Abstract

We present a general method to derive robust invariants of grayscale images under affine geometric transformation. In the literature, there are well studied affine moment invariants of grayscale images. The problem is that only few of the invariants are low orders. Higher order affine moment invariants are sensitive to noise and hard to implement. In this paper, we extend the traditional definition of the geometric moment by encapsulating the image functions by some wrapper functions. A general theorem to construct the affine invariants consisting of the extended moments of a grayscale image is presented. Using this method, different forms of low order affine moment invariants are constructed. The traditional affine moment invariants are a special type of the proposed new affine moment invariants. These forms of invariants are less sensitive to noise and easy to implement.DOI: http://dx.doi.org/10.5755/j01.eee.19.1.3262

Highlights

  • Invariants of an image are functions of the image that remain the same under some changes to the image [1]–[7]

  • We prove a general theorem for constructing affine moment invariants with respect to the generalized moments of images

  • We have presented a novel method to construct affine moment invariants of grayscale images through the generalized moments of images

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Summary

A Novel Form of Affine Moment Invariants of Grayscale Images

Abstract—We present a general method to derive robust invariants of grayscale images under affine geometric transformation. Higher order affine moment invariants are sensitive to noise and hard to implement. A general theorem to construct the affine invariants consisting of the extended moments of a grayscale image is presented. Using this method, different forms of low order affine moment invariants are constructed. The traditional affine moment invariants are a special type of the proposed new affine moment invariants. These forms of invariants are less sensitive to noise and easy to implement

INTRODUCTION
Moments
Invariants of Geometric Moments under Affine Transformation
Invariants of Geometric Moments under Similarity Transformation
GENERALIZED GEOMETRIC MOMENTS
INVARIANTS OF GENERALIZED MOMENTS UNDER AFFINE TRANSFORMATION
EXPERIMENTS
CONCLUSIONS

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