基于灰色关联分析的医学图像分割

医学图像分割处理为临床诊断、病理分析、治疗提供可靠的依据。为了分割出图像中感兴趣的区域,提出了一种基于灰色理论区域生长分割算法。该方法利用灰色关联理论对图像进行关联性分析,根据像素间全局和局部的关联度,指导区域生长的分割和停止。该方法的最大不同之处在利用灰色理论进行关联性分析,不需要大量数据的统计,算法简单,高效。实验证明,该方法能够有效地分割出目标区域,并且具有一定的抗噪能力,是一种较为有效的图像分割新方法。     

基于均值漂移和模糊积分融合的高光谱图像分割

针对高光谱图像的特殊性,给出了一种基于均值漂移和模糊积分融合的高光谱图像分割算法。依据高光谱图像各波段间高度的相关性将其分为若干组,通过主成分分析对各波段子集进行降维。在此基础上,采用均值漂移算法计算各波段子集图像的聚类中心进而实现分割,再利用模糊积分融合各波段子集的分割结果。仿真结果证明了该算法的有效性。     

Decay of correlations for the Rauzy-Veech-Zorich induction map on the space of interval exchange transformations and the central limit theorem for the Teichmüller flow on the moduli space of Abelian differentials

The aim of this paper is to prove a stretched-exponential bound for the decay of correlations for the Rauzy-Veech-Zorich induction map on the space of interval exchange transformations. A corollary is the Central Limit Theorem for the Teichmüller flow on the moduli space of abelian differentials with prescribed singularities.

     

Testing equivalence between two laboratories or two methods using paired-sample analysis and interval hypothesis testing

A modified interval hypothesis testing procedure based on paired-sample analysis is described, as well as its application in testing equivalence between two bioanalytical laboratories or two methods. This testing procedure has the advantage of reducing the risk of wrongly concluding equivalence when in fact two laboratories or two methods are not equivalent. The advantage of using paired-sample analysis is that the test is less confounded by the intersample variability than unpaired-sample analysis when incurred biological samples with a wide range of concentrations are included in the experiments. Practical aspects including experimental design, sample size calculation and power estimation are also discussed through examples.     

Local and union boxicity

The boxicity $box\left(H\right)$ of a graph $H$ is the smallest integer $d$ such that $H$ is the intersection of $d$ interval graphs, or equivalently, that $H$ is the intersection graph of axis-aligned boxes in ${\mathbb{R}}^d$. These intersection representations can be interpreted as covering representations of the complement $H^c$ of $H$ with co-interval graphs, that is, complements of interval graphs. We follow the recent framework of global, local and folded covering numbers (Knauer and Ueckerdt, 2016) to define two new parameters: the local boxicity ${box}_{?}\left(H\right)$ and the union boxicity $\overline{box}\left(H\right)$ of $H$. The union boxicity of $H$ is the smallest $d$ such that $H^c$ can be covered with $d$ vertex–disjoint unions of co-interval graphs, while the local boxicity of $H$ is the smallest $d$ such that $H^c$ can be covered with co-interval graphs, at most $d$ at every vertex.We show that for every graph $H$ we have ${box}_{?}\left(H\right)\le \overline{box}\left(H\right)\le box\left(H\right)$ and that each of these inequalities can be arbitrarily far apart. Moreover, we show that local and union boxicity are also characterized by intersection representations of appropriate axis-aligned boxes in ${\mathbb{R}}^d$. We demonstrate with a few striking examples, that in a sense, the local boxicity is a better indication for the complexity of a graph, than the classical boxicity.     

Some bounds on the number of colors in interval and cyclic interval edge colorings of graphs

An interval$t$-coloring of a multigraph $G$ is a proper edge coloring with colors $1,\dots ,t$ such that the colors of the edges incident with every vertex of $G$ are colored by consecutive colors. A cyclic interval$t$-coloring of a multigraph $G$ is a proper edge coloring with colors $1,\dots ,t$ such that the colors of the edges incident with every vertex of $G$ are colored by consecutive colors, under the condition that color $1$ is considered as consecutive to color $t$. Denote by $w\left(G\right)$ ($w_c\left(G\right)$) and $W\left(G\right)$ ($W_c\left(G\right)$) the minimum and maximum number of colors in a (cyclic) interval coloring of a multigraph $G$, respectively. We present some new sharp bounds on $w\left(G\right)$ and $W\left(G\right)$ for multigraphs $G$ satisfying various conditions. In particular, we show that if $G$ is a $2$-connected multigraph with an interval coloring, then $W\left(G\right)\le 1+?\frac{\left|V\left(G\right)\right|}{2}?(\Delta \left(G\right)?1)$. We also give several results towards the general conjecture that $W_c\left(G\right)\le \left|V\left(G\right)\right|$ for any triangle-free graph $G$ with a cyclic interval coloring; we establish that approximate versions of this conjecture hold for several families of graphs, and we prove that the conjecture is true for graphs with maximum degree at most $4$.     

A segmentation procedure of the pervious area of the aorta artery from CT images without contrast medium

In this paper, we develop an algorithm for the segmentation of the pervious lumen of the aorta artery in computed tomography (CT) images without contrast medium, a challenging task due to the closeness gray levels of the different zones to segment. The novel approach of the proposed procedure mainly resides in enhancing the resolution of the image by the application of the algorithm deduced from the mathematical theory of sampling Kantorovich operators. After the application of suitable digital image processing techniques, the pervious zone of the artery can be distinguished from the occluded one. Numerical tests have been performed using 233 CT images, and suitable numerical errors have been computed and introduced ex novo to evaluate the performance of the proposed method. The above procedure is completely automatic in all its parts after the initial region of interest (ROI) selection. The main advantages of this approach relies in the potential possibility of performing diagnosis concerning vascular pathologies even for patients with severe kidney diseases or allergic problems, for which CT images with contrast medium cannot be achieved.     

Generalized linear fractional programming under interval uncertainty

Data in many real-life engineering and economical problems suffer from inexactness. Herein we assume that we are given some intervals in which the data can simultaneously and independently perturb. We consider a generalized linear fractional programming problem with interval data and present an efficient method for computing the range of optimal values. The method reduces the problem to solving from two to four real-valued generalized linear fractional programs, which can be computed in polynomial time using an appropriate interior point method solver.     

Computation of symbolic dynamics for one-dimensional maps

In this paper we design and implement rigorous algorithms for computing symbolic dynamics for piecewise-monotone-continuous maps of the interval. The algorithms are based on computing forwards and backwards approximations of the boundary, discontinuity and critical points. We explain how to handle the discontinuities in the symbolic dynamics which occur when the computed partition element boundaries are not disjoint. The method is applied to compute the symbolic dynamics and entropy bounds for the return map of the singular limit of a switching system with hysteresis and the forced Van der Pol equation.     

Minmax regret approach and optimality evaluation in combinatorial optimization problems with interval and fuzzy weights

This paper deals with a general combinatorial optimization problem in which closed intervals and fuzzy intervals model uncertain element weights. The notion of a deviation interval is introduced, which allows us to characterize the optimality and the robustness of solutions and elements. The problem of computing deviation intervals is addressed and some new complexity results in this field are provided. Possibility theory is then applied to generalize a deviation interval and a solution concept to fuzzy ones.