彩色图像处理的可交换 Clifford 代数方法

采用可交换Clifford代数对彩色图像建模，充分利用彩色图像作为一个整体所具有的潜在颜色信息，实现彩色图像各颜色分量的并行处理，可完成彩色图像的整体处理。本文分析了彩色图像的表示方法，系统研究了一类可交换Clifford代数-Clcom2，定义了Clcom2上元素的四则运算规则、单位元、逆元、共轭、范数等。给出了基于可交换Clifford代数的彩色图像表示方法，并介绍了一个Clcom2架构下的彩色图像处理实例：彩色图像边缘检测。与传统的四元数彩色图像表示方法相比，本文所提出的方法最大限度地去除了数据冗余，其算法复杂度也大大降低。结果显示，基于可交换Clifford代数的彩色图像表示方法可以应用到彩色图像处理中。

Commutative Clifford algebra method for color image processing

By using the commutative Clifford algebra method to model for a color image , the parallel process-ing of R, G and B components in the color image can be realized in a holistic manner and the integrating pro-cessing for the color image can be implemented .This paper reviews the progress of color image modeling , re-searches a type of commutative Clifford algebra , namely Clcom2 and gives the definitions of the arithmetic opera-tions, unit element , inverse element , conjugation, and the norm for the commutative Clifford algebra .Then, it describes the expression of the color image based on the commutative Clifford algebra and introduces an ap -plication example of this method：the edge detection of color image .In comparison with the quaternion-based color image modeling , the proposed method can remove the data redundancy and reduce the computational complexity to the utmost extent .The proposed color image modeling method can be applied in color image pro-cessing tasks as a useful tool .