Automatic leukocyte nucleus segmentation by intuitionistic fuzzy divergence based thresholding

The paper proposes a robust approach to automatic segmentation of leukocyte's nucleus from microscopic blood smear images under normal as well as noisy environment by employing a new exponential intuitionistic fuzzy divergence based thresholding technique. The algorithm minimizes the divergence between the actual image and the ideally thresholded image to search for the final threshold. A new divergence formula based on exponential intuitionistic fuzzy entropy has been proposed. Further, to increase its noise handling capacity, a neighborhood-based membership function for the image pixels has been designed. The proposed scheme has been applied on 110 normal and 54 leukemia (chronic myelogenous leukemia) affected blood samples. The nucleus segmentation results have been validated by three expert hematologists. The algorithm achieves an average segmentation accuracy of 98.52% in noise-free environment. It beats the competitor algorithms in terms of several other metrics. The proposed scheme with neighborhood based membership function outperforms the competitor algorithms in terms of segmentation accuracy under noisy environment. It achieves 93.90% and 94.93% accuracies for Speckle and Gaussian noises, respectively. The average area under the ROC curves comes out to be 0.9514 in noisy conditions, which proves the robustness of the proposed algorithm.     

递归 IFS维数公式的推广

在文 [1]中 , Barnsley等在关联矩阵不可约的条件下 ,得到了递归 IFS的分形维数公式 ,本文证 明 ,在去掉关联矩阵为不可约的限制条件之后 ,维数公式仍是成立的.     

Construction of recurrent bivariate fractal interpolation surfaces and computation of their box-counting dimension

Recurrent bivariate fractal interpolation surfaces (RBFISs) generalise the notion of affine fractal interpolation surfaces (FISs) in that the iterated system of transformations used to construct such a surface is non-affine. The resulting limit surface is therefore no longer self-affine nor self-similar. Exact values for the box-counting dimension of the RBFISs are obtained. Finally, a methodology to approximate any natural surface using RBFISs is outlined.     

一种高速自适应分形图像编码算法

提出利用四叉树自适应图像划分、源块池柔性分类并结合人类视觉特性的高速分形图像编码算法．与其它同类算法相比，该算法在编码速度、压缩比和图像质量等方面均有显著提高．     

Absolute continuity of vector-valued self-affine measures

This paper is devoted to the absolute continuity of (scalar-valued or vector-valued) self-affine measures and their properties on the boundary of an invariant set. We first extend the definition of WSC to self-affine IFS, and then obtain a necessary and sufficient condition for the vector-valued self-affine measures to be absolutely continuous with respect to the Lebesgue measure. In addition, we prove that, for any IFS and any invariant open set V, the corresponding (scalar-valued or vector-valued) invariant measure is supported either in V or in ∂V.     

IFS ON BOUNDARIES OF HOMOGENEOUS TREES:WQB CONDITION AND MULTIFRACTAL ANALYSIS

We study, from the point of view of the multifractal analysis, iterated function systems on totally disconnected spaces, namely, the boundaries of homogeneous trees. In particular, we study in this setting the ＂weak quasi-Bernoulli property introduced by Testud [3, 4]. After projection on R or R2, we get new examples of self-similar measures which being WQB, obey the multifractal formalism for positive q,s.     

Vector-valued Ruelle operator with weakly contractive IFS

The vector-valued Ruelle operator defined by contractive iterated function systems (IFS) was discussed by the author [Y.L. Ye, Vector-valued Ruelle operator, J. Math. Anal. Appl. 299 (2004) 341-356]. In this paper we consider vector-valued Ruelle operators defined by weakly contractive IFS. And, a vector-valued analogue of the Ruelle-Perron-Frobenius theorem for the scalar Ruelle operator is set up. Our theorem gives a sufficient condition for the vector-valued Ruelle operator to be quasi-compact. Under this sufficient condition, we prove that the rate of convergence of the iterated operators is exponential.     

改进分形模型的图像降噪算法

利用分形几何中的迭代函数系统理论，针对空间域建立图像分形模型存在相似匹配速度慢的缺点，提出了一种变换域的改进分形模型方法，该方法用频域的搜索匹配代替空间域的搜索匹配，不但域块和区块达到相似匹配的速度更快，而且可以自适应的调整参与计算相似匹配的参数个数．实验结果表明改进的分形模型应用于图像降噪不但可以有效的保护图像的细节和边缘信息，并避免原方法在降噪的同时带来块效应的缺点．