Source Code for Calculating Zernike Invariant Moments Extracted from a Pattern Recognition Toolbox

The following source code is extracted from a pattern recognition toolbox for calculating Zernike invariant moments. This implementation computes n-th order m-repetition Zernike invariant moments for digital images. Zernike moments are mathematical tools used to describe shape and texture features of images, providing rotation-invariant characteristics that make them particularly valuable for pattern recognition applications. The algorithm employs Zernike polynomials as basis functions to achieve orthogonality and rotational invariance. The code typically involves several key computational steps: image preprocessing and normalization, calculation of radial polynomials, and moment computation through integration over the unit disk. Implementation usually includes functions for handling coordinate transformations to map image pixels to the unit circle and efficient computation of complex Zernike polynomials. By utilizing this source code, developers and researchers can better understand and apply Zernike moment concepts and algorithms, providing additional options and enhanced performance for various pattern recognition tasks including image recognition, classification, and analysis. The implementation demonstrates practical application of mathematical moments for feature extraction in computer vision systems.