Trees on Geometrical Deformations to Model the Statistical Variability of Organs in Medical Images

In medical image analysis, geometrical deformations are used to model intersubject variability. In orthopaedic applications, the geometrical variability is usually observable across anatomical scales. For instance, anatomical differences between mandible bones of different patients can be found on a coarse scale, between the entire left or right side, or on a fine scale, between teeth. Each level of granularity has specific regions of interest in clinical applications. The challenge is to connect the geometrical deformations to clinical regions across scales. In this thesis, we present this connection by introducing structured diffeomorphic registration. At the core of our method is the parametrization of geometrical deformations with trees of locally affine transformations describing intersubject variability across scales. In a second step, we statistically model the deformation parameters in a population by formulating a generative statistical model. This model allows us to incorporate deformation statistics as a prior in a Bayesian setting and it enables us to extend the classical sequential coarse to fine registration to a simultaneous optimization of all scales. This kind of group level prior is natural in a polyaffine context, if we assume one configuration of regions that describes an entire group of images with varying transformations for each region. We validate our approach on a wide range of orthopaedic applications: population-based implant design, biomechanical simulations and allograft selection for femur and mandibles. The improved intelligibility for clinicians and accuracy makes our method a good candidate for clinical use.