As the resolution of digital images increase significantly, the processing of images becomes more challenging in terms of accuracy and efficiency. In this paper, we consider image segmentation by solving a partial differentiation equation (PDE) model based on the Mumford-Shah functional. We develop a new algorithm by combining anisotropic mesh adaptation for image representation and finite element method for solving the PDE model. Comparing to traditional algorithms solved by finite difference method, our algorithm provides faster and better results without the need to resizing the images to lower quality. We also extend the algorithm to segment images with multiple regions.
University of Cambridge（剑桥大学）；University College London（伦敦大学学院）；City University of Hong Kong（香港城市大学）；University of Kaiserslautern（凯泽斯劳滕大学）；The Chinese University of Hong Kong（香港中文大学）
The piecewise constant Mumford-Shah (PCMS) model and the Rudin-Osher-Fatemi (ROF) model are two important variational models in image segmentation and image restoration, respectively. In this paper, we explore a linkage between these models. We prove that for the two-phase segmentation problem a partial minimizer of the PCMS model can be obtained by thresholding the minimizer of the ROF model. A similar linkage is still valid for multiphase segmentation under specific assumptions. Thus it opens a new segmentation paradigm: image segmentation can be done via image restoration plus thresholding.…
Korea Advanced Institute of Science and Technology (KAIST)（韩国科学技术院）
Recent state-of-the-art image segmentation algorithms are mostly based on deep neural networks, thanks to their high performance and fast computation time. However, these methods are usually trained in a supervised manner, which requires large number of high quality ground-truth segmentation masks. On the other hand, classical image segmentation approaches such as level-set methods are formulated in a self-supervised manner by minimizing energy functions such as Mumford-Shah functional, so they are still useful to help generation of segmentation masks without labels. Unfortunately, these algor…
RWTH Aachen University（亚琛工业大学）；University of Texas at Austin（德克萨斯大学奥斯汀分校）
Hyperspectral images provide a rich representation of the underlying spectrum for each pixel, allowing for a pixel-wise classification/segmentation into different classes. As the acquisition of labeled training data is very time-consuming, unsupervised methods become crucial in hyperspectral image analysis. The spectral variability and noise in hyperspectral data make this task very challenging and define special requirements for such methods. Here, we present a novel unsupervised hyperspectral segmentation framework. It starts with a denoising and dimensionality reduction step by the well-est…
University of California at Irvine（加州大学欧文分校）；Whittier College（惠蒂尔学院）；University of Texas at Dallas（德克萨斯大学达拉斯分校）
In a class of piecewise-constant image segmentation models, we propose to incorporate a weighted difference of anisotropic and isotropic total variation (AITV) to regularize the partition boundaries in an image. In particular, we replace the total variation regularization in the Chan-Vese segmentation model and a fuzzy region competition model by the proposed AITV. To deal with the nonconvex nature of AITV, we apply the difference-of-convex algorithm (DCA), in which the subproblems can be minimized by the primal-dual hybrid gradient method with linesearch. The convergence of the DCA scheme is …
EPITA Research and Development Laboratory（EPITA研究与发展实验室）；Telecom ParisTech（巴黎高等电信学院）；Université Paris-Est（巴黎东大学）；ESIEE Paris（巴黎高等电子与电工技术工程师学院）
Hierarchies, such as the tree of shapes, are popular representations for image simplification and segmentation thanks to their multiscale structures. Selecting meaningful level lines (boundaries of shapes) yields to simplify image while preserving intact salient structures. Many image simplification and segmentation methods are driven by the optimization of an energy functional, for instance the celebrated Mumford-Shah functional. In this paper, we propose an efficient approach to hierarchical image simplification and segmentation based on the minimization of the piecewise-constant Mumford-Sha…
University of Nottingham（诺丁汉大学）；Shenzhen University（深圳大学）；Wuhan University of Technology（武汉理工大学）；University of Leicester（莱斯特大学）
In this paper, we propose a novel retinal layer boundary model for segmentation of optical coherence tomography (OCT) images. The retinal layer boundary model consists of 9 open parametric contours representing the 9 retinal layers in OCT images. An intensity-based Mumford-Shah (MS) variational functional is first defined to evolve the retinal layer boundary model to segment the 9 layers simultaneously. By making use of the normals of open parametric contours, we construct equal sized adjacent narrowbands that are divided by each contour. Regional information in each narrowband can thus be int…
Variational Image Segmentation Model Coupled with Image Restoration Achievements
Department of Plant Sciences（植物科学系）；Department of Applied Mathematics（应用数学系）；Theoretical Physics, University of Cambridge, Cambridge, UK（理论物理，剑桥大学，剑桥，英国）
Relaxed Total Generalized Variation Regularized Piecewise Smooth Mumford-Shah Model for Triangulated Surface Segmentation
School of Computer Science and Technology, Tiangong University, Tianjin, China（计算机科学与技术学院，天津工业大学）；School of Mathmatics, Tiangong University,Tianjin, China（数学学院，天津工业大学）
