随机Hough变换的概率模型:有限数据点

该文研究了基于有限个数据点的随机Hough变的的概率模型，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，有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Hough变换的进一步研究和应用提供了较为严格的理论依据。

Probability Model of Randomized Hough Transform: Limited Data

In this paper, we provide a probability model of randomized Hough transform based on limited data. In this model, we mainly discuss the two crucial quantities: the control threshold value of the accumulator arrays and the total number of random sampling for extracting all the primitives from the image. The two quantities are quite useful for designing some effective algorithms of randomized Hough transform and determining their stopping rule. The main result of this paper contains two parts. Firstly, we introduce the multinomial distribution related to the accumulator arrays, and study the probability structure of accumulator arrays and their relations. Also, we compute the distribution of the total number of random sampling for extracting all primitives from the images, and its mean and variance. Secondly, we apply multidimensional pure-birth process to describe the changes of the accumulator arrays caused by continuous random sampling. In particular, we prove that the total number of random sampling for extracting all primitives has a discrete PH distribution, thus we also give a unified and simple matrix algorithm for computing any moments of the total number. Besides, we present the stable primitive extraction probability in order to describe the inherent properties of the image. Finally, we give a numerical example in order to illustrate the results of this paper. This paper gives a stricter theory foundation of randomized Hough transform with respect to further theory research and applications.