Variational Image Segmentation Model Coupled with Image Restoration Achievements

Image segmentation and image restoration are two important topics in image processing with great achievements. In this paper, we propose a new multiphase segmentation model by combining image restoration and image segmentation models. Utilizing image restoration aspects, the proposed segmentation model can effectively and robustly tackle high noisy images, blurry images, images with missing pixels, and vector-valued images. In particular, one of the most important segmentation models, the piecewise constant Mumford-Shah model, can be extended easily in this way to segment gray and vector-valued images corrupted for example by noise, blur or missing pixels after coupling a new data fidelity term which comes from image restoration topics. It can be solved efficiently using the alternating minimization algorithm, and we prove the convergence of this algorithm with three variables under mild condition. Experiments on many synthetic and real-world images demonstrate that our method gives better segmentation results in comparison to others state-of-the-art segmentation models especially for blurry images and images with missing pixels values.Comment: 23 page

Unsupervised Texture Segmentation Using Active Contour Model and Oscillating Information

Textures often occur in real-world images and may cause considerable difficulties in image segmentation. In order to segment texture images, we propose a new segmentation model that combines image decomposition model and active contour model. The former model is capable of decomposing structural and oscillating components separately from texture image, and the latter model can be used to provide smooth segmentation contour. In detail, we just replace the data term of piecewise constant/smooth approximation in CCV (convex Chan-Vese) model with that of image decomposition model-VO (Vese-Osher). Therefore, our proposed model can estimate both structural and oscillating components of texture images as well as segment textures simultaneously. In addition, we design fast Split-Bregman algorithm for our proposed model. Finally, the performance of our method is demonstrated by segmenting some synthetic and real texture images

A Two-stage Classification Method for High-dimensional Data and Point Clouds

High-dimensional data classification is a fundamental task in machine learning and imaging science. In this paper, we propose a two-stage multiphase semi-supervised classification method for classifying high-dimensional data and unstructured point clouds. To begin with, a fuzzy classification method such as the standard support vector machine is used to generate a warm initialization. We then apply a two-stage approach named SaT (smoothing and thresholding) to improve the classification. In the first stage, an unconstraint convex variational model is implemented to purify and smooth the initialization, followed by the second stage which is to project the smoothed partition obtained at stage one to a binary partition. These two stages can be repeated, with the latest result as a new initialization, to keep improving the classification quality. We show that the convex model of the smoothing stage has a unique solution and can be solved by a specifically designed primal-dual algorithm whose convergence is guaranteed. We test our method and compare it with the state-of-the-art methods on several benchmark data sets. The experimental results demonstrate clearly that our method is superior in both the classification accuracy and computation speed for high-dimensional data and point clouds.Comment: 21 pages, 4 figure

Variational Image Segmentation with Constraints

The research of Huizhu Pan addresses the problem of image segmentation with constraints though designing and solving various variational models. A novel constraint term is designed for the use of landmarks in image segmentation. Two region-based segmentation models were proposed where the segmentation contour passes through landmark points. A more stable and memory efficient solution to the self-repelling snakes model, a variational model with the topology preservation constraint, was also designed

CT Image Reconstruction by Spatial-Radon Domain Data-Driven Tight Frame Regularization

This paper proposes a spatial-Radon domain CT image reconstruction model based on data-driven tight frames (SRD-DDTF). The proposed SRD-DDTF model combines the idea of joint image and Radon domain inpainting model of \cite{Dong2013X} and that of the data-driven tight frames for image denoising \cite{cai2014data}. It is different from existing models in that both CT image and its corresponding high quality projection image are reconstructed simultaneously using sparsity priors by tight frames that are adaptively learned from the data to provide optimal sparse approximations. An alternative minimization algorithm is designed to solve the proposed model which is nonsmooth and nonconvex. Convergence analysis of the algorithm is provided. Numerical experiments showed that the SRD-DDTF model is superior to the model by \cite{Dong2013X} especially in recovering some subtle structures in the images