Commutative Clifford algebra method for color image processing
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摘要: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Cl2com,定义了Cl2com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Cl2com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。
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关键词:
- 彩色图像/
- 图像处理/
- 可交换性/
- Clifford代数
Abstract:By using the commutative Clifford algebra method to model for a color image, the parallel processing of R, G and B components in the color image can be realized in a holistic manner and the integrating processing for the color image can be implemented. This paper reviews the progress of color image modeling, researches a type of commutative Clifford algebra, namely Cl2com and gives the definitions of the arithmetic operations, 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 application 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 processing tasks as a useful tool.-
Key words:
- color image/
- image processing/
- commutativity/
- Clifford algebra
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