9 research outputs found

    Segmentation of nerve bundles and ganglia in spine MRI using particle filters

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    14th International Conference, Toronto, Canada, September 18-22, 2011, Proceedings, Part IIIAutomatic segmentation of spinal nerve bundles that originate within the dural sac and exit the spinal canal is important for diagnosis and surgical planning. The variability in intensity, contrast, shape and direction of nerves seen in high resolution myelographic MR images makes segmentation a challenging task. In this paper, we present an automatic tracking method for nerve segmentation based on particle filters. We develop a novel approach to particle representation and dynamics, based on Bรฉzier splines. Moreover, we introduce a robust image likelihood model that enables delineation of nerve bundles and ganglia from the surrounding anatomical structures. We demonstrate accurate and fast nerve tracking and compare it to expert manual segmentation.National Institutes of Health (U.S.) (NAMIC award U54-EB005149)National Science Foundation (U.S.) (CAREER grant 0642971

    Deep convolutional neural networks for segmenting 3D in vivo multiphoton images of vasculature in Alzheimer disease mouse models

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    The health and function of tissue rely on its vasculature network to provide reliable blood perfusion. Volumetric imaging approaches, such as multiphoton microscopy, are able to generate detailed 3D images of blood vessels that could contribute to our understanding of the role of vascular structure in normal physiology and in disease mechanisms. The segmentation of vessels, a core image analysis problem, is a bottleneck that has prevented the systematic comparison of 3D vascular architecture across experimental populations. We explored the use of convolutional neural networks to segment 3D vessels within volumetric in vivo images acquired by multiphoton microscopy. We evaluated different network architectures and machine learning techniques in the context of this segmentation problem. We show that our optimized convolutional neural network architecture, which we call DeepVess, yielded a segmentation accuracy that was better than both the current state-of-the-art and a trained human annotator, while also being orders of magnitude faster. To explore the effects of aging and Alzheimer's disease on capillaries, we applied DeepVess to 3D images of cortical blood vessels