随机Hough变换的概率模型:有限数据点

Probability Model of Randomized Hough Transform: Limited Data

该文研究了基于有限个数据点的随机 Hough变换的概率模型 .在这个模型中 ,主要讨论了在随机 Hough变换的基本算法中起相当关键作用的两个量 :累加器数组的控制阈值以及从图像中提取全部基元所需随机抽样的总次数 .这两个量对随机 Hough变换的算法设计及其终止规则是相当有用的 .该文的主要结果包括两部分 :其一是对累加器数组引入了多项分布 ,系统地研究了累加器数组的概率结构及其相互关系 .同时也计算了提取全部基元所需的随机抽样总次数的分布、均值和方差 .另者是基于不断的随机抽样而使得累加器数组的随机变化 .作者引入了多维纯生过程 ,证明了提取全部基元所需随机抽样的总次数服从离散的 PH分布 ,从而它的各阶矩都可用简洁的矩阵形式统一地表出 .针对于图像的固有因素 ,作者也讨论了基元的平稳提取概率 .该文的结果为随机

A probability model of randomized Hough transform based on limited data is provided. Firstly, the multinomial distribution related to the accumulator arrays is introduced, and the probability structure of accumulator arrays and their relations is studied. Also, the distribution of the total number of random sampling for extracting all primitives from the images, and its mean and variance are computed. Secondly, multidimensional pure-birth process is applied to describe the changes of the accumulator arrays caused by continuous random sampling. In particular, it is proved that the total number of random sampling for extracting all primitives has a discrete PH distribution, thus a unified and simple matrix algorithm for computing any moments of the total number is also given. Besides, the stable primitive extraction probability is presented in order to describe the inherent properties of the image. Finally, a numerical example is given in order to illustrate the results of this paper.