image stacks from the Mouse Brain Architecture Project

Proceedings of the Third International Workshop on Mathematical Foundations of Computational Anatomy - Geometrical and Statistical Methods for Modelling Biological Shape Variability

International audienceComputational anatomy is an emerging discipline at the interface of geometry, statistics and image analysis which aims at modeling and analyzing the biological shape of tissues and organs. The goal is to estimate representative organ anatomies across diseases, populations, species or ages, to model the organ development across time (growth or aging), to establish their variability, and to correlate this variability information with other functional, genetic or structural information. The Mathematical Foundations of Computational Anatomy (MFCA) workshop aims at fostering the interactions between the mathematical community around shapes and the MICCAI community in view of computational anatomy applications. It targets more particularly researchers investigating the combination of statistical and geometrical aspects in the modeling of the variability of biological shapes. The workshop is a forum for the exchange of the theoretical ideas and aims at being a source of inspiration for new methodological developments in computational anatomy. A special emphasis is put on theoretical developments, applications and results being welcomed as illustrations. Following the successful rst edition of this workshop in 20061 and second edition in New-York in 20082, the third edition was held in Toronto on September 22 20113. Contributions were solicited in Riemannian and group theoretical methods, geometric measurements of the anatomy, advanced statistics on deformations and shapes, metrics for computational anatomy, statistics of surfaces, modeling of growth and longitudinal shape changes. 22 submissions were reviewed by three members of the program committee. To guaranty a high level program, 11 papers only were selected for oral presentation in 4 sessions. Two of these sessions regroups classical themes of the workshop: statistics on manifolds and diff eomorphisms for surface or longitudinal registration. One session gathers papers exploring new mathematical structures beyond Riemannian geometry while the last oral session deals with the emerging theme of statistics on graphs and trees. Finally, a poster session of 5 papers addresses more application oriented works on computational anatomy