in young and old mouse models of Alzheimer's disease and wild type littermates. We found little difference in the distribution of capillary diameter or tortuosity between these groups, but did note a decrease in the number of longer capillary segments (>75ฮผm>75\mu m) in aged animals as compared to young, in both wild type and Alzheimer's disease mouse models.Comment: 34 pages, 9 figure

    A novel statistical cerebrovascular segmentation algorithm with particle swarm optimization

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    AbstractWe present an automatic statistical intensity-based approach to extract the 3D cerebrovascular structure from time-of flight (TOF) magnetic resonance angiography (MRA) data. We use the finite mixture model (FMM) to fit the intensity histogram of the brain image sequence, where the cerebral vascular structure is modeled by a Gaussian distribution function and the other low intensity tissues are modeled by Gaussian and Rayleigh distribution functions. To estimate the parameters of the FMM, we propose an improved particle swarm optimization (PSO) algorithm, which has a disturbing term in speeding updating the formula of PSO to ensure its convergence. We also use the ring shape topology of the particles neighborhood to improve the performance of the algorithm. Computational results on 34 test data show that the proposed method provides accurate segmentation, especially for those blood vessels of small sizes

    ๋ณต๋ถ€ CT์—์„œ ๊ฐ„๊ณผ ํ˜ˆ๊ด€ ๋ถ„ํ•  ๊ธฐ๋ฒ•

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    ํ•™์œ„๋…ผ๋ฌธ(๋ฐ•์‚ฌ)--์„œ์šธ๋Œ€ํ•™๊ต ๋Œ€ํ•™์› :๊ณต๊ณผ๋Œ€ํ•™ ์ปดํ“จํ„ฐ๊ณตํ•™๋ถ€,2020. 2. ์‹ ์˜๊ธธ.๋ณต๋ถ€ ์ „์‚ฐํ™” ๋‹จ์ธต ์ดฌ์˜ (CT) ์˜์ƒ์—์„œ ์ •ํ™•ํ•œ ๊ฐ„ ๋ฐ ํ˜ˆ๊ด€ ๋ถ„ํ• ์€ ์ฒด์  ์ธก์ •, ์น˜๋ฃŒ ๊ณ„ํš ์ˆ˜๋ฆฝ ๋ฐ ์ถ”๊ฐ€์ ์ธ ์ฆ๊ฐ• ํ˜„์‹ค ๊ธฐ๋ฐ˜ ์ˆ˜์ˆ  ๊ฐ€์ด๋“œ์™€ ๊ฐ™์€ ์ปดํ“จํ„ฐ ์ง„๋‹จ ๋ณด์กฐ ์‹œ์Šคํ…œ์„ ๊ตฌ์ถ•ํ•˜๋Š”๋ฐ ํ•„์ˆ˜์ ์ธ ์š”์†Œ์ด๋‹ค. ์ตœ๊ทผ ๋“ค์–ด ์ปจ๋ณผ๋ฃจ์…”๋„ ์ธ๊ณต ์‹ ๊ฒฝ๋ง (CNN) ํ˜•ํƒœ์˜ ๋”ฅ ๋Ÿฌ๋‹์ด ๋งŽ์ด ์ ์šฉ๋˜๋ฉด์„œ ์˜๋ฃŒ ์˜์ƒ ๋ถ„ํ• ์˜ ์„ฑ๋Šฅ์ด ํ–ฅ์ƒ๋˜๊ณ  ์žˆ์ง€๋งŒ, ์‹ค์ œ ์ž„์ƒ์— ์ ์šฉํ•  ์ˆ˜ ์žˆ๋Š” ๋†’์€ ์ผ๋ฐ˜ํ™” ์„ฑ๋Šฅ์„ ์ œ๊ณตํ•˜๊ธฐ๋Š” ์—ฌ์ „ํžˆ ์–ด๋ ต๋‹ค. ๋˜ํ•œ ๋ฌผ์ฒด์˜ ๊ฒฝ๊ณ„๋Š” ์ „ํ†ต์ ์œผ๋กœ ์˜์ƒ ๋ถ„ํ• ์—์„œ ๋งค์šฐ ์ค‘์š”ํ•œ ์š”์†Œ๋กœ ์ด์šฉ๋˜์—ˆ์ง€๋งŒ, CT ์˜์ƒ์—์„œ ๊ฐ„์˜ ๋ถˆ๋ถ„๋ช…ํ•œ ๊ฒฝ๊ณ„๋ฅผ ์ถ”์ถœํ•˜๊ธฐ๊ฐ€ ์–ด๋ ต๊ธฐ ๋•Œ๋ฌธ์— ํ˜„๋Œ€ CNN์—์„œ๋Š” ์ด๋ฅผ ์‚ฌ์šฉํ•˜์ง€ ์•Š๊ณ  ์žˆ๋‹ค. ๊ฐ„ ํ˜ˆ๊ด€ ๋ถ„ํ•  ์ž‘์—…์˜ ๊ฒฝ์šฐ, ๋ณต์žกํ•œ ํ˜ˆ๊ด€ ์˜์ƒ์œผ๋กœ๋ถ€ํ„ฐ ํ•™์Šต ๋ฐ์ดํ„ฐ๋ฅผ ๋งŒ๋“ค๊ธฐ ์–ด๋ ต๊ธฐ ๋•Œ๋ฌธ์— ๋”ฅ ๋Ÿฌ๋‹์„ ์ ์šฉํ•˜๊ธฐ๊ฐ€ ์–ด๋ ต๋‹ค. ๋˜ํ•œ ์–‡์€ ํ˜ˆ๊ด€ ๋ถ€๋ถ„์˜ ์˜์ƒ ๋ฐ๊ธฐ ๋Œ€๋น„๊ฐ€ ์•ฝํ•˜์—ฌ ์›๋ณธ ์˜์ƒ์—์„œ ์‹๋ณ„ํ•˜๊ธฐ๊ฐ€ ๋งค์šฐ ์–ด๋ ต๋‹ค. ๋ณธ ๋…ผ๋ฌธ์—์„œ๋Š” ์œ„ ์–ธ๊ธ‰ํ•œ ๋ฌธ์ œ๋“ค์„ ํ•ด๊ฒฐํ•˜๊ธฐ ์œ„ํ•ด ์ผ๋ฐ˜ํ™” ์„ฑ๋Šฅ์ด ํ–ฅ์ƒ๋œ CNN๊ณผ ์–‡์€ ํ˜ˆ๊ด€์„ ํฌํ•จํ•˜๋Š” ๋ณต์žกํ•œ ๊ฐ„ ํ˜ˆ๊ด€์„ ์ •ํ™•ํ•˜๊ฒŒ ๋ถ„ํ• ํ•˜๋Š” ์•Œ๊ณ ๋ฆฌ์ฆ˜์„ ์ œ์•ˆํ•œ๋‹ค. ๊ฐ„ ๋ถ„ํ•  ์ž‘์—…์—์„œ ์šฐ์ˆ˜ํ•œ ์ผ๋ฐ˜ํ™” ์„ฑ๋Šฅ์„ ๊ฐ–๋Š” CNN์„ ๊ตฌ์ถ•ํ•˜๊ธฐ ์œ„ํ•ด, ๋‚ด๋ถ€์ ์œผ๋กœ ๊ฐ„ ๋ชจ์–‘์„ ์ถ”์ •ํ•˜๋Š” ๋ถ€๋ถ„์ด ํฌํ•จ๋œ ์ž๋™ ์ปจํ…์ŠคํŠธ ์•Œ๊ณ ๋ฆฌ์ฆ˜์„ ์ œ์•ˆํ•œ๋‹ค. ๋˜ํ•œ, CNN์„ ์‚ฌ์šฉํ•œ ํ•™์Šต์— ๊ฒฝ๊ณ„์„ ์˜ ๊ฐœ๋…์ด ์ƒˆ๋กญ๊ฒŒ ์ œ์•ˆ๋œ๋‹ค. ๋ชจํ˜ธํ•œ ๊ฒฝ๊ณ„๋ถ€๊ฐ€ ํฌํ•จ๋˜์–ด ์žˆ์–ด ์ „์ฒด ๊ฒฝ๊ณ„ ์˜์—ญ์„ CNN์— ํ›ˆ๋ จํ•˜๋Š” ๊ฒƒ์€ ๋งค์šฐ ์–ด๋ ต๊ธฐ ๋•Œ๋ฌธ์— ๋ฐ˜๋ณต๋˜๋Š” ํ•™์Šต ๊ณผ์ •์—์„œ ์ธ๊ณต ์‹ ๊ฒฝ๋ง์ด ์Šค์Šค๋กœ ์˜ˆ์ธกํ•œ ํ™•๋ฅ ์—์„œ ๋ถ€์ •ํ™•ํ•˜๊ฒŒ ์ถ”์ •๋œ ๋ถ€๋ถ„์  ๊ฒฝ๊ณ„๋งŒ์„ ์‚ฌ์šฉํ•˜์—ฌ ์ธ๊ณต ์‹ ๊ฒฝ๋ง์„ ํ•™์Šตํ•œ๋‹ค. ์‹คํ—˜์  ๊ฒฐ๊ณผ๋ฅผ ํ†ตํ•ด ์ œ์•ˆ๋œ CNN์ด ๋‹ค๋ฅธ ์ตœ์‹  ๊ธฐ๋ฒ•๋“ค๋ณด๋‹ค ์ •ํ™•๋„๊ฐ€ ์šฐ์ˆ˜ํ•˜๋‹ค๋Š” ๊ฒƒ์„ ๋ณด์ธ๋‹ค. ๋˜ํ•œ, ์ œ์•ˆ๋œ CNN์˜ ์ผ๋ฐ˜ํ™” ์„ฑ๋Šฅ์„ ๊ฒ€์ฆํ•˜๊ธฐ ์œ„ํ•ด ๋‹ค์–‘ํ•œ ์‹คํ—˜์„ ์ˆ˜ํ–‰ํ•œ๋‹ค. ๊ฐ„ ํ˜ˆ๊ด€ ๋ถ„ํ• ์—์„œ๋Š” ๊ฐ„ ๋‚ด๋ถ€์˜ ๊ด€์‹ฌ ์˜์—ญ์„ ์ง€์ •ํ•˜๊ธฐ ์œ„ํ•ด ์•ž์„œ ํš๋“ํ•œ ๊ฐ„ ์˜์—ญ์„ ํ™œ์šฉํ•œ๋‹ค. ์ •ํ™•ํ•œ ๊ฐ„ ํ˜ˆ๊ด€ ๋ถ„ํ• ์„ ์œ„ํ•ด ํ˜ˆ๊ด€ ํ›„๋ณด ์ ๋“ค์„ ์ถ”์ถœํ•˜์—ฌ ์‚ฌ์šฉํ•˜๋Š” ์•Œ๊ณ ๋ฆฌ์ฆ˜์„ ์ œ์•ˆํ•œ๋‹ค. ํ™•์‹คํ•œ ํ›„๋ณด ์ ๋“ค์„ ์–ป๊ธฐ ์œ„ํ•ด, ์‚ผ์ฐจ์› ์˜์ƒ์˜ ์ฐจ์›์„ ๋จผ์ € ์ตœ๋Œ€ ๊ฐ•๋„ ํˆฌ์˜ ๊ธฐ๋ฒ•์„ ํ†ตํ•ด ์ด์ฐจ์›์œผ๋กœ ๋‚ฎ์ถ˜๋‹ค. ์ด์ฐจ์› ์˜์ƒ์—์„œ๋Š” ๋ณต์žกํ•œ ํ˜ˆ๊ด€์˜ ๊ตฌ์กฐ๊ฐ€ ๋ณด๋‹ค ๋‹จ์ˆœํ™”๋  ์ˆ˜ ์žˆ๋‹ค. ์ด์–ด์„œ, ์ด์ฐจ์› ์˜์ƒ์—์„œ ํ˜ˆ๊ด€ ๋ถ„ํ• ์„ ์ˆ˜ํ–‰ํ•˜๊ณ  ํ˜ˆ๊ด€ ํ”ฝ์…€๋“ค์€ ์›๋ž˜์˜ ์‚ผ์ฐจ์› ๊ณต๊ฐ„์ƒ์œผ๋กœ ์—ญ ํˆฌ์˜๋œ๋‹ค. ๋งˆ์ง€๋ง‰์œผ๋กœ, ์ „์ฒด ํ˜ˆ๊ด€์˜ ๋ถ„ํ• ์„ ์œ„ํ•ด ์›๋ณธ ์˜์ƒ๊ณผ ํ˜ˆ๊ด€ ํ›„๋ณด ์ ๋“ค์„ ๋ชจ๋‘ ์‚ฌ์šฉํ•˜๋Š” ์ƒˆ๋กœ์šด ๋ ˆ๋ฒจ ์…‹ ๊ธฐ๋ฐ˜ ์•Œ๊ณ ๋ฆฌ์ฆ˜์„ ์ œ์•ˆํ•œ๋‹ค. ์ œ์•ˆ๋œ ์•Œ๊ณ ๋ฆฌ์ฆ˜์€ ๋ณต์žกํ•œ ๊ตฌ์กฐ๊ฐ€ ๋‹จ์ˆœํ™”๋˜๊ณ  ์–‡์€ ํ˜ˆ๊ด€์ด ๋” ์ž˜ ๋ณด์ด๋Š” ์ด์ฐจ์› ์˜์ƒ์—์„œ ์–ป์€ ํ›„๋ณด ์ ๋“ค์„ ์‚ฌ์šฉํ•˜๊ธฐ ๋•Œ๋ฌธ์— ์–‡์€ ํ˜ˆ๊ด€ ๋ถ„ํ• ์—์„œ ๋†’์€ ์ •ํ™•๋„๋ฅผ ๋ณด์ธ๋‹ค. ์‹คํ—˜์  ๊ฒฐ๊ณผ์— ์˜ํ•˜๋ฉด ์ œ์•ˆ๋œ ์•Œ๊ณ ๋ฆฌ์ฆ˜์€ ์ž˜๋ชป๋œ ์˜์—ญ์˜ ์ถ”์ถœ ์—†์ด ๋‹ค๋ฅธ ๋ ˆ๋ฒจ ์…‹ ๊ธฐ๋ฐ˜ ์•Œ๊ณ ๋ฆฌ์ฆ˜๋“ค๋ณด๋‹ค ์šฐ์ˆ˜ํ•œ ์„ฑ๋Šฅ์„ ๋ณด์ธ๋‹ค. ์ œ์•ˆ๋œ ์•Œ๊ณ ๋ฆฌ์ฆ˜์€ ๊ฐ„๊ณผ ํ˜ˆ๊ด€์„ ๋ถ„ํ• ํ•˜๋Š” ์ƒˆ๋กœ์šด ๋ฐฉ๋ฒ•์„ ์ œ์‹œํ•œ๋‹ค. ์ œ์•ˆ๋œ ์ž๋™ ์ปจํ…์ŠคํŠธ ๊ตฌ์กฐ๋Š” ์‚ฌ๋žŒ์ด ๋””์ž์ธํ•œ ํ•™์Šต ๊ณผ์ •์ด ์ผ๋ฐ˜ํ™” ์„ฑ๋Šฅ์„ ํฌ๊ฒŒ ํ–ฅ์ƒํ•  ์ˆ˜ ์žˆ๋‹ค๋Š” ๊ฒƒ์„ ๋ณด์ธ๋‹ค. ๊ทธ๋ฆฌ๊ณ  ์ œ์•ˆ๋œ ๊ฒฝ๊ณ„์„  ํ•™์Šต ๊ธฐ๋ฒ•์œผ๋กœ CNN์„ ์‚ฌ์šฉํ•œ ์˜์ƒ ๋ถ„ํ• ์˜ ์„ฑ๋Šฅ์„ ํ–ฅ์ƒํ•  ์ˆ˜ ์žˆ์Œ์„ ๋‚ดํฌํ•œ๋‹ค. ๊ฐ„ ํ˜ˆ๊ด€์˜ ๋ถ„ํ• ์€ ์ด์ฐจ์› ์ตœ๋Œ€ ๊ฐ•๋„ ํˆฌ์˜ ๊ธฐ๋ฐ˜ ์ด๋ฏธ์ง€๋กœ๋ถ€ํ„ฐ ํš๋“๋œ ํ˜ˆ๊ด€ ํ›„๋ณด ์ ๋“ค์„ ํ†ตํ•ด ์–‡์€ ํ˜ˆ๊ด€๋“ค์ด ์„ฑ๊ณต์ ์œผ๋กœ ๋ถ„ํ• ๋  ์ˆ˜ ์žˆ์Œ์„ ๋ณด์ธ๋‹ค. ๋ณธ ๋…ผ๋ฌธ์—์„œ ์ œ์•ˆ๋œ ์•Œ๊ณ ๋ฆฌ์ฆ˜์€ ๊ฐ„์˜ ํ•ด๋ถ€ํ•™์  ๋ถ„์„๊ณผ ์ž๋™ํ™”๋œ ์ปดํ“จํ„ฐ ์ง„๋‹จ ๋ณด์กฐ ์‹œ์Šคํ…œ์„ ๊ตฌ์ถ•ํ•˜๋Š” ๋ฐ ๋งค์šฐ ์ค‘์š”ํ•œ ๊ธฐ์ˆ ์ด๋‹ค.Accurate liver and its vessel segmentation on abdominal computed tomography (CT) images is one of the most important prerequisites for computer-aided diagnosis (CAD) systems such as volumetric measurement, treatment planning, and further augmented reality-based surgical guide. In recent years, the application of deep learning in the form of convolutional neural network (CNN) has improved the performance of medical image segmentation, but it is difficult to provide high generalization performance for the actual clinical practice. Furthermore, although the contour features are an important factor in the image segmentation problem, they are hard to be employed on CNN due to many unclear boundaries on the image. In case of a liver vessel segmentation, a deep learning approach is impractical because it is difficult to obtain training data from complex vessel images. Furthermore, thin vessels are hard to be identified in the original image due to weak intensity contrasts and noise. In this dissertation, a CNN with high generalization performance and a contour learning scheme is first proposed for liver segmentation. Secondly, a liver vessel segmentation algorithm is presented that accurately segments even thin vessels. To build a CNN with high generalization performance, the auto-context algorithm is employed. The auto-context algorithm goes through two pipelines: the first predicts the overall area of a liver and the second predicts the final liver using the first prediction as a prior. This process improves generalization performance because the network internally estimates shape-prior. In addition to the auto-context, a contour learning method is proposed that uses only sparse contours rather than the entire contour. Sparse contours are obtained and trained by using only the mispredicted part of the network's final prediction. Experimental studies show that the proposed network is superior in accuracy to other modern networks. Multiple N-fold tests are also performed to verify the generalization performance. An algorithm for accurate liver vessel segmentation is also proposed by introducing vessel candidate points. To obtain confident