Image segmentation is to separate an image into distinct homogeneous regions belonging to different objects. It is an essential step in image analysis and computer vision. This paper compares some segmentation technologies and attempts to find an automated way to better determine the parameters for image segmentation, especially the connectivity value of $λ$ in $λ$-connected segmentation. Based on the theories on the maximum entropy method and Otsu's minimum variance method, we propose:(1)maximum entropy connectedness determination: a method that uses maximum entropy to determine the best $λ$ …
CoRIS Institute（CoRIS研究所）；Oregon State University（俄勒冈州立大学）；Stony Brook University（石溪大学）
Instance Segmentation, which seeks to obtain both class and instance labels for each pixel in the input image, is a challenging task in computer vision. State-of-the-art algorithms often employ two separate stages, the first one generating object proposals and the second one recognizing and refining the boundaries. Further, proposals are usually based on detectors such as faster R-CNN which search for boxes in the entire image exhaustively. In this paper, we propose a novel algorithm that directly utilizes a fully convolutional network (FCN) to predict instance labels. Specifically, we propose…
RWTH Aachen University（亚琛工业大学）；University of Twente（特温特大学）；Monash University（莫纳什大学）；AICES Graduate School（AICES研究生院）
The hemocompatibility of blood-contacting medical devices remains one of the major challenges in biomedical engineering and makes research in the field of new and improved materials inevitable. However, current in-vitro test and analysis methods are still lacking standardization and comparability, which impedes advances in material design. For example, the optical platelet analysis of material in-vitro hemocompatibility tests is carried out manually or semi-manually by each research group individually. As a step towards standardization, this paper proposes an automation approach for the optica…
Xiangtan University（湘潭大学）；Hunan National Applied Mathematics Center（湖南国家应用数学中心）
Solving variational image segmentation problems with hidden physics is often expensive and requires different algorithms and manually tunes model parameter. The deep learning methods based on the U-Net structure have obtained outstanding performances in many different medical image segmentation tasks, but designing such networks requires a lot of parameters and training data, not always available for practical problems. In this paper, inspired by traditional multi-phase convexity Mumford-Shah variational model and full approximation scheme (FAS) solving the nonlinear systems, we propose a nove…
Signals and images with discontinuities appear in many problems in such diverse areas as biology, medicine, mechanics, and electrical engineering. The concrete data are often discrete, indirect and noisy measurements of some quantities describing the signal under consideration. A frequent task is to find the segments of the signal or image which corresponds to finding the discontinuities or jumps in the data. Methods based on minimizing the piecewise constant Mumford-Shah functional -- whose discretized version is known as Potts functional -- are advantageous in this scenario, in particular, i…
We propose a novel method for multi-phase segmentation of images based on high-dimensional local feature vectors. While the method was developed for the segmentation of extremely noisy crystal images based on localized Fourier transforms, the resulting framework is not tied to specific feature descriptors. For instance, using local spectral histograms as features, it allows for robust texture segmentation. The segmentation itself is based on the multi-phase Mumford-Shah model. Initializing the high-dimensional mean features directly is computationally too demanding and ill-posed in practice. T…
Segmentation is the process of partitioning a digital image into multiple segments (sets of pixels). Such common segmentation tasks including segmenting written text or segmenting tumors from healthy brain tissue in an MRI image, etc. Chan-Vese model for active contours is a powerful and flexible method which is able to segment many types of images, including some that would be quite difficult to segment in means of "classical" segmentation - i.e., using thresholding or gradient based methods. This model is based on the Mumford-Shah functional for segmentation, and is used widely in the medica…
Deutsches Zentrum für Luft- und Raumfahrt (DLR)（德国航空航天中心（DLR））；Universität Regensburg（雷根斯堡大学）
In this paper, we introduce a novel parametric method for segmentation of three-dimensional images. We consider a piecewise constant version of the Mumford-Shah and the Chan-Vese functionals and perform a region-based segmentation of 3D image data. An evolution law is derived from energy minimization problems which push the surfaces to the boundaries of 3D objects in the image. We propose a parametric scheme which describes the evolution of parametric surfaces. An efficient finite element scheme is proposed for a numerical approximation of the evolution equations. Since standard parametric met…
Technical University of Munich（慕尼黑工业大学）；Universität Heidelberg（海德堡大学）；Darmstadt University of Applied Sciences（达姆施塔特应用科学大学）；Helmholtz Center Munich（慕尼黑亥姆霍兹中心）
Features that capture well the textural patterns of a certain class of images are crucial for the performance of texture segmentation methods. The manual selection of features or designing new ones can be a tedious task. Therefore, it is desirable to automatically adapt the features to a certain image or class of images. Typically, this requires a large set of training images with similar textures and ground truth segmentation. In this work, we propose a framework to learn features for texture segmentation when no such training data is available. The cost function for our learning process is c…
