Bridge Simulation and Metric Estimation on Landmark Manifolds

We present an inference algorithm and connected Monte Carlo based estimation procedures for metric estimation from landmark configurations distributed according to the transition distribution of a Riemannian Brownian motion arising from the Large Deformation Diffeomorphic Metric Mapping (LDDMM) metric. The distribution possesses properties similar to the regular Euclidean normal distribution but its transition density is governed by a high-dimensional PDE with no closed-form solution in the nonlinear case. We show how the density can be numerically approximated by Monte Carlo sampling of conditioned Brownian bridges, and we use this to estimate parameters of the LDDMM kernel and thus the metric structure by maximum likelihood

Dynamical models and machine learning for supervised segmentation

This thesis is concerned with the problem of how to outline regions of interest in medical images, when the boundaries are weak or ambiguous and the region shapes are irregular. The focus on machine learning and interactivity leads to a common theme of the need to balance conflicting requirements. First, any machine learning method must strike a balance between how much it can learn and how well it generalises. Second, interactive methods must balance minimal user demand with maximal user control. To address the problem of weak boundaries,methods of supervised texture classification are investigated that do not use explicit texture features. These methods enable prior knowledge about the image to benefit any segmentation framework. A chosen dynamic contour model, based on probabilistic boundary tracking, combines these image priors with efficient modes of interaction. We show the benefits of the texture classifiers over intensity and gradient-based image models, in both classification and boundary extraction. To address the problem of irregular region shape, we devise a new type of statistical shape model (SSM) that does not use explicit boundary features or assume high-level similarity between region shapes. First, the models are used for shape discrimination, to constrain any segmentation framework by way of regularisation. Second, the SSMs are used for shape generation, allowing probabilistic segmentation frameworks to draw shapes from a prior distribution. The generative models also include novel methods to constrain shape generation according to information from both the image and user interactions. The shape models are first evaluated in terms of discrimination capability, and shown to out-perform other shape descriptors. Experiments also show that the shape models can benefit a standard type of segmentation algorithm by providing shape regularisers. We finally show how to exploit the shape models in supervised segmentation frameworks, and evaluate their benefits in user trials

Directional Estimation for Robotic Beating Heart Surgery

In robotic beating heart surgery, a remote-controlled robot can be used to carry out the operation while automatically canceling out the heart motion. The surgeon controlling the robot is shown a stabilized view of the heart. First, we consider the use of directional statistics for estimation of the phase of the heartbeat. Second, we deal with reconstruction of a moving and deformable surface. Third, we address the question of obtaining a stabilized image of the heart

The determination of the rotational state of celestial bodies

Determination of the rotation of a celestial body using the imaging from orbit; here the applied rotational models and the developed technique are presented. The applications for the determination of the rotational state of Titan using data from Cassini and the simulation of the rotation experiment for the BepiColombo Mission to Mercury are also reported

The determination of the rotational state of celestial bodies

Determination of the rotation of a celestial body using the imaging from orbit; here the applied rotational models and the developed technique are presented. The applications for the determination of the rotational state of Titan using data from Cassini and the simulation of the rotation experiment for the BepiColombo Mission to Mercury are also reported