vessel candidates, the 3D image is first reduced to 2D through maximum intensity projection. Subsequently, vessel segmentation is performed from the 2D images and the segmented pixels are back-projected into the original 3D space. Finally, a new level set function is proposed that utilizes both the original image and vessel candidate points. The proposed algorithm can segment thin vessels with high accuracy by mainly using vessel candidate points. The reliability of the points can be higher through robust segmentation in the projected 2D images where complex structures are simplified and thin vessels are more visible. Experimental results show that the proposed algorithm is superior to other active contour models. The proposed algorithms present a new method of segmenting the liver and its vessels. The auto-context algorithm shows that a human-designed curriculum (i.e., shape-prior learning) can improve generalization performance. The proposed contour learning technique can increase the accuracy of a CNN for image segmentation by focusing on its failures, represented by sparse contours. The vessel segmentation shows that minor vessel branches can be successfully segmented through vessel candidate points obtained by reducing the image dimension. The algorithms presented in this dissertation can be employed for later analysis of liver anatomy that requires accurate segmentation techniques.Chapter 1 Introduction 1 1.1 Background and motivation 1 1.2 Problem statement 3 1.3 Main contributions 6 1.4 Contents and organization 9 Chapter 2 Related Works 10 2.1 Overview 10 2.2 Convolutional neural networks 11 2.2.1 Architectures of convolutional neural networks 11 2.2.2 Convolutional neural networks in medical image segmentation 21 2.3 Liver and vessel segmentation 37 2.3.1 Classical methods for liver segmentation 37 2.3.2 Vascular image segmentation 40 2.3.3 Active contour models 46 2.3.4 Vessel topology-based active contour model 54 2.4 Motivation 60 Chapter 3 Liver Segmentation via Auto-Context Neural Network with Self-Supervised Contour Attention 62 3.1 Overview 62 3.2 Single-pass auto-context neural network 65 3.2.1 Skip-attention module 66 3.2.2 V-transition module 69 3.2.3 Liver-prior inference and auto-context 70 3.2.4 Understanding the network 74 3.3 Self-supervising contour attention 75 3.4 Learning the network 81 3.4.1 Overall loss function 81 3.4.2 Data augmentation 81 3.5 Experimental Results 83 3.5.1 Overview 83 3.5.2 Data configurations and target of comparison 84 