调节数学形态学算子分析及其应用研究

在G ady A gam等人工作的基础上,结合结构元素和约束参数的选择,对调节形态学基本算子进行了一定的分析,得到了几个等价定义和一个颇有意义的结论.最后结合实例,比较了调节形态学与普通形态学对噪声图像处理的结果和性能.实验结果表明,这种新形态学算子比经典形态学算子具有更好的噪声抑制能力.     

数学形态学中结构元素的分解

本文讨论了数学形态学中结构元素的分解问题(B=B_1⊕…⊕B_n)并给出了一系列结果。本文的重点是二维结构元素的1-D分解和点对分解。且相应的可分解必要条件和分解算法被提出。我们的算法是高效的,它们的时间复杂度均为o(n~2),这里n是被分解结构元素中点的个数。     

基于数学形态学与Radon变换的车牌定位法

从粗定位和精定位方面考虑车牌定位.利用腐蚀、膨胀和差运算将RGB车牌图像转换为车牌图像位置为彩色的而其余位置是灰色的图像,将所获得的图像转化为灰度图像,利用Robert算子进行边缘检测,再进行腐蚀和膨胀运算,根据阈值获得连通区域,利用颜色特征实现车牌的粗定位.将粗定位后的图像进行二值化、差运算、Radon变换,再进行腐蚀运算,图像的填充等步骤,再考虑图像的上下左右边界实现车牌的精定位,对185幅车牌图像进行定位.通过实验,车牌定位准确率达到91.89%.说明所提出的方法简单易行,具有一定的实效性.     

基于数学形态学滤波的多刻度法

本文主要讨论了用数学形态学开运算滤波形成二维图形的刻度空间图象,给出了保证开滤波单调性的定理,即当开滤波参数从较细刻度向粗刻度变化时,作为图象特征的过零点数目不增。所得结论不同于Poggio等人关于Gauss滤波器是唯一具有这种单调性的滤波器之结论。此外,开滤波运算的计算量比Gauss滤波要少得多。     

基于完备格的模糊数学形态学

数学形态学被广泛应用于信号与图像处理。本文在完备格的框架下,利用模糊逻辑运算及其伴随,给出模糊数学形态学运算的定义,并深入讨论了这些运算的性质。特别是,由这种途径定义的模糊形态学,模糊闭和模糊开具有很好的性质。本文还探讨了模糊形态学运算和古典形态学运算之间的关系。     

二值形态运算的感知器模型及其应用

给出了二值形态运算模型与感知器模型之间的关系.以此为基础对传统的二值数学形态学基本运算进行了推广,建立了基于感知器的形态运算模型.新的模型为传统的二值形态运算赋予了可调节机制.计算机模拟实验表明该方法较传统的二值形态运算有效.     

基于混合单纯形算法的模糊均值图像分割

针对模糊C均值算法用于图像分割时对初始值敏感、容易陷入局部极值的问题,提出基于混合单纯形算法的模糊均值图像分割算法.算法利用Nelder-Mead单纯形算法计算量小、搜索速度快和粒子群算法自适应能力强、具有较好的全局搜索能力的特点,将混合单纯形算法的结果作为模糊C均值算法的输入,并将其用于图像分割.实验结果表明:基于混合单纯形算法的模糊均值图像分割算法在改善图像分割质量的同时,提高了算法的运行速度.     

求解图像分割CV模型的BB算法

给出图像分割的一种新算法——BB算法.该方法的优点在于利用迭代过程中当前点和前一点的信息确定搜索步长,从而更有效地搜索最优解.为此,首先通过变分水平集方法将CV模型转化为最优化问题;其次,将BB算法引入该优化问题进行求解;然后,对BB算法进行收敛性分析,为该算法应用在CV模型中提供了理论依据;最后将该方法与已有的最速下降法、共轭梯度法的分割结果进行比较.结果表明,跟其他两种方法相比,BB算法在保证较好分割效果的前提下,提高了算法的速度和性能.     

基于微分进化算法的FCM图像分割算法

为提高模糊C均值(FCM)算法的自动化程度,提出基于微分进化算法的FCM图像分割算法(DEFCM),利用微分进化算法全局性和鲁棒性的特点自动确定分类数和初始聚类中心,再将其作为模糊c均值聚类的初始聚类中心,弥补FCM算法的不足.实验表明该算法不仅能够正确地对图像分类,而且能获得较好的图像分割效果和质量.     

基于混合细菌趋药性的聚类分割算法

为解决模糊C均值算法对初始值敏感、容易陷入局部极值的问题,提出基于混合细菌趋药性的聚类分割算法,在简单细菌趋药性算法的基础上,将粒子群算法引入.新算法使用粒子群算法、细菌趋药性算法两步优化得到的结果作为模糊C均值算法的初始值,同时新算法中引入精英保持策略,进一步提高算法效率.实验结果表明,新算法具有较快的收敛速度,.同时能够获得较好的图像分割效果和质量.     

A Fritz John Approach to First Order Optimality Conditions for Mathematical Programs with Equilibrium Constraints

Mathematical programs with equilibrium constraints (MPECs) are nonlinear programs which do not satisfy any of the common constraint qualifications. In order to obtain first order optimality conditions, constraint qualifications tailored to MPECs have been developed and researched in the past. This has been done by falling back on technical proofs or results from nonsmooth analysis. In this article, we use a completely different approach and show how the standard Fritz John conditions may be used in order to obtain short and elementary proofs for the most important optimality conditions for MPECs. As a by-product, we obtain a new stationarity concept.     

