Research And Application Of Image Moment Invariants

If we consider a binary or a gray level image as a two-dimensional density distribution function, moment invariants may be used to describe characteristic information of a digital image and may be used in image analysis. Moment invariants with the description of the image statistics and global characteristic information have become a hot focus at present and have aroused great attention. Researchers have got some research achievements. However, moment invariants’ research still encountered some difficulties that have to be overcome, such as, moment invariants are defined under the two-dimensional continuous density distribution function, but the computer stored and processed digital images. If we directly calculate moment invariants, they generate numerical errors and influenced the accuracy of the calculation results. If we calculate moment invariants according to the definition formula, they will produce a phenomenon with high complexity and low efficiency, and not meet the requirements of real-time in some application fields, so it is necessary to study their fast algorithm. For these problems of studying moment invariants, it is necessary to continually study image moment invariants and their applications.In this article, we first summarize the definition and properties of moment invariants and compare and evaluate the performance of moment invariants in image representation, noise sensitivity, and information redundancy. We find that Zernike moments are the best on the overall performance. We normalized Zernike moments, so that the amplitude of Zernike moments has RST invariance. Because the accuracy of Zernike moments is not high in the past, there are numerical errors consists of numerical integration error and geometric error in the calculation process. By rearrangement of pixels in polar coordinates, we eliminate errors and improve the accuracy. By improving the fast algorithm of square-to-circular transformation, we greatly improve the computational efficiency of Zernike moments. According to the method of structuring the feature vector, we select the appropriate Zernike moment to structure the feature vector. We use the feature vector to math or identify digital images. Zernike moments are used in the digital image watermarking technique and license plate recognition finally.