OTSU: Simplified Algorithm for Optimal Threshold Calculation

Otsu's algorithm (OTSU algorithm) is a classic adaptive threshold segmentation method commonly used for image binarization in digital image processing. Its core principle involves determining the optimal segmentation threshold by maximizing the inter-class variance, thereby achieving optimal separation between foreground and background regions.

### Algorithm Principle Calculate grayscale histogram: Count the number of pixels for each grayscale level in the image. Iterate through all possible thresholds: Assume a grayscale value as the segmentation threshold, dividing pixels into foreground (above threshold) and background (below threshold) classes. Compute inter-class variance: Calculate the variance between classes based on the pixel proportions and mean grayscale values of foreground and background regions. Find optimal threshold: Select the grayscale value that yields the maximum inter-class variance as the final segmentation threshold.

### MATLAB Implementation Approach Statistical grayscale distribution: Use `imhist` function or manual histogram calculation to gather pixel intensity distribution data. Calculate cumulative probabilities and means: Iterate through each potential threshold value, computing pixel ratios and mean values for both foreground and background classes using probability mass functions. Optimize threshold selection: Compare inter-class variance values across all thresholds and record the threshold corresponding to the maximum variance using vectorized operations for efficiency.

### Advantages Adaptive capability: Requires no manual threshold specification, making it suitable for images under varying illumination conditions. Computational efficiency: The algorithm has relatively low complexity (O(L) where L is the number of grayscale levels), making it appropriate for real-time processing applications.

This algorithm is widely applied in medical imaging, license plate recognition, and various other fields, serving as a fundamental tool in image segmentation tasks. The implementation typically involves histogram normalization, probability calculation, and efficient search for the maximum variance criterion.