3D shape matching and registration : a probabilistic perspective

Dense correspondence is a key area in computer vision and medical image analysis. It has applications in registration and shape analysis. In this thesis, we develop a technique to recover dense correspondences between the surfaces of neuroanatomical objects over heterogeneous populations of individuals. We recover dense correspondences based on 3D shape matching. In this thesis, the 3D shape matching problem is formulated under the framework of Markov Random Fields (MRFs). We represent the surfaces of neuroanatomical objects as genus zero voxel-based meshes. The surface meshes are projected into a Markov random field space. The projection carries both geometric and topological information in terms of Gaussian curvature and mesh neighbourhood from the original space to the random field space. Gaussian curvature is projected to the nodes of the MRF, and the mesh neighbourhood structure is projected to the edges. 3D shape matching between two surface meshes is then performed by solving an energy function minimisation problem formulated with MRFs. The outcome of the 3D shape matching is dense point-to-point correspondences. However, the minimisation of the energy function is NP hard. In this thesis, we use belief propagation to perform the probabilistic inference for 3D shape matching. A sparse update loopy belief propagation algorithm adapted to the 3D shape matching is proposed to obtain an approximate global solution for the 3D shape matching problem. The sparse update loopy belief propagation algorithm demonstrates significant efficiency gain compared to standard belief propagation. The computational complexity and convergence property analysis for the sparse update loopy belief propagation algorithm are also conducted in the thesis. We also investigate randomised algorithms to minimise the energy function. In order to enhance the shape matching rate and increase the inlier support set, we propose a novel clamping technique. The clamping technique is realized by combining the loopy belief propagation message updating rule with the feedback from 3D rigid body registration. By using this clamping technique, the correct shape matching rate is increased significantly. Finally, we investigate 3D shape registration techniques based on the 3D shape matching result. Based on the point-to-point dense correspondences obtained from the 3D shape matching, a three-point based transformation estimation technique is combined with the RANdom SAmple Consensus (RANSAC) algorithm to obtain the inlier support set. The global registration approach is purely dependent on point-wise correspondences between two meshed surfaces. It has the advantage that the need for orientation initialisation is eliminated and that all shapes of spherical topology. The comparison of our MRF based 3D registration approach with a state-of-the-art registration algorithm, the first order ellipsoid template, is conducted in the experiments. These show dense correspondence for pairs of hippocampi from two different data sets, each of around 20 60+ year old healthy individuals

Strukturální podklady kognitivního deficitu v zobrazování magnetické rezonance.

Předkládaná dizertační práce se ve své hlavní části zabývá možnostmi detekce strukturálních a difuzních změn v MR zobrazení u pacientů s kognitivním deficitem. V širším kontextu je nejprve zmíněn podklad klinických změn a nálezů při neurozobrazení u pacientů s demencí, a to se zvláštním zaměřením na Alzheimerovu chorobu (ACh) a její diferenciální diagnostiku. Druhá část práce obsahuje čtyři experimentální studie v rámci našeho výzkumu. Hlavním cílem prvních dvou studií bylo získání strukturální a mikrostrukturální informace o neurodegenerativních procesech charakteristických pro ACh - na globální i regionální úrovni. Pro tento účel bylo použito několik komplementárních přístupů se zaměřením především na evaluaci šedé, a následně i bílé hmoty mozku. V následujících částech jsme se zaměřili na popis kontextu mikrostrukturálních změn bílé hmoty u normotenzního hydrocefalu (NPH) a charakteristických vzorců dezintegrace bílé hmoty u epilepsií temporálního laloku (TLE). Nejdůležitějším závěrem, který lze vyvodit z našich studií je, že strukturální a difuzní zobrazování se ukázalo jako užitečné při identifikaci regionálně specifické a disproporcionální ztráty objemu mozku a mikrostruktury u některých patologických procesů, které jsou základem kognitivního zhoršení. Použití několika různých morfometrických...Structural and diffusion imaging patterns that can be evaluated using MRI in patients with cognitive deficits are the central theme of the proposed work. First, the clinical and neuroimaging background of dementias has been reviewed in a broader context, with a special focus on Alzheimer's disease (AD) and differential diagnoses. The second part of this thesis contains four consecutive experimental studies. The primary objective of the first two studies was to obtain structural and microstructural information on the neurodegenerative processes characteristic for AD on global and regional levels. For this purpose, several complementary approaches were used and the focus was shifted from grey to white matter (GM/WM). The following two studies focused on the differential context of WM microstructural alterations in normal pressure hydrocephalus (NPH) and distinctive patterns of WM disintegrity in temporal lobe epilepsy (TLE). The most important conclusion of our studies is that structural and diffusion imaging proved to be useful in identifying regionally specific and disproportionate loss of brain volume and microstructure in several pathological processes underlying cognitive deterioration. The use of distinctive morphometric methods yielded complementary information on AD-related atrophy patterns,...Department of Neurosurgery and Neurooncology First Faculty of Medicine and Central Military HospitalNeurochirurgická a neuroonkologická klinika 1. LF UK a ÚVN1. lékařská fakultaFirst Faculty of Medicin

