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Discrete scale spaces via heat equation

Anderson CunhaRalph TeixeiraLuiz Velho

Scale spaces allow us to organize, compare and analyse differently sized structures of an object. The linear scale space of a monochromatic image is the solution of the heat equation using that image as an initial condition. Alternatively, this linear scale space can also be obtained applying Gaussian filters of increasing variances to the original image. In this work, we compare (by looking at theoretical properties, running time and output differences) three ways of discretizing this Gaussian scale-space: sampling Gaussian distributions; approximating by first-order generators; and finally, by a new method we call "Crossed Convolutions".In particular, we explicity present a corret way of initializing the recursive method approximate Gaussian convolutions.

http://sibgrapi.sid.inpe.br/rep-/sid.inpe.br/banon/2002/11.29.10.44

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