A Multiscale Approach for Statistical Characterization of Functional Images

Increasingly, scientific studies yield functional image data, in which the observed data consist of sets of curves recorded on the pixels of the image. Examples include temporal brain response intensities measured by fMRI and NMR frequency spectra measured at each pixel.

This article presents a new methodology for improving the characterization of pixels in functional imaging, formulated as a spatial curve clustering problem. Our method operates on curves as a unit. It is nonparametric and involves multiple stages: (i) wavelet thresholding, aggregation, and Neyman truncation to effectively reduce dimensionality; (ii) clustering based on an extended EM algorithm; and (iii) multiscale penalized dyadic partitioning to create a spatial segmentation. We motivate the different stages with theoretical considerations and arguments, and illustrate the overall procedure on simulated and real datasets. Our method appears to offer substantial improvements over monoscale pixel-wise methods.

An Appendix which gives some theoretical justifications of the methodology, computer code, documentation and dataset are available in the online supplements.     

A Mathematical Model of Intermittent Androgen Suppression for Prostate Cancer

For several decades, androgen suppression has been the principal modality for treatment of advanced prostate cancer. Although the androgen deprivation is initially effective, most patients experience a relapse within several years due to the proliferation of so-called androgen-independent tumor cells. Bruchovsky et al. suggested in animal models that intermittent androgen suppression (IAS) can prolong the time to relapse when compared with continuous androgen suppression (CAS). Therefore, IAS has been expected to enhance clinical efficacy in conjunction with reduction in adverse effects and improvement in quality of life of patients during off-treatment periods. This paper presents a mathematical model that describes the growth of a prostate tumor under IAS therapy based on monitoring of the serum prostate-specific antigen (PSA). By treating the cancer tumor as a mixed assembly of androgen-dependent and androgen-independent cells, we investigate the difference between CAS and IAS with respect to factors affecting an androgen-independent relapse. Numerical and bifurcation analyses show how the tumor growth and the relapse time are influenced by the net growth rate of the androgen-independent cells, a protocol of the IAS therapy, and the mutation rate from androgen-dependent cells to androgen-independent ones.

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证券投资基金管理人选择中的信号传递博弈

本文通过对证券投资基金这种资金运作方式的分析和研究,结合信号传递博弈模型,提出一种对资金管理人投资能力的评估方法.主要分析基金管理人的努力成本对最后投资能力评估结果的影响,为投资人选择基金管理人提供新的思路,也为基金管理人争取融资成功提供一定的帮助.     

Combination of Statistical Similarity Measure and Derivative Morphological Profile Approach for Oil Slick Detection in SAR Images

Synthetic Aperture Radar (SAR) is widely used to detect and monitor oil pollution on the sea surface. As it is sensitive to surface roughness, the presence of oil film on the sea surface decreases the backscattering of this target type resulting in a dark feature patches in SAR images. In this paper, a new approach for oil slicks detection is presented. It is mainly based on SAR image texture analysis using the combination of a statistical similarity measure and a derivative morphological profile. Oil slicks signature is extracted trough two steps procedure. First, SAR image inspection is performed in order to highlight the dark spots suspected to be oil slicks. The inspection is achieved through a similarity measure between a local probability density function (lpdf) of clean water and the lpdf of the area to be inspected. The local distribution is estimated in the neighbourhood of each pixel and compared to a reference one using the Kullback-Leibler KL distance between distributions. Second, and once spots highlighted, texture features extraction using the Derivative Morphological Profile is porformed in order to improve the detection results. algorithm has been applied to Envisat Advanced Synthetic Aperture Radar (ASAR) and European Remote Sensing (ERS) images and it yields an accurate segmentation results. Indeed, the features extraction improves the detection slicks probability Pd of ASAR, respectively ERS, images from 93.08 %to 97.37 %and from 96.32 to 99.57 % on one hand, and reduces the false alarms probability respectively from 6.92 to 2.63 %and from 3.68 to 0.59 % on the other hand.     

A Mathematical Programming Incremental Formulation for Unilateral Frictional Contact Problems of Linear Elasticity

In this article a detailed analytical formulation of the unilateral contact boundary conditions with Coulomb's law of dry friction is first attempted and the quasi-static contact problem between 3-D elastic bodies is studied thereafter. Discretizing the bodies by the Finite Element Method, introducing fictitious contact bonds and using the concept of the equivalent structural system, an incremental Nonlinear Complementarity Problem is finally formulated. Then, using additional simplifying assumptions, this problem can be transformed into an incremental Linear Complementarity Problem.     

Using Conventional Edge Detectors and Postsmoothing for Segmentation of Spotted Microarray Images

Segmentation of spotted microarray images is important in generating gene expression data. It aims to distinguish foreground pixels from background pixels for a given spot of a microarray image. Edge detection in the image processing literature is a closely related research area, because spot boundary curves separating foregrounds from backgrounds in a microarray image can be treated as edges. However, for generating gene expression data, segmentation methods for handling spotted microarray images are required to classify each pixel as either a foreground or a background pixel; most conventional edge detectors in the image processing literature do not have this classification property, because their detected edge pixels are often scattered in the whole design space and consequently the foreground or background pixels are not defined. In this article, we propose a general postsmoothing procedure for estimating spot boundary curves from the detected edge pixels of conventional edge detectors, such that these conventional edge detectors together with the proposed postsmoothing procedure can be used for segmentation of spotted microarray images. Numerical studies show that this proposal works well in applications.

Datasets and computer code are available in the online supplements.