Image Segmentation and Its Applications Based on the Mumford-Shah Model

Image segmentation is an important topic in computer vision and image processing. As a region-based (global) approach, the Mumford and Shah (MS) model is a powerful and robust segmentation technique as compared to edge-based (local) methods. In this thesis we apply the MS model to two interesting problems: image inpainting and text line detection. We further extend it by proposing a new image segmentation model to overcome some of the difficulties of the original model. As a demonstration of the new model, we apply it to the segmentation of retinal images. The results are better than the state-of-the-art approaches. In image inpainting, the MS model is used to detect and estimate the object boundaries inside the inpainting areas. These boundaries are preserved in the inpainting results. We present a hierarchical segmentation method to detect boundaries of both the main structure and the details. The inpainting result can preserve detailed edges. In text line detection, we use a combination of Gaussian blurring, the MS model, and morphing method. Different from other general text image detection approaches, our method segments text documents without any knowledge of the written texts, so it can detect handwriting text lines of different languages. It can also handle different gaps and overlaps among the text lines. Although the MS model has been used successfully in many applications, its implementation has always been based on some forms of approximation. These approximations are either inefficient computationally or applicable only to some special cases. Our new model consists of only one variable, the segmentation curve, therefore the computation is very efficient. Furthermore, no approximation is required, hence the method can segment objects with complicated intensity distribution. The new model can detect both step and roof edges, and can use different filters to detect objects of different levels of intensity. To show the advantages of the new model, we use a combination of the new model and Gabor filter to detect blood vessels in retinal images. This new model can detect objects with complicated image intensity distribution, and can handle non-uniform illumination cases effectively

Differential geometry methods for biomedical image processing : from segmentation to 2D/3D registration

This thesis establishes a biomedical image analysis framework for the advanced visualization of biological structures. It consists of two important parts: 1) the segmentation of some structures of interest in 3D medical scans, and 2) the registration of patient-specific 3D models with 2D interventional images. Segmenting biological structures results in 3D computational models that are simple to visualize and that can be analyzed quantitatively. Registering a 3D model with interventional images permits to position the 3D model within the physical world. By combining the information from a 3D model and 2D interventional images, the proposed framework can improve the guidance of surgical intervention by reducing the ambiguities inherent to the interpretation of 2D images. Two specific segmentation problems are considered: 1) the segmentation of large structures with low frequency intensity nonuniformity, and 2) the detection of fine curvilinear structures. First, we directed our attention toward the segmentation of relatively large structures with low frequency intensity nonuniformity. Such structures are important in medical imaging since they are commonly encountered in MRI. Also, the nonuniform diffusion of the contrast agent in some other modalities, such as CTA, leads to structures of nonuniform appearance. A level-set method that uses a local-linear region model is defined, and applied to the challenging problem of segmenting brain tissues in MRI. The unique characteristics of the proposed method permit to account for important image nonuniformity implicitly. To the best of our knowledge, this is the first time a region-based level-set model has been used to perform the segmentation of real world MRI brain scans with convincing results. The second segmentation problem considered is the detection of fine curvilinear structures in 3D medical images. Detecting those structures is crucial since they can represent veins, arteries, bronchi or other important tissues. Unfortunately, most currently available curvilinear structure detection filters incur significant signal lost at bifurcations of two structures. This peculiarity limits the performance of all subsequent processes, whether it be understanding an angiography acquisition, computing an accurate tractography, or automatically classifying the image voxels. This thesis presents a new curvilinear structure detection filter that is robust to the presence of X- and Y-junctions. At the same time, it is conceptually simple and deterministic, and allows for an intuitive representation of the structure’s principal directions. Once a 3D computational model is available, it can be used to enhance surgical guidance. A 2D/3D non-rigid method is proposed that brings a 3D centerline model of the coronary arteries into correspondence with bi-plane fluoroscopic angiograms. The registered model is overlaid on top of the interventional angiograms to provide surgical assistance during image-guided chronic total occlusion procedures, which reduces the uncertainty inherent in 2D interventional images. A fully non-rigid registration model is proposed and used to compensate for any local shape discrepancy. This method is based on a variational framework, and uses a simultaneous matching and reconstruction process. With a typical run time of less than 3 seconds, the algorithms are fast enough for interactive applications