圆形直方图阈值分割法研究

方向数据统计是数理统计学的重要分支，圆形直方图是单变量方向数据(称为圆形数据)的表示形式，HSI颜色空间的H分量是圆形直方图的示例之一。本项目立足HSI颜色空间的图像分割，研究圆形直方图的阈值分割法及其应用。内容包括：1)基于断点的圆形阈值分割法。通过断点将圆形直方图展成线性直方图，利用线性直方图成熟的阈值选取准则获得阈值；2)基于圆形统计分布的阈值分割法。在圆形直方图上，直接利用统计量给出阈值选取准则；3)基于HSI颜色空间的阈值分割法。立足H分量的周期(循环)特性，结合S分量，给出阈值选取准则。.线性直方图采用线性序，其阈值法研究至今仍是图像分割的热点。圆形直方图采用圆序并涉及模运算，表述和处理难度大，使得圆形阈值法研究具有挑战性。鉴于此，本项目依据圆形直方图的统计分布特性，对圆形直方图阈值选取准则进行探讨，丰富图像阈值分割法的内容，展示圆形直方图阈值具有的重要理论和应用价值。

Statistics of direction data is an important branch of mathematical statistics. Circular histogram is the representation of univariate direction data (called circular data). H component of HSI color space is one of the examples of circular histogram. Based on the image segmentation of HSI color space, this project studies the threshold segmentation methods of circular histogram and its applications. The content includes: 1) Circular threshold segmentation methods based on breakpoint. The circular histogram is expanded into a linearized histogram by appropriate breakpoint, and the threshold is obtained by the mature threshold selection criterions of linear histogram; 2) Circular threshold segmentation methods based on circular statistical distribution. Threshold selection criterions are directly given on the circular histogram by using statistics. 3) Threshold segmentation methods based on the HSI color space. Threshold selection criterions are given based on the period (cycle) characteristics of H component, and combined with the S component.. Linear histogram adopts linear order and the study of threshold segmentation methods is still a hot topic in image segmentation. Circular histogram adopts circular order and involves modular operation, which is difficult to express and process, making the research of circular threshold method challenging. In view of this, based on the statistical distribution characteristics of circular histogram, this project discusses the threshold selection criterias of circular histogram, enriches the content of image threshold segmentation method, and shows the important theoretical and application value of circular histogram thresholding.