A fractional order derivative based active contour model for inhomogeneous image segmentation

Segmenting intensity inhomogeneous images is a challenging task for both local and global methods. Some hybrid methods have great advantages over the traditional methods in inhomogeneous image segmentation. In this paper, a new hybrid method is presented, which incorporates image gradient, local environment and global information into a framework, called adaptive-weighting active contour model. The energy or level set functions in the framework mainly include two parts: a global term and local term. The global term aims to enhance the image contrast, and it can also accelerate the convergence rate when minimizing the energy function. The local term integrates fractional order differentiation, fractional order gradient magnitude, and difference image information into the well-known local Chan–Vese model, which has been shown to be effective and efficient in modeling the local information. The local term can also enhance low frequency information and improve the inhomogeneous image segmentation. An adaptive weighting strategy is proposed to balance the actions of the global and local terms automatically. When minimizing the level set functions, regularization can be imposed by applying Gaussian filtering to ensure smoothness in the evolution process. In addition, a corresponding stopping criterion is proposed to ensure the evolving curve automatically stops on true boundaries of objects. Dice similarity coefficient is employed as the comparative quantitative measures for the segmented results. Experiments on synthetic images as well as real images are performed to demonstrate the segmentation accuracy and computational efficiency of the presented hybrid method.     

基于小波域的多尺度非参数图像分割方法

主要介绍了一种基于信息熵理论及图像多尺度信息来对图像进行非参数主动轮廓模型分割的有效方法.由于小波多分辨率特性的引入,可以最大程度地利用图像多尺度信息以确保分割的准确性和完整性.又由于小波变换的特性,低频信息的使用更是进一步降低了噪声影响.文中把图像分割问题定义为在分割区域边缘长度满足一定约束条件下,图像标记场与各个尺度图像像素值之间的互信息熵最大化过程.该方法可以有效地降低噪声对于分割的影响,及确保分割的准确性和完整性.     

Noisy image segmentation based on nonlinear diffusion equation model

This paper addresses the segmentation problem in noisy image based on nonlinear diffusion equation model and proposes a new adaptive segmentation model based on gray-level image segmentation model. This model also can be extended to the vector value image segmentation. By virtue of the prior information of regions and boundary of image, a framework is established to construct different segmentation models using different probability density functions. A segmentation model exploiting Gauss probability density function is given in this paper. An efficient and unconditional stable algorithm based on locally one-dimensional (LOD) scheme is developed and it is used to segment the gray image and the vector values image. Comparing with existing classical models, the proposed approach gives the best performance.     

Control the Fibre Orientation Distribution at the Outlet of Contraction

A two dimensional model of the orientation distribution of fibres in a paper machine headbox is studied. The goal is to control the fibre orientation distribution at the outlet of contraction by changing its shape. The mathematical formulation leads to an optimization problem with control in coefficients of a linear convection-diffusion equation as the state problem. Then, the problem is expressed as an optimal control problem governed by variational forms. By using an embedding method, the class of admissible shapes is replaced by a class of positive Radon measures. The optimization problem in measure space is then approximated by a linear programming problem. The optimal measure representing optimal shape is approximated by the solution of this linear programming problem. In this paper, we have shown that the embedding method (embedding the admissible set into a subset of measures), successfully can be applied to shape variation design to a one dimensional headbox. The usefulness of this idea is that the method is not iterative and it does not need any initial guess of the solution.      

多源验前信息之下Bayes可靠性估计

本文考虑存在多源验前信息的情况，以二项分布为例，首先把各种验前信息化成不同的约束条件，并运用最大熵准则推导出各种验前信息所对应的验前分布，然后将这些分布综合成最终的验前分布，最后根据系统的寿命试验数据得出可靠性参数的验后分布并进行了Ｂａｙｅｓ推断，文中给出了仿真实例以说明方法的有效性。     

A novel digital image covert communication scheme based on generalized FCM in DCT domain

A novel covert communication method of digital image is presented, based on generalized fuzzy c-means clustering (GFCM), human visual system (HVS) and discrete cosine transform (DCT). Therefore, the original image blocks are classified into two classes according to specified characteristic parameters. So one block is suited for embedding security information, but the other block is not. Hence the appropriate blocks can be selected in an image to embed the security information by selectively modifying the middle-frequency part of the original image in conjunction with HVS and DCT. Furthermore the maximal information strength is fixed based to the frequency masking. Also to improve performances of the proposed algorithm, the security information is modulated into the chaotic modulation array. The simulation results show that we can remarkably extract the hiding security information and can achieve good robustness with common signal distortion or geometric distortion and the quality of the embedded image is guaranteed.     

