Over 50 Years of Image Moments and Moment Invariants

Abstract

This chapter aims to analyze the research eld of moments and moment invariants in a holistic way. Initially, a literature analysis of the last 50 years is presented and discussed in order to highlight the potential of this topic and the increasing interest in many disciplines. A more in depth study of the issues addressed through the years by the researchers is next presented both in theory and applications of moments. The most representative works in each research direction are discussed in a chronological order to point out the progress in each specic eld of action. This analysis concludes with the challenges and perspectives that should motivate researchers towards the promotion of the moments and their invariants to new scientic horizons. For the rst time, this chapter gives a global overview of what happened in the last 50 years in moments and moment invariants research eld, but most of all it brings to light the open issues that should be addressed and highlights the rising topics that will occupy the scientists in the coming years. This chapter serves as a guide to those who nd the eld of moments and moment invariants a brilliant eld of action since it encloses all the milestones of this eld.

Fuzzy knowledge-based adaptive image watermarking by the method of moments

“…Orthogonal image moments have gained significant attention as compact content descriptors with minimum information redundancy [9], in pattern recognition [10], computer vision [11][12][13] and image processing [14] applications.…”

“…Another popular, moment-based watermarking research area is the watermarking of color images. Following the successful application of several quaternionic image transformations in image watermarking [6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23][24][25], Tsougenis et al [26] introduced quaternion radial moments as the embedding domain of the color images for watermark insertion. Wang et al [27] studied the quaternion exponent moments as alternative moment domain for color image watermarking to improve robustness.…”

Accelerating Computation of Zernike and Pseudo-Zernike Moments with a GPU Algorithm

“…Computational efficiency and numerical accuracy are two major issues involved in the research of Zernike moments and pseudo-Zernike moments [3,21]. Different methods have been proposed to calculate the two kinds of moments more efficiently and accurately [2, 7-10, 20, 23-26].…”

“…Image moments are real or complex-valued scalar quantities that describe the pixels distribution of an image [3,15]. Mathematically, moments can be seen as projections of a image function onto a polynomial basis.…”

“…Zernike moments and pseudo-Zernike moments are orthogonal moments defined on a circular domain. They are widely applied in many scientific areas, such as image analysis, pattern recognition, and watermarking [3].…”