伪球滤波及其在图像特征检测中的应用研究

Pseudosphere function in mathematics has no definition at origin and thus it is incompetent as kernel function of filters. Aiming at overcoming the defect of pseudosphere in filtering, in this project pseudosphere is redefined to be qualified as the kernel function of filters like Gaussian function. For the proposed pseudosphere filter, an feature-preserving parameter is introduced besides a scale parameter, that makes a better trade-off between noise suppression and feature preserving. Furthermore, the pseudosphere filter can be used to improve existing algorithms or develop new algorithms in the field of image feature detection. The main contents of this project include: (1)Redefinition of pseudosphere, which mainly reseaches on how to select a function attached with the pseudosphere to make it satisfy the smoothing condition as the kernel function of filters. (2)Pseudosphere filters, which mainly focus on how to construct different types of pseudosphere filters. (3)Pseudosphere based feature detection, which mainly studies on improving the classic algorithms by replacing Gaussian filter with pseudosphere filter and developing new algorithms of greater performance using the characteristics of pseudosphere. Pseudosphere redefined in this project can be considered as an important supplement to Gaussian function, and thus can be widely used in the field of image feature detection,which is of great significance for promoting the development of image processing.

本课题通过对数学上原点处无定义的伪球进行补充定义，克服原始伪球不能用于滤波的自身缺陷，使其像高斯函数一样能够作为构造滤波器的核函数。基于伪球函数的滤波器不仅具有尺度参数，还增加了特征保持参数，能够更好地解决噪音抑制与特征保持之间的矛盾，可用于改进或设计特征检测算法。本课题的主要研究内容包括：(1)伪球的补充定义，主要研究如何选取合适函数与伪球对接使其满足作为滤波器核函数的光滑条件；(2)伪球滤波器，主要研究各阶伪球滤波器的设计与实现；(3)基于伪球的特征检测，主要研究如何利用伪球滤波改进经典特征检测算法以及如何利用伪球自身特性设计特征检测算法。补充定义后的伪球函数可作为高斯函数的一种重要补充，能够广泛用于图像特征检测领域，对于推动图像处理领域相关技术的发展具有重要意义。

图像特征检测是计算机视觉与图像处理领域最为经典的难点问题之一。特征保持和噪音抑制是所有特征检测算法相互矛盾的两个性能要求。本项目从图像滤波器的核函数出发，引入数学中的伪球函数，构造伪球滤波器，研究伪球的滤波特性及其在图像特征检测方面的应用。主要内容包括：(1)伪球滤波研究，使用拼接后的伪球函数作为核函数，构造自适应伪球滤波器；(2)图像特征检测，利用图形的结构和几何形状信息，实现了任意多边形和规则几何图形的简单快速检测；(3)图像匹配研究，分析直线曲线的尺度空间变化特性与形状尺度特性，提出了基于亮度序的直线曲线匹配描述子。相关成果获得发明专利授权6项；发表SCI收录期刊论文5篇，EI收录期刊论文3篇，其他期刊论文2篇，1篇论文投稿中。本课题的研究成果使得伪球及伪球滤波在图像处理领域成为高斯函数及高斯滤波的一种重要补充，从而丰富图像滤波与特征检测相关理论。