3.5.3 Evaluation metric 85 3.5.4 Accuracy evaluation 87 3.5.5 Ablation study 93 3.5.6 Performance of generalization 110 3.5.7 Results from ground-truth variations 114 3.6 Discussion 116 Chapter 4 Liver Vessel Segmentation via Active Contour Model with Dense Vessel Candidates 119 4.1 Overview 119 4.2 Dense vessel candidates 124 4.2.1 Maximum intensity slab images 125 4.2.2 Segmentation of 2D vessel candidates and back-projection 130 4.3 Clustering of dense vessel candidates 135 4.3.1 Virtual gradient-assisted regional ACM 136 4.3.2 Localized regional ACM 142 4.4 Experimental results 145 4.4.1 Overview 145 4.4.2 Data configurations and environment 146 4.4.3 2D segmentation 146 4.4.4 ACM comparisons 149 4.4.5 Evaluation of bifurcation points 154 4.4.6 Computational performance 159 4.4.7 Ablation study 160 4.4.8 Parameter study 162 4.5 Application to portal vein analysis 164 4.6 Discussion 168 Chapter 5 Conclusion and Future Works 170 Bibliography 172 ์ดˆ๋ก 197Docto

    Image Analysis and Visualization of the Human Mastoid Air Cell System

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    Implicit deformable models for biomedical image segmentation.

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    In this thesis, new methods for the efficient segmentation of images are presented. The proposed methods are based on the deformable model approach, and can be used efficiently in the segmentation of complex geometries from various imaging modalities. A novel deformable model that is based on a geometrically induced external force field which can be conveniently generalized to arbitrary dimensions is presented. This external force field is based on hypothesized interactions between the relative geometries of the deformable model and the object boundary characterized by image gradient. The evolution of the deformable model is solved using the level set method so that topological changes are handled automatically. The relative geometrical configurations between the deformable model and the object boundaries contributes to a dynamic vector force field that changes accordingly as the deformable model evolves. The geometrically induced dynamic interaction force has been shown to greatly improve the deformable model performance in acquiring complex geometries and highly concave boundaries, and give the deformable model a high invariance in initialization configurations. The voxel interactions across the whole image domain provides a global view of the object boundary