Computational complexity lower bounds of certain discrete Radon transform approximations

01/03/2018

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by   Timur M. Khanipov, et al.

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For the computational model where only additions are allowed, the Ω(n^2 n) lower bound on operations count with respect to image size n× n is obtained for two types of the discrete Radon transform implementations: the fast Hough transform and a generic strip pattern class which includes the classical Hough transform, implying the fast Hough transform algorithm asymptotic optimality. The proofs are based on a specific result from the boolean circuits complexity theory and are generalized for the case of boolean ∨ binary operation.