1Fast Generic Polar Harmonic Transforms

Abstract—Generic polar harmonic transforms have recently been proposed to extract rotation-invariant features from images and their usefulness has been demonstrated in a number of pattern recognition problems. However, direct computation of these transforms from their definition is inefficient and is usually slower than some efficient computation strategies that have been proposed for other competing methods. This paper presents a number of novel strategies to compute these transforms rapidly. The proposed methods are based on the inherent recurrence relations among complex exponential and trigonometric functions used in the definition of the radial and angular kernels of these transforms. The employment of these relations leads to recursive and addition chain-based strategies for fast computa-tion of harmonic function-based kernels. Experimental results show that the proposed method is about 10 × faster than direct computation and 5 × faster than fast computation of Zernike moments using the q-recursive strategy. Thus, among all existing rotation-invariant feature extraction methods, polar harmonic transforms are the fastest. Index Terms—Polar harmonic transforms; orthogonal mo-ments; recurrence relation; shortest addition chain; Chebyshev polynomials; fast computation I