Iterative Method for Optimal Threshold Selection Using Information Entropy

The iterative method for optimal threshold selection based on information entropy is a classical approach widely applied in fields such as image segmentation and signal processing. This method determines the optimal segmentation threshold by maximizing the information entropy difference between the foreground and background of an image, characterized by its computational simplicity and strong adaptability.

Core Algorithm Logic The main concept of this method is based on the image grayscale histogram, iteratively calculating information entropy under different thresholds to find the threshold that maximizes the sum of foreground and background entropy. Key implementation steps include: Threshold Initialization: Typically using the median or mean grayscale value of the image as the initial threshold Entropy Calculation: Divide the image into foreground and background regions, computing probability distributions and corresponding entropy values for both parts Threshold Update: Adjust the threshold iteratively toward the direction that maximizes total entropy until convergence is achieved Code Implementation Insight: In practice, programmers typically use histogram normalization to obtain probability distributions, then implement entropy calculation using logarithmic functions. The iterative process can be optimized through binary search or gradient ascent methods to improve computational efficiency.

KSW Entropy Method: An improved version of information entropy thresholding proposed by Kapur, Sahoo, and Wong. This enhancement optimizes entropy calculation methodology, significantly improving threshold selection robustness, particularly suitable for complex background image segmentation scenarios. Algorithm Enhancement: The KSW method introduces weighted entropy calculations that better handle non-uniform distributions, with implementation typically involving probability weighting factors and normalized entropy metrics.

Reference Paper Kapur, J. N., Sahoo, P. K., & Wong, A. K. C. (1985). A new method for gray-level picture thresholding using the entropy of the histogram. Computer Vision, Graphics, and Image Processing, 29(3), 273-285 Additional literature can further explore entropy optimization variants and multi-threshold segmentation methods, including implementations using recursive algorithms or dynamic programming approaches for multi-level thresholding.

This method finds extensive applications in medical image analysis and industrial detection. Through experimental validation, program implementation ensures high computational efficiency and accuracy, with typical code structures including histogram computation modules, entropy calculation functions, and convergence detection mechanisms.