基于可交换Clifford代数的彩色图像矩不变量研究

矩不变量被广泛应用于图像处理、计算机视觉与模式识别等领域。目前，国内外有关这方面的研究成果基本上都是针对灰度图像的，有关彩色图像矩不变量的研究尚处于起步阶段。如何构造彩色图像的矩不变量是本项目将要解决的核心问题。本项目拟采用具有可交换性质的Clifford代数来对彩色图像进行建模，研究可交换Clifford代数层面上彩色图像的矩函数及其不变量的构造。预期构造出彩色图像的相似和仿射矩不变量以及光照条件变化时的矩不变量。本项目研究的意义就在于它将增加我们对可交换Clifford代数的认识，同时为探索在更广泛代数系统上矩不变量的构造规律奠定了理论基础。这一项目的研究为将来利用可交换Clifford代数实现彩色图像处理及其在计算机视觉与模式识别领域的应用研究提供了一个新的发展方向。

Moment invariants have been widely applided in the fields of image processing, computer vision and pattern recognition. However, most of existing moment invariants are focused on the grayscale image, and the study of corresponding theory for color image is still in the infancy stage. How to construct moment invariants for color image is the main concern in this proposal. We plan to adopt commutative Clifford algebra to represent a color image, study the moment function and its invariants for color image. This proposal aims to constructing the color image moment invariants under the condition of geometric transform, such as similarity and affine transforms, and illumination. The significant of this research is that we can get a better understanding of commutative Clifford algebra, and lay a theoretical foundation for the study of constructing moment invariants in a more extensive algebra system. This research will give us an outlook for the application of commutative Clifford algebra in the fields of color image processing, computer vision and pattern recognition.