HUMAN BRAIN WHITE MATTER ANALYSIS USING TRACTOGRAPHY —AN ATLAS-BASED APPROACH

The human brain is connected via a vastly complex network of white matter fiber pathways. However, this structural connectivity information cannot be obtained from conventional MRI, in which much of white matter appears homogeneous. Diffusion tensor imaging can estimate fiber orientation by measuring the anisotropy of water diffusion. Using tractography, the brain connectivity can be studied non-invasively. Past tractography studies have shown that the cores of prominent white matter tracts can be faithfully reconstructed. Superimposing the tract coordinates on various MR images, MR metrics can be quantified in a tract-specific manner. However, tractography results are often contaminated by partial volume effect and imaging noise. Particularly, tractography often fails under white matter pathological conditions, which render tract-specific analysis impractical. In order to address these issues, we introduced an atlas-based approach. Four novel atlas-based approaches were included in this data analysis framework. First, statistical templates of major white matter tracts were created using a DTI database of normal subjects. The statistical white matter tract templates can serve two purposes. First, the statistical template can be used as a reference to detect abnormal white matter anatomy in neurodegenerative diseases. Second, the statistical template can be applied to individual patient data for automated white matter parcellation and tract-specific quantification. In the second approach, the trajectory of white matter fiber bundles was used to estimate the cortical regions associated with specific tracts of interest. Using this approach, cortical regions were reproducibly identified on the population-averaged cortical maps of brain connectivity. Third, we improved the accuracy of the population-based tract analysis by incorporating a highly elastic image transformation technique, called Large Deformation Diffeomorphic Metric Mapping (LDDMM). As a testament to the power of this algorithm, we successfully applied tract-specific analysis on Alzheimer’s patients. The last approach was to analyze the brain cortical connection networks using automatic fiber tracking. A tracking pipeline was built by combining White Matter Parcellation Map (WMPM), brute-force tractography and topology-preserving image transformation LDDMM. This novel tracking pipeline was applied on patient group with Alzheimer’s disease. The connectivity networks of Alzheimer’s patients were compared with age-matched controls using multivariate pattern classification

Proceedings of the fifth international workshop on Mathematical Foundations of Computational Anatomy (MFCA 2015)

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 20061, the second edition in New-York in 20082, the third edition in Toronto in 20113, the forth edition in Nagoya Japan on September 22 20134, the fifth edition was held in Munich on October 9 20155.Contributions were solicited in Riemannian, sub-Riemannian and group theoretical methods, advanced statistics on deformations and shapes, metrics for computational anatomy, statistics of surfaces, time-evolving geometric processes, stratified spaces, optimal transport, approximation methods in statistical learning and related subjects. Among the submitted papers, 14 were selected andorganized in 4 oral sessions

Parallel transport in diffeomorphisms distinguishes the time-dependent pattern of hippocampal surface deformation due to healthy aging and the dementia of the Alzheimer's type

10.1016/j.neuroimage.2007.11.041NeuroImage40168-76NEIM