基于多项式一致逼近的多阈值图像分割算法

摘要

针对传统多阈值图像分割算法的计算复杂性，以及由图像直方图中毛刺的干扰带来的算法不稳定等缺点，提出一种基于伯恩斯坦多项式一致逼近的多阈值图像分割算法。首先根据逼近论中的威尔斯托拉斯定理构造图像直方图曲线的伯恩斯坦多项式，然后将图像直方图的峰谷值计算问题化简为伯恩斯坦多项式的极值问题，该极值问题可由伯恩斯坦多项式函数的一次、二次微分导出，最后依据这些极值和极性应用分类算法自动标注图像直方图的实际峰谷值，由此完成基于多阈值的图像分割。实验结果表明所提算法不受直方图中毛刺的干扰，算法整体稳定，冗余计算少，时间复杂度小，用时少，效率高，逼近性能和分割效果更好。%Aiming at those shortcomings of previous multi-threshold image segmentation algorithm such as large com-plexity and instability caused by the image histogram glitch interference, a new multi-threshold image segmentation algo-rithm was proposed using Bernstein polynomial to uniformly approximate histogram curve. First, according to the ap-proximation theory of Weierstrass to construct Bernstein polynomial for the histogram curve, then more difficult peak value calculating of the histogram was reduced to the Bernstein polynomial extremal generating, that was exported easily by the first and second derivative of Bernstein polynomial function, and finally obtain the actual peak value of the image histogram by picking up these extremes and polar values and filtering through classification algorithm, and finish multi-threshold image segmentation. Experimental results show that the algorithm is insensitive for histogram glitch in-terference, the overall is stable, the redundant computation and time complexity are smaller, with less time and high effi-ciency, the approximate performance and segmentation effect are better.