This chapter discusses the decomposition of the image by direction images, which is based on the concept of the tensor representation and its advanced form, the paired representation [41]-[48]. The 2-D image is considered to be of the size N × N, where N is prime, a power of two, and a power of odd prime. The tensor and paired representations in the frequency-and-time domain define the image as a set of 1-D splitting-signals. Each of such splitting-signals is calculated as the sum of the image along the parallel lines, and it defines the direction image as a component of the original image. The unique decomposition of the image by direction images is described and formulas for the inverse tensor and paired transforms are ...
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