四向加权香农熵最大化导向的自动阈值分割方法

Automatic thresholding method guided by maximizing four-directional weighted Shannon entropy

灰度图像的灰度直方图可以呈现出无峰、单峰、双峰或多峰的形态特征,但传统熵阈值分割方法大多仅适合处理具有单峰或双峰形态特征的灰度图像。为了提高熵阈值分割方法的分割精度和分割适应性,提出一种四向加权香农熵最大化导向的自动阈值分割方法 FWSE(Four-directional Weighted Shannon Entropy)。首先用新设计的方向性Prewitt卷积核在4个方向进行多尺度乘积变换(MPT),以获得一系列方向性MPT图像;再基于三次样条插值函数和曲率最大化准则自动计算出每个方向的最优MPT图像;其次在每个方向上通过内外轮廓图像对最优MPT图像的像素进行重新取样,以获取重构的灰度直方图,并在此基础上计算相应的香农熵;最后以4个方向的加权香农熵最大化为准则选取最佳分割阈值。与新近的3种阈值分割方法以及2种非阈值分割方法在4幅合成图像和100幅真实世界图像上进行实验,结果显示:在合成图像上,FWSE方法的平均马修斯相关系数(MCC)达到了0.999;在真实世界图像上,FWSE方法与其他5个分割方法的平均MCC分别是0.974、0.927、0.668、0.595、0.550和0.525。这表明FWSE方法具有更高的分割精度和更灵活的分割适应性。

The grayscale histogram of a grayscale image may have non-modal,unimodal,bimodal,or multi-modal morphological characteristics.However,most traditional entropy thresholding methods are only suitable for processing the grayscale images with unimodal or bimodal morphological characteristics.To improve the segmentation accuracy and adaptability of entropy thresholding methods,an automatic thresholding method guided by maximizing four-directional weighted Shannon entropy was proposed,namely FWSE(Four-directional Weighted Shannon Entropy).Firstly,a series of Multi-scale Product Transformation(MPT)images were obtained by performing MPTs with the directional Prewitt convolution kernels in four directions.Secondly,the optimal MPT image in each direction was computed automatically based on the cubic spline interpolation function and the curvature maximization criterion.Thirdly,the pixels on each optimal MPT image were resampled by using inner and outer contour images to reconstruct the grayscale histogram,and the corresponding Shannon entropy was calculated based on the above.Finally,the optimal segmentation threshold was selected based on the criterion of maximizing weighted Shannon entropy in four directions.FWSE method was compared with three recent thresholding methods and two recent non-thresholding methods on 4 synthetic images and 100 real-world images.Experimental results show that:on the synthesis images,the average Matthews Correlation Coefficient(MCC)of the FWSE method reaches 0.999;on the real-world images,the average MCCs of the FWSE method and the other five segmentation methods are 0.974,0.927,0.668,0.595,0.550,and 0.525 respectively.It can be seen that the FWSE method has higher segmentation accuracy and more flexible segmentation adaptability.