MATLAB Implementation of 7 Hu Moments

Below, I present MATLAB code for computing 7 invariant moments for reference. These invariant moments represent special matrix descriptors with significant applications in machine vision and computer graphics. The provided code demonstrates both basic moment calculations and normalized central moments, helping you gain deeper understanding of invariant moments and their implementation. If you're interested in MATLAB programming and applications of invariant moments, this code will be particularly useful. The implementation includes a function for calculating normalized central moments, which are crucial for achieving scale and translation invariance. The algorithm first computes the centroid (x_bar, y_bar) of the binary image using raw moments, then iterates through all pixels to calculate central moments relative to the centroid. The normalization step ensures invariance to scale changes by dividing by an appropriate power of the zero-order moment. Here's the core MATLAB function: % Calculate normalized central moments function [mu, nu] = normalized_moments(binary_image, p, q) [rows, cols] = size(binary_image); x_bar = moment(binary_image, 1, 0) / moment(binary_image, 0, 0); y_bar = moment(binary_image, 0, 1) / moment(binary_image, 0, 0); mu = 0; nu = 0; for i = 1:rows for j = 1:cols if binary_image(i, j) == 1 mu = mu + (i - x_bar)^p * (j - y_bar)^q; end end end mu = mu / moment(binary_image, 0, 0)^(1+(p+q)/2); nu = mu^(1+(p+q)/2) / moment(binary_image, 0, 0); end This function serves as a foundation for computing the seven Hu moments by combining different orders of normalized moments (typically up to third order). The key implementation aspects include efficient centroid calculation and proper normalization for achieving true invariance properties. If you have any questions about the implementation or mathematical foundations, please feel free to ask.