MATLAB Implementation of Otsu's Method for Optimal Thresholding

<p>Otsu's method is a classic image thresholding technique that automatically determines the optimal segmentation threshold by maximizing inter-class variance. The core concept involves dividing the image's grayscale histogram into foreground and background components, then identifying the grayscale value that maximizes the statistical separation between these two classes as the segmentation threshold.</p> <p>Implementing Otsu's algorithm in MATLAB typically involves these computational steps: first calculate the image's grayscale histogram to obtain pixel frequency distribution across intensity levels; then iterate through all possible threshold values to compute corresponding inter-class variances; finally select the threshold yielding maximum variance as the optimal segmentation point. Since Otsu relies on global grayscale distribution, it works best with bimodal histograms and may have limitations with unimodal distributions or uneven lighting conditions. The key mathematical operation involves calculating weighted variances using probability distributions of the two classes separated by each candidate threshold.</p> <p>MATLAB provides a built-in function `graythresh` that directly implements Otsu's algorithm, returning a normalized optimal threshold when supplied with an image matrix. In practical applications, this is commonly combined with `im2bw` (for older versions) or `imbinarize` (R2016a+) for binary conversion. For educational implementation, one can manually code the algorithm using loop structures to compute inter-class variances and compare maximum values - this approach helps deepen understanding of the method's statistical fundamentals. A sample implementation would involve initializing histogram counts, calculating cumulative probabilities and means for both classes, then applying the variance formula: σ² = ω₁ω₂(μ₁-μ₂)² where ω represents class probabilities and μ denotes class means.</p> <p>As a parameter-free, completely data-driven approach, Otsu's method excels in document scanning, simple object detection, and other applications with clear foreground-background separation. However, for complex lighting conditions or multi-object images, it may require integration with local thresholding techniques or hybrid segmentation methods to improve performance. The algorithm's computational complexity is O(L) where L represents the number of grayscale levels, making it efficient for standard 8-bit images with 256 intensity levels.</p>