Partial Differential Equation Based Methods in Medical Image Processing

This dissertation, "Partial Differential Equation Based Methods in Medical Image Processing" by Kwok-wing, Anthony, Sum, 岑國榮, was obtained from The University of Hong Kong (Pokfulam, Hong Kong) and is being sold pursuant to Creative Commons: Attribution 3.0 Hong Kong License. The content of this dissertation has not been altered in any way. We have altered the formatting in order to facilitate the ease of printing and reading of the dissertation. All rights not granted by the above license are retained by the author. Abstract: Abstract of thesis entitled Partial Di(R)erential Equation Based Methods in Medical Image Processing Submitted by Anthony Kwok Wing SUM for the degree of Doctor of Philosophy at The University of Hong Kong in August 2007 Medical image analysis is essential for clinical diagnosis and surgical planning. To cope with the rapid development of modern imaging technologies, there is a continuingneedforadvancedimageprocessingtechniquestoimproveimagequality and automate the analytical processes. The two most important and fundamental image processing techniques required for fully utilizing and e(R)ectively interpreting the acquired images are image segmentation and image ltering. They play an indispensableroleintheentiremedicalimageanalysisprocess. Inthisthesis, image segmentation and ltering methods using partial di(R)erential equation (PDE) are studied and explored. iiIn daily clinical practice, physicians are required to identify anatomical struc- tures from a large number of medical images. This identication process can be aidedbyimagesegmentationtechniques. Inthisthesis, newdevelopmentsinactive contour models are introduced for image segmentation. First, parametric active contoursaredesirabletoextractobjectswithaconnedboundary. Arobustpara- metric active contour model with a novel external force, namely boundary vector eld (BVF), is proposed. This new model is shown to be more ecient than other existing parametric active contour models in terms of ease of initialization, extrac- tion capability and speed. Second, geometric active contour models are found to be well suited for extracting topologically complex objects such as vessels in an- giograms. However, angiograms and other medical images commonly su(R)er from a nonuniform illumination artifact. This artifact induces serious problem in object extraction during image segmentation. Thus, a novel segmentation scheme is pro- posed based on level set methods and incorporating local contrast information in the formulation. This scheme improves the extraction outcomes even if the image su(R)ers from nonuniform illuminations artifacts. Di(R)erent imaging modalities and imaging environments may generate di(R)erent levels of noise during the data acquisition phase. Image ltering is therefore an essential technique for reducing the noise level and improving the visual quality of an image. Anisotropic di(R)usion is a PDE based ltering method, which has found useful practical applications since its introduction. The kernel of an anisotropic iiidi(R)usionmodelisthedi(R)usioncoecient, whichcharacterizestheoverallbehavior of the entire model. In this study, a new class of anisotropic di(R)usion model is formulated and its outstanding performance is demonstrated with experimental results. Itisshownthatbothsignal-to-noise ratio andvisualqualityofthe ltered images using the new di(R)usion model are improved. In summary, several creative and innovative developments of low level image processing techniques are reported in the thesis. These low level techniques are a critical requirement for advanced high level image analysis procedures, and are indispensable for the automation of many medical image analysis tasks. An abstract of exactly 434 words iv DOI: 10.5353/th_b3895862 Subjects: Differential equations, Partial Diagnostic imaging - Mathematical models Image processing - Mathematics