Research On Image Segmentation And Registration Based On Partial Differential Equations

Image segmentation and image registration are two fundamental tasks in image processing and analysis. The two problems have been existed since the birth of image. Many researchers have proposed a large number of methods to implement image segmentation and registration, however, the difference between images and applications make the research of the two problems be hot all the time. Partial differential equation is one of the most popular theories for image processing. Image segmentation methods based on active contour model, and non-rigid image registration methods based on physical models are the typical applications of partial differential equation in image project. This paper studies several special problems of image segmentation and image registration based on the theory of partial differential equation. The primary work and remarks of this paper are as follows:(1) This paper presents a more robust and efficient level set method than the original LBF model for image segmentation under a constrained energy minimization framework. LBF model is able to address intensity inhomogeneities, but it often suffers from the problem of being stuck in local minima. LBF model formulates image segmentation as a problem of seeking an optimal contour and two fitting functions that best approximate local intensities on the two sides of the contour. The local property enables the model to deal with intensity inhomogenities, however, it makes the model tend to stick in local minima. We introduce a contrast constraint on the fitting functions to effectively prevent the contour from being stuck in spurious local minima, which thereby makes our model more robust to the initialization of contour. Comparisons with the LBF model and the piecewise smooth (PS) model demonstrate the superior performance of our model in terms of robustness, accuracy, and efficiency.(2) We propose a novel and efficient narrow band level set evolution algorithm based on the LBF model. The full domain implementation of the LBF model is computationally expensive and makes the model often suffer from the problem of being stuck in local minima. Thus, we propose a novel narrow band level set evolution algorithm to implement the LBF model. Com-putational efficiency is further improved by avoiding unnecessary computation for updating the level set function at those points where the level set function has converged after a number of iterations. Therefore, the proposed algorithm only updates the level set function at those points where the level set function still actively evolve. These points, called active points, typically consist of only a small portion of the narrow band. Computation time is therefore dramatically reduced by confining the computation to the active points. The narrow band implementation offers more localized computation of the fitting functions in the LBF model. Compared with the original LBF algorithm, the enhanced localization property of the narrow band algorithm leads to the following desirable features:1) more accurate segmentation of images with inten-sity inhomogeneities; 2) more stable performance; 3) allows for the segmentation of regions of interest only. Our algorithm has been validated on synthetic and real images with desirable results.(3) An improved optical flow model within the differential framework is employed in non-rigid image registration. Aiming at eliminating the severe image blurring caused by the Horn model, the anisotropic flow-driven diffusion is used as the regularization term to keep the image feature during the evolution, and the proposed diffusion tensor possesses the capability of edge preserving and coherence enhancing. The data term employs the nonquadratic penalization function to improve the robustness to image noise. The improved model is validated on complex brain images.(4) A color image registration model within the framework of abstract matching flow is proposed to deal with the problem of serious color difference and large displacement between images to be registered. The model is composed of a data term and a regularization term. The data term employs the cross correlation as the similarity measurement to deal with the serious color difference between images. We bring the theory of anisotropic diffusion to the defini-tion of the regularization term. The regularization term is defined as a flow-driven anisotropic diffusion function based on the vector-valued structure tensor. New defined diffusion function integrates the intensity and structure information of multi-channels, and possesses the property of preserving image features during image evolution.(5) A novel variational model for integrating registration and segmentation via level set evolution is proposed. A non-parametric registration method based on the abstract matching flow model is used as the registration term to go along with the non-parametric segmentation term. An edge-based active contour model is used to segment the region of interested, and the model is improved by adding region statistic information to deal with the problem of sensitivity to the initialization. The integrated model is defined by the level set function and can be im-plemented straightforward. Comparisons with classic method demonstrate the advantage of the proposed method in terms of accuracy.