1 September 1999 Image factorization: a new hierarchical decomposition technique
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Optical Engineering, 38(9), (1999). doi:10.1117/1.602202
A new method of image decomposition is described. It uses a depth-of-contrast approach in which the image is factored into an ordered set of component images, the order being from coarse to fine in degree of contrast. The decomposition technique is unique in that it is completely independent of any geometrical structure, yet its application shows a clear trend from coarse to fine spatial frequency with the degree of contrast. For images with spatial structure and noise, the first factors contain more of the geometrical structure and the higher-level factors contain more of the noise. The factorization is expressed as an infinite product rather than as an infinite sum, and its convergence is shown. A conservative lower bound is derived that ensures that any positive definite real image can be fully factored.
John L. Johnson, Jaime R. Taylor, "Image factorization: a new hierarchical decomposition technique," Optical Engineering 38(9), (1 September 1999). https://doi.org/10.1117/1.602202


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