Visual analytics methods for shape analysis of biomedical images exemplified on rodent skull morphology

In morphometrics and its application fields like medicine and biology experts are interested in causal relations of variation in organismic shape to phylogenetic, ecological, geographical, epidemiological or disease factors - or put more succinctly by Fred L. Bookstein, morphometrics is "the study of covariances of biological form". In order to reveal causes for shape variability, targeted statistical analysis correlating shape features against external and internal factors is necessary but due to the complexity of the problem often not feasible in an automated way. Therefore, a visual analytics approach is proposed in this thesis that couples interactive visualizations with automated statistical analyses in order to stimulate generation and qualitative assessment of hypotheses on relevant shape features and their potentially affecting factors. To this end long established morphometric techniques are combined with recent shape modeling approaches from geometry processing and medical imaging, leading to novel visual analytics methods for shape analysis. When used in concert these methods facilitate targeted analysis of characteristic shape differences between groups, co-variation between different structures on the same anatomy and correlation of shape to extrinsic attributes. Here a special focus is put on accurate modeling and interactive rendering of image deformations at high spatial resolution, because that allows for faithful representation and communication of diminutive shape features, large shape differences and volumetric structures. The utility of the presented methods is demonstrated in case studies conducted together with a collaborating morphometrics expert. As exemplary model structure serves the rodent skull and its mandible that are assessed via computed tomography scans

Singular geodesic coordinates for representing diffeomorphic maps in computational anatomy, with application to the morphometry of early Alzheimer's disease in the medial temporal lobe

In this work we develop novel algorithms for building one to one correspondences between anatomical forms by providing a sparse representation of dense registration information. These sparse parameterizations of complex high dimensional data allow robustness in the face of noise and anomalies, and a platform for inference that is effective in the face of multiple comparisons. We review background in the theory of generating smooth, invertible transformations (the diffeomorphism group), and build our parameterization as a function supported on surfaces bounding anatomical structures of interest. We show how dimensionality can be reduced even further and still provide a rich family of mappings using principal component analysis or Laplace Beltrami eigenfunctions supported on the surface. We develop algorithms for surface matching and image matching within this model, and demonstrate the desired robustness by working with published large neuroimaging datasets that include many low quality examples. Finally we turn to addressing challenges associated with some specific data types: images with multiple labels, and longitudinal data. We use the mapping tools developed to draw conclusions about the progression of early Alzheimer's disease in the medial temporal lobe

Proceedings of the Second International Workshop on Mathematical Foundations of Computational Anatomy (MFCA'08) - Geometrical and Statistical Methods for Modelling Biological Shape Variability

International audienceThe goal of computational anatomy is to analyze and to statistically model the anatomy of organs in different subjects. Computational anatomic methods are generally based on the extraction of anatomical features or manifolds which are then statistically analyzed, often through a non-linear registration. There are nowadays a growing number of methods that can faithfully deal with the underlying biomechanical behavior of intra-subject deformations. However, it is more difficult to relate the anatomies of different subjects. In the absence of any justified physical model, diffeomorphisms provide a general mathematical framework that enforce topological consistency. Working with such infinite dimensional space raises some deep computational and mathematical problems, in particular for doing statistics. Likewise, modeling the variability of surfaces leads to rely on shape spaces that are much more complex than for curves. To cope with these, different methodological and computational frameworks have been proposed (e.g. smooth left-invariant metrics, focus on well-behaved subspaces of diffeomorphisms, modeling surfaces using courants, etc.) The goal of the Mathematical Foundations of Computational Anatomy (MFCA) workshop is to foster the interactions between the mathematical community around shapes and the MICCAI community around 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 aims at being a forum for the exchange of the theoretical ideas and 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 very successful first edition of this workshop in 2006 (see http://www.inria.fr/sophia/asclepios/events/MFCA06/), the second edition was held in New-York on September 6, in conjunction with MICCAI 2008. 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. 34 submissions were received, among which 9 were accepted to MICCAI and had to be withdrawn from the workshop. Each of the remaining 25 paper was reviewed by three members of the program committee. To guaranty a high level program, 16 papers only were selected