MATLAB Implementation of Zernike Moments with Code Description

Zernike moments are image feature descriptors based on Zernike polynomials, known for their rotation invariance and noise resistance, widely applied in image analysis and pattern recognition domains.

Core implementation approach: The main function handles parameter validation and workflow control, determining processing mode (single-order or full-order moment computation) based on input parameter count. Image preprocessing stages include: - Grayscale conversion (for RGB images) using rgb2gray() function - Coordinate normalization to unit circle through linear mapping - Removal of invalid pixel regions using circular masking Zernike polynomial computation employs radial polynomials in polar coordinates, optimized with recursive relations for computational efficiency. Moment calculation uses discrete summation to approximate integration, performing weighted accumulation for each valid image pixel.

Key subroutine functionalities: - Order validity check: Ensures Zernike moment orders n and repetition m satisfy n≥|m| with n-|m| being even through conditional statements - Radial polynomial computation: Implements orthogonal basis function construction using recurrence relations - Unit circle mapping: Transforms image pixel coordinates to [-1,1]×[-1,1] range via coordinate scaling - Complex moment combination: Combines real and imaginary parts into complex-valued moment descriptors using complex() function

Visualization components: Result presentation includes three graphical components: - Original input image superimposed with unit circle mask using imshow() and viscircles() - 3D surface plots of different-order Zernike polynomials via surf() function - Reconstructed image comparison (verifying moment completeness through inverse transformation) using inverse Zernike moment calculation

Usage recommendations: - For large-sized images, implement downsampling using imresize() to improve computation speed - Numerical instability may occur when computing high-order moments (n>15) due to polynomial growth - For biomedical image analysis, recommend using 3-8 order moment combinations for optimal feature extraction