Variational Methods for Medical Ultrasound Imaging - Tenbrinck, Daniel (Friedrich-Alexander-Universität Erlangen-Nürnberg, 2013)
This thesis is focused on variational methods for fully-automatic processing and analysis of medical ultrasound images. In particular, the e↵ect of appropriate data modeling in the presence of non-Gaussian noise is investigated for typical computer vision tasks. Novel methods for segmentation and motion estimation of medical ultrasound images are developed and evaluated qualitatively and quantitatively on both synthetic and real patient data. The first part of the thesis is dedicated to the problem of low-level segmentation. Two di↵erent segmentation concepts are introduced. On the one hand, segmentation is formulated as a statistically motivated inverse problem based on Bayesian modeling. Using recent results from global convex relaxation, a variational region-based segmentation framework is proposed. This framework generalizes popular approaches from the literature and o↵ers great flexibility for segmentation of medical images. On the other hand, the concept of level set methods is elaborated to perform segmentation based on the results of a discriminant analysis of medical ultrasound images. The proposed method is compared to the popular Chan-Vese segmentation method. In the second part of the thesis, the concept of shape modeling and shape analysis is described to perform high-level segmentation of medical ultrasound images. Motivated by structural artifacts in the data, e.g., shadowing e↵ects, the latter two segmentation methods are extended by a shape prior based on Legendre moments. Ecient numerical schemes for encoding and reconstruction of shapes are discussed and the proposed highlevel segmentation methods are compared to their respective low-level variants. The last part of the thesis deals with the challenge of motion estimation in medical ultrasound imaging. A broad overview on optical flow methods is given and typical assumptions and models are discussed. The inapplicability of the popular intensity constancy constraint is shown for the special case of images perturbed by multiplicative noise both mathematically and experimentally. Based on the idea of modeling image intensities as random variables, a novel data constraint based on local statistics is proposed and their validity is proven. The incorporation of this constraint into a variational model for optical flow estimation leads to a novel method which outperforms state-of-the-art methods from the literature on medical ultrasound images. This thesis aims to give a balanced view on the di↵erent stages involved in solving computer vision tasks in medical imaging: Starting from modeling problems, to their analysis and ecient numerical realization, to their final application and adaption to real world conditions.<br
Keywords: Image Processing; Medical Image Analysis; Denoising; Segmentation; Motion Estimation; Variational Methods; Variational Regularization; Optical Flow; Bayesian Modeling; Expectation-Maximization Algorithm; Noise Modeling; Additive Gaussian Noise; Rayleigh Noise; Ultrasound Speckle Noise; Generalized Mumford-Shah Formulation; Chan-Vese Algorithm; Medical Ultrasound Imaging; Echocardiography