关键词: 阈值分割, 香农熵, 多尺度乘积变换, 三次样条插值函数, 曲率最大化

Abstract: The gray level histogram of a gray level image may exhibit non-modal, unimodal, bimodal, or multi-modal shape. However, most traditional entropy thresholding methods are only suitable for processing the gray level images with unimodal or bimodal shape. To improve the segmentation accuracy and adaptability of entropy thresholding methods, an automatic thresholding method guided by maximizing four-directional weighted Shannon entropy is prposed. A series of multi-scale product transformation images are first obtained by performing multi-scale product transformations with the directional Prewitt convolution kernels in four directions. Optimal multi-scale product transformation image in each direction is automatically computed based on the cubic spline interpolation function and the curvature maximization criterion. Then the method resamples the pixels on each optimal multi-scale product transformation image using inner and outer contour images to reconstruct the grayscale histogram, and the corrsponding Shannon entropy is calculated based on this. Finally, the optimal segmentation threshold is selected based on the criterion of maximizing weighted Shannon entropy in the four directions. The proposed method was compared with three recent thresholding methods and two non-thresholding methods on 4 synthetic images and 100 real-world images. On the synthesis images, the average Matthews correlation coefficient of the proposed method reaches 0.999. On the real-world images, the average Matthews correlation coefficients of the proposed method and the other five segmentation methods are 0.974, 0.927, 0.668, 0.595, 0.550, and 0.525. The experimental results show that the proposed method has higher segmentation accuracy and more flexible segmentation adaptability.

Key words: image thresholding, shannon entropy, multi-scale product transformation, cubic spline interpolation function, curvature maximization