MATLAB Code Implementation for Calculating Image Information Entropy

How to Calculate Information Entropy of Remote Sensing Fusion Images Using MATLAB

Image information entropy serves as a critical metric for quantifying the richness of image information, particularly valuable for evaluating remote sensing image fusion results (e.g., IHS and PCA fusion outcomes of TM and SPOT images). The core principle involves calculating pixel value uncertainty by statistically analyzing the probability distribution of image gray levels.

The implementation logic consists of three steps: Gray Level Probability Statistics Convert the fused image (e.g., IHS or PCA results) to grayscale (extract single band first if multispectral), then count the frequency of each gray level (0-255) and calculate the probability p(i) for each gray level.

Information Entropy Formula Application Apply the information theory formula H=-Σ(p(i)*log2(p(i))), where p(i)≠0. In MATLAB, probability statistics can be efficiently performed through pixel-wise traversal or using the histcounts function, followed by logarithmic operations to accumulate results.

Result Comparison Analysis Calculate information entropy separately for original TM images, original SPOT images, and IHS/PCA fusion results. Typically, high-quality fusion images exhibit higher entropy than individual source images, indicating richer detail information.

Extended Considerations: For multi-band images, calculate the average entropy across all bands Combine with standard deviation and other metrics for comprehensive fusion quality assessment Note that entropy gain isn't always better - avoid excessive noise introduction