Statistical methods for out-of-plane ultrasound transducer motion estimation

Freehand 3D ultrasound imaging usually involves moving a conventional tracked 2D ultrasound probe over a subject and combining the images into a volume to be interpreted for medical purposes. Tracking devices can be cumbersome; thus, there is interest in inferring the trajectory of the transducer based on the images themselves. This thesis focuses on new methods for the recovery of the out-of-plane component of the transducer trajectory using the predictive relationship between the elevational decorrelation of ultrasound speckle patterns and transducer displacement. To resolve the directional ambiguities associated with this approach, combinatorial optimisation techniques and robust statistics are combined to recover non-monotonic motion and frame intersections. In order to account for the variability of the sample correlation coefficient between corresponding image patches of fully developed speckle, a new probabilistic speckle decorrelation model is developed. This model can be used to quantify the uncertainty of any displacement estimate, thereby facilitating the use of a new maximum likelihood out-of-plane trajectory estimation approach which fully exploits the information available from multiple redundant and noisy correlation measurements collected in imagery of fully developed speckle. To generalise the applicability of these methods to the case of imagery of real tissue, a new data-driven method is proposed for locally estimating elevational correlation length based on statistical features collected within the image plane. In this approach, the relationship between the image features and local elevational correlation length is learned by sparse Gaussian process regression using a training set of synthetic ultrasound image sequences. The synthetic imagery used for learning is created via a new statistical model for the spatial distribution of ultrasound scatterers which maps realisations of a 1D generalised Poisson point process to a 3D Hilbert space-filling curve. In experiments with imagery of animal tissue, the learning-based approach is shown to give distance estimates more accurate than those obtained using a speckle detection filter and comparable to the state-of-the-art heuristic method. Remaining modelling imperfections are accounted for by a new iterative algorithm which extends the proposed maximum likelihood measurement fusion approach. In this algorithm, probabilistic measurement fusion and measurement selection steps based on statistical hypothesis testing alternate in order to establish a trajectory estimate based on measurements which agree with each other. This approach succeeds in avoiding distance under-estimates arising from image structures exhibiting significant but uninformative correlation over long distances.