Optimal control solutions to the maximum volume isoperimetric pillars problem

This paper extends the isoperimetric problem. The problem is to find an enclosed cross-sectional/base region of a pillar defined by a simple closed curve of fixed perimeter such that the volume of the constructed pillar, bounded above by a relatively smooth ceiling, is maximized. Green’s Theorem is applied in the formulation of the problem such that the problem can be transformed into canonical form handled by MISER3. For the case of multiple pillars, a novel elliptic separation technique is developed for multiple pillars constructions. This technique is used to ensure that the cross-sectional regions of any pillars are separated. Illustrative examples are provided to demonstrate the effectiveness of the technique developed.     

基于视觉感知和等周割的二维阈值分割算法

二维阈值分割方法没有考虑人类视觉感知的特性,将整个灰度级区域作为分割阈值的搜索空间.同时等周割图像分割方法没有直接考虑图像的灰度信息以及迭代终止条件难以确定的问题,因而对灰度图像的分割效果不甚理想.因此提出了一种融合视觉感知和等周割的二维阈值分割方法,该方法首先利用视觉感知的特性选择候选阈值向量所在的灰度区域,再将等周割作为准则,从候选阈值向量中选出最小等周率所对应的候选阈值向量作为最佳的分割阈值向量.在一系列图像上的实验结果表明,与几种经典的二维阈值分割方法相比,所提算法的分割效果更好.     

等周问题的一个证明并用于横截条件的推导

本文首先对古典变分法中条件泛函极值的等周问题给出了一个证法,然后将终端约束条件与等周约束条件联系起来推导横截条件.     

Effcient Mining of Heterogeneous Star-Structured Data

Many of the real world clustering problems arising in data mining applications are heterogeneous in nature. Heterogeneous co-clustering involves simultaneous clustering of objects of two or more data types. While pairwise co-clustering of two data types has been well studied in the literature, research on high-order heterogeneous co-clustering is still limited. In this paper, we propose a graph theoretical framework for addressing starstructured co-clustering problems in which a central data type is connected to all the other data types. Partitioning this graph leads to co-clustering of all the data types under the constraints of the star-structure. Although, graph partitioning approach has been adopted before to address star-structured heterogeneous complex problems, the main contribution of this work lies in an e cient algorithm that we propose for partitioning the star-structured graph. Computationally, our algorithm is very quick as it requires a simple solution to a sparse system of overdetermined linear equations. Theoretical analysis and extensive experiments performed on toy and real datasets demonstrate the quality, e ciency and stability of the proposed algorithm.     

基于图论Isoperimetric算法的岩心图像分割

基于图论的图像分割算法是当前图像分割领域研究的热点,其中归一化分割（Ncut）是一种典型的图论分割算法。但Ncut分割的速度慢,分割结果容易受图像的噪声和虚假边缘的影响,难以应用到实际。为此,提出一种基于图论的等周（Isoperimetric）改进分割算法。该算法使用解线性方程的方法代替解特征向量的方法、用4-邻接的方法代替全连接,避免了复杂的空间滤波。该算法运用到岩心图像分割中,提高了分割的效率,取得了较好的分割效果。