MATLAB Bhattacharyya Distance Computation with Code Implementation

This documentation presents methods for computing Bhattacharyya distance using MATLAB. To enhance understanding, we provide detailed technical explanations below.

The Bhattacharyya distance is a statistical measure for quantifying the similarity between two probability distributions. In image processing and pattern recognition applications, it is commonly employed to compare similarities between images or feature sets. Specifically, this distance metric calculates the overlap between two probability distributions to determine their similarity. In computer vision, it finds extensive use in image comparison, object tracking, and pattern recognition tasks. The mathematical formulation involves calculating the Bhattacharyya coefficient BC = Σ√(p(i)q(i)) where p and q represent discrete probability distributions, with the distance derived as D = -ln(BC).

MATLAB, as a widely-used scientific computing platform, offers robust support for computer vision applications. Computing Bhattacharyya distance in MATLAB is particularly convenient due to its built-in functions and toolboxes. For instance, the Statistics and Machine Learning Toolbox provides the 'bhattacharyyaDistance' function which calculates the distance between two probability distributions using the formula: distance = -log(sum(sqrt(p .* q))). Additionally, MATLAB's Image Processing Toolbox and Computer Vision Toolbox offer integrated functions for histogram comparison and distribution analysis, enabling straightforward implementation of Bhattacharyya distance calculations for image data through histogram normalization and probability distribution extraction.

In practical implementation, users can compute the distance between two image histograms by first normalizing the histograms to obtain probability distributions, then applying the Bhattacharyya coefficient calculation. The key MATLAB functions involved include 'imhist' for histogram extraction, 'normalize' for probability conversion, and custom implementation of the distance calculation when specialized toolboxes are unavailable. For multidimensional distributions, the 'mvnpdf' function can generate probability density functions for Bhattacharyya distance computation between multivariate normal distributions.

In summary, MATLAB provides an efficient and practical environment for Bhattacharyya distance computation, widely adopted in computer vision and image processing domains due to its comprehensive mathematical libraries and specialized toolboxes.