We present a new theoretical approach to the processing of multidimensional and multicomponent images based on the theory of commutative hypercomplex algebras, which generalize the algebra of complex numbers. The main goal of the paper is to show that commutative hypercomplex numbers can be used in multichannel image processing in a natural and effective manner. We suppose that animal brains operate with hypercomplex numbers when processing multichannel retinal images. In our approach, each multichannel pixel is regarded as a \(K\)-dimensional (\(K\)D) hypercomplex number rather than a \(K\)D vector, where \(K\) is the number of different optical channels. This creates an effective mathematical basis for various function–number transformations of multichannel images and invariant pattern recognition.

我们提出了一种基于交换超复代数理论的多维和多分量图像处理的新理论方法，该理论概括了复数的代数。该论文的主要目标是表明可交换超复数可以以自然有效的方式用于多通道图像处理。我们假设动物大脑在处理多通道视网膜图像时使用超复杂数。在我们的方法中，每个多通道像素被视为一个\(K\)维（\(K\) D) 超复数而不是\(K\) D 向量，其中 \(K\)是不同光通道的数量。这为多通道图像的各种函数-数变换和不变模式识别创造了有效的数学基础。