Junction detection and filtering

Models for image smoothing have not fully incorporated the restrictions imposed by the physics of image generation. In particular, any image smoothing process should respect the essential singularities of images (which we call junctions) and should be invariant with respect to contrast changes. We conclude that local image smoothing is possible provided singular points of the image have been previously detected and preserved. We define the associated degenerate partial differential equation and sketch the proof of its mathematical validity. Our analysis uses the phenomenological theory of image perception of Gaetano Kanizsa, whose mathematical translation yields an algorithm for the detection of the discontinuity points of digital images.

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