Quaternion angular radial transform and properties transformation for color-based object recognition

Abstract

Nowadays, with the increased use of digital images, almost all of which are in color format. Conventional methods process color images by converting them into gray scale, which is definitely not effective in representing and which may lose some significant color information. Recently, a novel method of the Color Angular Radial Transform (CART) is presented. This transform combines the information by considering the shape information inherent in the color. However, ART is adapted on the MPEG-7 standard is only limited to binary images and gray-scale images has many properties: invariant to rotation, Translation and scaling, ability to describe complex objects, so it cannot handle color images directly. To solve this problem we proposed in this article to generalize ART from complex domain to hypercomplex domain using quaternion algebras to achieve the Quaternion Angular Radial Transform (QART) to describe finally two dimensional color images and to insure these properties robustness to all possible rotations and translation and scaling. The performance of QART is then evaluated with large database of color image as an example. We first provide a general formula of ART from which we derive a set of quaternion-valued QART properties transformations by eliminating the influence of transformation parameters. The experimental results show that the QART performs better than the commonly used Quaternion form Zernike Moment (QZM) in terms of image representation capability and numerical stability.