用二分法加速奥茨阈值分割，速度提升97%以上
Fast OTSU Thresholding Using Bisection Method
- 利用二分法搜索最优阈值，替代传统遍历所有灰度级
- 实验显示计算量减少91.63%，迭代次数减少97.21%
- 精度高且可保证实时性，适合嵌入式系统应用
Otsu阈值分割是图像分割的基础方法，但其计算效率受遍历所有可能阈值的限制。本文提出一种基于二分法的优化实现，利用类间方差函数的单峰特性，将计算复杂度从O(L)降低至O(log L)，同时保持分割精度。在48张标准测试图像上的实验表明，该方法相比传统穷举法减少了91.63%的方差计算和97.21%的算法迭代次数。二分法在66.67%的测试案例中实现精确阈值匹配，95.83%的偏差控制在5个灰度级以内。算法在理论对数边界内保证全局收敛，具备确定性性能，适用于实时应用场景。该优化在不牺牲原始Otsu方法理论基础和分割质量的前提下，解决了大规模图像处理系统的计算瓶颈。
原文摘要 · Abstract (English)
The Otsu thresholding algorithm represents a fundamental technique in image segmentation, yet its computational efficiency is severely limited by exhaustive search requirements across all possible threshold values. This work presents an optimized implementation that leverages the bisection method to exploit the unimodal characteristics of the between-class variance function. Our approach reduces the computational complexity from O(L) to O(log L) evaluations while preserving segmentation accuracy. Experimental validation on 48 standard test images demonstrates a 91.63% reduction in variance computations and 97.21% reduction in algorithmic iterations compared to conventional exhaustive search. The bisection method achieves exact threshold matches in 66.67% of test cases, with 95.83% exhibiting deviations within 5 gray levels. The algorithm maintains universal convergence within theoretical logarithmic bounds while providing deterministic performance guarantees suitable for real-time applications. This optimization addresses critical computational bottlenecks in large-scale image processing systems without compromising the theoretical foundations or segmentation quality of the original Otsu method.
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