representation, giving the external force a long attraction range. The bidirectionality of the external force held allows the new deformable model to deal with arbitrary cross-boundary initializations, and facilitates the handling of weak edges and broken boundaries. In addition, it is shown that by enhancing the geometrical interaction field with a nonlocal edge-preserving algorithm, the new deformable model can effectively overcome image noise. A comparative study on the segmentation of various geometries with different topologies from both synthetic and real images is provided, and the proposed method is shown to achieve significant improvements against several existing techniques. A robust framework for the segmentation of vascular geometries is described. In particular, the framework consists of image denoising, optimal object edge representation, and segmentation using implicit deformable model. The image denoising is based on vessel enhancing diffusion which can be used to smooth out image noise and enhance the vessel structures. The image object boundaries are derived using an edge detection technique which can produce object edges of single pixel width. The image edge information is then used to derive the geometric interaction field for optimal object edge representation. The vascular geometries are segmented using an implict deformable model. A region constraint is added to the deformable model which allows it to easily get around calcified regions and propagate across the vessels to segment the structures efficiently. The presented framework is ai)plied in the accurate segmentation of carotid geometries from medical images. A new segmentation model with statistical shape prior using a variational approach is also presented in this thesis. The proposed model consists of an image attraction force that propagates contours towards image object boundaries, and a global shape force that attracts the model towards similar shapes in the statistical shape distribution. The image attraction force is derived from gradient vector interactions across the whole image domain, which makes the model more robust to image noise, weak edges and initializations. The statistical shape information is incorporated using kernel density estimation, which allows the shape prior model to handle arbitrary shape variations. It is shown that the proposed model with shape prior can be used to segment object shapes from images efficiently
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