Research On Level Set Methods And The Space Of Functions Of Bounded Variation In Biomedical Image Processing

To solve the key problems of the segmentation and measurement of optic nerve head medical images , which are of poor quality, very low contrast, obscure due to blood vessels, and distinct inter-differences of individuals, for the computer aided diagnostics of glaucoma, Diabetic Retinopathy, and Age-related Macular Degeneration diseases, several novel models and methods are proposed based on level set methods and Mumford–Shah functional defined in the class of Special functions of Bounded Variation(SBV), which are the hierarchical Mumford–Shah functional model(HMSM or HMSMv) for the simultaneous segmentation, denoise and reconstruction of the given scalar or vector-valued image, the narrow band level set based statistical shape distribution model (NLDM) for the representation of the prior knowledge of"legal"variation in the shape of a class of object, the statistical shape prior-based hierarchical Mumford–Shah model by incorporating prior knowledge(SHMSMv) for the recognition of the object in an image which is similar to the training shapes. Several experimental results for the segmentation and measurement of the color medical images of the optic nerve head, the segmentation and reconstruction of a pathology image of the human brain and a color Doppler ultrasound image of the heart, and the phase unwrapping of a SAR interferogram are supplied, demonstrating the effectiveness of our proposed solutions and indicating their potential.To summarize, the original contributions and applications of our work are the following:1)A novel hierarchical Mumford–Shah functional model is addressed to simultaneously segment, denoise and reconstruct the data within a given scalar or vector-valued image(HMSM or HMSMv), and to handle important image features such as triple points and other multiple junctions, which can be seen as a hierarchical case of the Mumford–Shah minimal partition problem. At the same time, a new iterative tier-by-tier algorithm based on techniques of level set is proposed to minimize the functional, which is more effective and more simply than existing algorithms such as the hierarchical approach proposed by Tsai A et al. and the multiphase level set methods proposed by Chan T et al. 2)A novel narrow band level set based statistical shape distribution model is proposed, namely NLDM, which is to modeling the pattern of"legal"variation in the shape of an object from a given class of training images which are of complex and variable structures and provide noisy and possibly incomplete evidence, such as medical images. At the same time, a new alignment model based on narrow band level set is proposed also, which is a modified version of the gradient-based approach from a variational perspective proposed by A. Tsai et al. and align more efficiently all the training shapes to eliminate variations in pose. Modeling the shape of the optic nerve head in color fundus medical images demonstrates its efficacy.3)A novel NLDM-based statistical hierarchical Mumford–Shah model(SHMSMv) by incorporating prior knowledge is proposed to segment medical images. First, a statistical shape model based on NLDM is established to represent the prior knowledge of the expected shapes of structures from a given class of training images. Then, the statistical shape model is integrated with a level set-based hierarchical Mumford–Shah modelm by maximum a posteriori(MAP). This novel model can segment vector-valued images whose boundaries are not necessarily defined by gradient, and specially recognise the object in an image which is similar to the training shapes. We demonstrate this technique by applying it to the segmentation of the optic disk in color optic nerve head images of early glaucoma patients.4)A HMSMv-based method was proposed to reconstruct, segment and measure the optic cup and disk in a color image of optic nerve heads for the computer aided diagnostics of glaucoma diseases. First, a hierarchical Mumford–Shah model was employed to reconstruct the optic cup and disk. Then, the optic cup and disk characteristic rectangles and edge points were extracted based on the color reconstruct image of an optic nerve head by incorporating the prior knowledge of the optic cup and disk shapes. Finally, smoothing spline curve fitting was resorted to reconstruct the edges of the optic cup and disk obscured by blood vessels, and the measurements of the optic cup and disk were estimated. The tests with the color optic nerve head images of different glaucoma patients showed that this method is able to handle this kind of images, which are of poor quality, very low contrast, obscure due to blood vessels, and distinct inter-differences of individuals and to effectively segment, reconstruct and measure the optic cup and disk in a color of optic nerve head images of glaucoma patients.5)A novel HMSM-based algorithm was proposed in this paper for InSAR phase unwrapping. To determine the connected components in an InSAR whose quality are distinct, the quality image defined by the variance of the derivative of the phase of an InSAR was first segmented based on the hierarchical Mumford--Shah functional model by an iterative tier-by-tier level set algorithm. Then, SAR interferogram was unwrapped independently in these components by improved Itoh unwrapping algorithm ,first in the best quality component, then the better quality one, and finally the worst quality one, and so on. The phase unwrapping results on real and simulated SAR interferograms show that the algorithm is more effective than some existing algorithms such as the branch-cut algorithm.