Duality Principles in Image Processing and Analysis

Duality is a well-established concept in quantum physics. It formalises the fact that what one observes is not nature in itself, but---in Heisenberg's words---"nature exposed to our method of questioning". In the context of image analysis "question" pertains to some task while "nature" (empirical facts and natural laws) could be taken as the totality of image data supplemented with relevant external factors (knowledge or hypotheses). However, the analogy with quantum physics falls short in at least one fundamental aspect. Whereas the physicist studies nature for nature's sake, endeavouring to reveal natural laws, the image scientist pursues a certain task. This implies a shift of paradigm from the retrospect to the prospect. It will be argued that this leads to a subtle but important difference in the role duality plays in image processing and analysis as compared to the technically similar "bracket" formalism in quantum physics. Duality in the context of image processing and analysis ..