Estimation of Binary Markov Random Fields Using Markov chain Monte Carlo

This article compares three binary Markov random fields (MRFs) which are popular Bayesian priors for spatial smoothing. These are the Ising prior and two priors based on latent Gaussian MRFs. Concern is given to the selection of a suitable Markov chain Monte Carlo (MCMC) sampling scheme for each prior. The properties of the three priors and sampling schemes are investigated in the context of three empirical examples. The first is a simulated dataset, the second involves a confocal fluorescence microscopy dataset, while the third is based on the analysis of functional magnetic resonance imaging (fMRI) data. In the case of the Ising prior, single site and multi-site Swendsen-Wang sampling schemes are both considered. The single site scheme is shown to work consistently well, while it is shown that the Swendsen-Wang algorithm can have convergence problems. The sampling schemes for the priors are extended to generate the smoothing parameters, so that estimation becomes fully automatic. Although this works well, it is found that for highly contiguous images fixing smoothing parameters to very high values can improve results by injecting additional prior information concerning the level of contiguity in the image. The relative properties of the three binary MRFs are investigated, and it is shown how the Ising prior in particular defines sharp edges and encourages clustering. In addition, one of the latent Gaussian MRF priors is shown to be unable to distinguish between higher levels of smoothing. In the context of the fMRI example we also undertake a simulation study.     

New normalized nonlocal hybrid level set method for image segmentation

This article introduces a new normalized nonlocal hybrid level set method for image segmentation. Due to intensity overlapping, blurred edges with complex backgrounds, simple intensity and texture information, such kind of image segmentation is still a challenging task. The proposed method uses both the region and boundary information to achieve accurate segmentation results. The region information can help to identify rough region of interest and prevent the boundary leakage problem. It makes use of normalized nonlocal comparisons between pairs of patches in each region, and a heuristic intensity model is proposed to suppress irrelevant strong edges and constrain the segmentation. The boundary information can help to detect the precise location of the target object, it makes use of the geodesic active contour model to obtain the target boundary. The corresponding variational segmentation problem is implemented by a level set formulation. We use an internal energy term for geometric active contours to penalize the deviation of the level set function from a signed distance function. At last, experimental results on synthetic images and real images are shown in the paper with promising results.     

Comparison of Methods for Image Analysis on cDNA Microarray Data

Microarrays are part of a new class of biotechnologies which allow the monitoring of expression levels for thousands of genes simultaneously. Image analysis is an important aspect of microarray experiments, one that can have a potentially large impact on subsequent analyses such as clustering or the identification of differentially expressed genes. This article reviews a number of existing image analysis approaches for cDNA microarray experiments and proposes new addressing, segmentation, and background correction methods for extracting information from microarray scanned images. The segmentation component uses a seeded region growing algorithm which makes provision for spots of different shapes and sizes. The background estimation approach is based on an image analysis technique known as morphological opening. These new image analysis procedures are implemented in a software package named Spot, built on the R environment for statistical computing. The statistical properties of the different segmentation and background adjustment methods are examined using microarray data from a study of lipid metabolism in mice. It is shown that in some cases background adjustment can substantially reduce the precision—that is, increase the variability—of low-intensity spot values. In contrast, the choice of segmentation procedure has a smaller impact. The comparison further suggests that seeded region growing segmentation with morphological background correction provides precise and accurate estimates of foreground and background intensities.     

Testing Hypotheses About the Power Law Process Under Failure Truncation Using Intrinsic Bayes Factors

Conventional Bayes factors for hypotheses testing cannot typically accommodate the use of standard noninformative priors, as such priors are defined only up to arbitrary constants which affect the values of the Bayes factors. To circumvent this problem, Berger and Pericchi (1996, J. Amer. Statist. Assoc., 19, 109-122) introduced a new criterion called the Intrinsic Bayes Factor (IBF). In this paper, we use their methodology to test several hypotheses regarding the shape parameter of the power law process. Assuming that we have data from the process according to the failure-truncation sampling scheme, we derive the arithmetic and geometric IBF's using the reference priors. We deduce a set of intrinsic priors that correspond to these IBF's, as the observed number of failures tends to infinity. We then use these results to analyze an actual data set on the failures of an aircraft generator.     

