Accurate and Efficient Computation of High Order Zernike Moments

Abstract

Abstract. Zernike Moments are useful tools in pattern recognition and image analysis due to their orthogonality and rotation invariance property. However, direct computation of these moments is very expensive, limiting their use especially at high orders. There has been some efforts to reduce the computational cost by employing quantized polar coordinate systems, which also reduces the accuracy of the moments. In this paper, we propose an efficient algorithm to accurately calculate Zernike moments at high orders. To preserve accuracy, we do not use any form of coordinate transformation and employ arbitrary precision arithmetic. The computational complexity is reduced by detecting the common terms in Zernike moments with different order and repetition. Experimental results show that our method is more accurate than the other methods and it has comparable computational complexity especially in case of using large images and high order moments.

Shape Based Image Retrieval using Lower Order Zernike Moments

“…There is a great need to limit their use at higher orders. The cause behind is not only a computational complexity, but also highly sensitive to noise [11], [12]. The performance of the system may diminish if the order and moment are chosen properly.…”

Image Analysis Using Radial Bi-Tchebichef Moments

“…,, Amayeh's method [5], Chong's method [6] and Xin's method [7] are proposed to reduce the complexity of Zernike radial polynomials. …”

Semantic Image Retrieval Using Multiple Features

“…In this paper, we have used Zernike [7] moment to demonstrate shape feature. We first apply Scale Invariant feature Transform (SIFT) [8] method to all images and then apply shape feature to avoid any scaling effect and to produce better results.…”