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Color digital images are made of pixels, and pixels are made of combinations of primary colors represented by a series of code. A channel in this context is the grayscale image of the same size as a color image, made of just one of these primary colors. For instance, an image from a standard digital camera will have a red, green and blue channel. A grayscale image has just one channel.
In geographic information systems, channels are often referred to as raster bands. Another closely related concept is feature maps, which are used in convolutional neural networks.