Noninformative priors for the ratio of the shape parameters of two Weibull distributions

The Weibull distribution is one of the most widely used lifetime distributions in reliability engineering. Here, the noninformative priors for the ratio of the shape parameters of two Weibull models are introduced. The first criterion used is the asymptotic matching of the coverage probabilities of Bayesian credible intervals with the corresponding frequentist coverage probabilities. We develop the probability matching priors for the ratio of the shape parameters using the following matching criteria: quantile matching, matching of the distribution function, highest posterior density matching, and matching via inversion of the test statistics. We obtain one particular prior that meets all the matching criteria. Next, we derive the reference priors for different groups of ordering. Our findings show that some of the reference priors satisfy a first-order matching criterion and the one-at-a-time reference prior is a second-order matching prior. Lastly, we perform a simulation study and provide a real-world example.     

Application of the Level-Set Model with Constraints in Image Segmentation

We propose and analyze a constrained level-set method for semi-automatic image segmentation. Our level-set model with constraints on the level-set function enables us to specify which parts of the image lie inside respectively outside the segmented objects. Such a-priori information can be expressed in terms of upper and lower constraints prescribed for the level-set function. Constraints have the same conceptual meaning as initial seeds of the popular graph-cuts based methods for image segmentation. A numerical approximation scheme is based on the complementary-finite volumes method combined with the Projected successive overrelaxation method adopted for solving constrained linear complementarity problems. The advantage of the constrained level-set method is demonstrated on several artificial images as well as on cardiac MRI data.     

基于小波多分辨率分析和改进窄带法的C-V水平集图像分割模型

本文研究了基于小波分析改进的C-V模型图像分割问题.利用小波多分辨率分析和改进的窄带水平集方法,获得了比传统C-V模型分割速度更快、准确度更高、算法复杂度更低的分割结果.推广了C-V水平集模型如何快速准确地分割灰度不均匀的图像和窄带水平集法等结果.     

Bilipschitz Embeddings of Metric Spaces into Space Forms

The paper describes some basic geometric tools to construct bilipschitz embeddings of metric spaces into (finite-dimensional) Euclidean or hyperbolic spaces. One of the main results implies the following: If X is a geodesic metric space with convex distance function and the property that geodesic segments can be extended to rays, then X admits a bilipschitz embedding into some Euclidean space iff X has the doubling property, and X admits a bilipschitz embedding into some hyperbolic space iff X is Gromov hyperbolic and doubling up to some scale. In either case the image of the embedding is shown to be a Lipschitz retract in the target space, provided X is complete.     

基于改进C-V水平集模型的SAR图像分割

本文研究了SAR图像分割的问题.利用一种加入图像边缘信息且无需重新初始化的改进水平集方法,获得了比传统C-V模型分割速度更快、准确度更高的分割结果.推广了C-V水平集模型分割灰度不均匀的SAR图像以及零水平集曲线的初始化等结果.     

Idempotent Block Splitting on Partial Partitions,I: Isotone Operators

Image segmentation algorithms can be modelled as image-guided operators (maps) on the complete lattice of partitions of space, or on the one of partial partitions (i.e., partitions of subsets of the space). In particular region-splitting segmentation algorithms correspond to block splitting operators on the lattice of partial partitions, in other words anti-extensive operators that act by splitting each block independently. This first paper studies in detail block splitting operators and their lattice-theoretical and monoid properties; in particular we consider their idempotence (a requirement in image segmentation). We characterize block splitting openings (kernel operators) as operators splitting each block into its connected components according to a partial connection; furthermore, block splitting openings constitute a complete sublattice of the complete lattice of all openings on partial partitions. Our results underlie the connective approach to image segmentation introduced by Serra. The second paper will study two classes of non-isotone idempotent block splitting operators, that are also relevant to image segmentation.     

Invertible chaotic fragile watermarking for robust image authentication

Fragile watermarking is a popular method for image authentication. In such schemes, a fragile signal that is sensitive to manipulations is embedded in the image, so that it becomes undetectable after any modification of the original work. Most algorithms focus either on the ability to retrieve the original work after watermark detection (invertibility) or on detecting which image parts have been altered (localization). Furthermore, the majority of fragile watermarking schemes suffer from robustness flaws. We propose a new technique that combines localization and invertibility. Moreover, watermark dependency on the original image and the non-linear watermark embedding procedure guarantees that no malicious attacks will manage to create information leaks.