Real-Time Segmentation of 4D Ultrasound by Active Geometric Functions

Four-dimensional ultrasound based on matrix phased array transducers can capture the complex 4D cardiac motion in a complete and real-time fashion. However, the large amount of information residing in 4D ultrasound scans and novel applications under interventional settings pose a big challenge in efficiency for workflow and computer-aided diagnostic algorithms such as segmentation. In this context, a novel formulation framework of the minimal surface problem, called active geometric functions (AGF), is proposed to reach truly real-time performance in segmenting 4D ultrasound data. A specific instance of AGF based on finite element modeling and Hermite surface descriptors was implemented and evaluated on 35 4D ultrasound data sets with a total of 425 time frames. Quantitative comparison to manual tracing showed that the proposed method provides LV contours close to manual segmentation and that the discrepancy was comparable to inter-observer tracing variability. The ability of such realtime segmentation will not only facilitate the diagnoses and workflow, but also enables novel applications such as interventional guidance and interactive image acquisition with online segmentation

Mathematical Approaches for Image Enhancement Problems

This thesis develops novel techniques that can solve some image enhancement problems using theoretically and technically proven and very useful mathematical tools to image processing such as wavelet transforms, partial differential equations, and variational models. Three subtopics are mainly covered. First, color image denoising framework is introduced to achieve high quality denoising results by considering correlations between color components while existing denoising approaches can be plugged in flexibly. Second, a new and efficient framework for image contrast and color enhancement in the compressed wavelet domain is proposed. The proposed approach is capable of enhancing both global and local contrast and brightness as well as preserving color consistency. The framework does not require inverse transform for image enhancement since linear scale factors are directly applied to both scaling and wavelet coefficients in the compressed domain, which results in high computational efficiency. Also contaminated noise in the image can be efficiently reduced by introducing wavelet shrinkage terms adaptively in different scales. The proposed method is able to enhance a wavelet-coded image computationally efficiently with high image quality and less noise or other artifact. The experimental results show that the proposed method produces encouraging results both visually and numerically compared to some existing approaches. Finally, image inpainting problem is discussed. Literature review, psychological analysis, and challenges on image inpainting problem and related topics are described. An inpainting algorithm using energy minimization and texture mapping is proposed. Mumford-Shah energy minimization model detects and preserves edges in the inpainting domain by detecting both the main structure and the detailed edges. This approach utilizes faster hierarchical level set method and guarantees convergence independent of initial conditions. The estimated segmentation results in the inpainting domain are stored in segmentation map, which is referred by a texture mapping algorithm for filling textured regions. We also propose an inpainting algorithm using wavelet transform that can expect better global structure estimation of the unknown region in addition to shape and texture properties since wavelet transforms have been used for various image analysis problems due to its nice multi-resolution properties and decoupling characteristics