Fast Hypercomplex Polar Fourier Analysis

Abstract

SUMMARYHypercomplex polar Fourier analysis treats a signal as a vector field and generalizes the conventional polar Fourier analysis. It can handle signals represented by hypercomplex numbers such as color images. Hypercomplex polar Fourier analysis is reversible that means it can reconstruct image. Its coefficient has rotation invariance property that can be used for feature extraction. However in order to increase the computation speed, fast algorithm is needed especially for image processing applications like realtime systems and limited resource platforms. This paper presents fast hypercomplex polar Fourier analysis based on symmetric properties and mathematical properties of trigonometric functions. Proposed fast hypercomplex polar Fourier analysis computes symmetric points simultaneously, which significantly reduce the computation time. key words: fast hypercomplex polar Fourier analysis, hypercomplex polar Fourier analysis, Fourier analysis

Quaternion generic Fourier descriptor for color object recognition

“…A hypercomplex polar Fourier descriptor, which can be utilized to represent and reconstruct images, was proposed by Yang and Kamata [23] using basis functions. And in the following research, they reported the fast computational version of the descriptor [24]. Chen et al [25] extended the conventional Zernike moment defined in gray-scale image to color image using the algebra of quaternions in 2012.…”