概率分布双向稀疏化下的单一Tsallis熵阈值选取方法
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孙水发,E-mail:watersun@ctgu.edu.cn

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国家自然科学基金(61871258,61502274);国家重点研发计划资助项目(2016YFB0800403)


Automatic Threshold Selection Method Using Single Tsallis Entropy Under Bidirectional Sparse Probability Distribution
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    摘要:

    现有基于熵最大准则选取阈值的方法涉及两个或两个以上的随机变量,它们都忽视了一个约束条件而影响到它们的分割精度和适用范围:参与随机系统整体熵计算的各随机变量应当相互独立.本文提出了一种概率分布双向稀疏化下的单一Tsallis熵最大化导向的自动阈值选取方法,可以自然规避多个随机变量需要相互独立的约束条件.在多尺度卷积乘变换所得两幅图像上,该方法先构建了一个具有双向稀疏概率分布特征的二维随机变量,然后在该二维随机变量基础上定义了一个二维Tsallis熵.在将二维Tsallis熵的计算简化到只涉及二维随机变量的边缘概率分布后,选取单一Tsallis熵取最大值时对应的阈值作为最终分割阈值.提出的方法和1个交互式阈值方法、4个自动阈值方法以及1个自动聚类分割方法进行了比较.所用测试图像集由44幅合成图像和44幅真实世界图像组成,这些测试图像具有单峰、双峰、多峰或无峰灰度直方图模式.结果表明,提出方法的计算效率虽然不优于5个自动分割方法,但是它的分割适应性和分割精度有显著提高.

    Abstract:

    The existing methods of selecting threshold based on the maximum entropy criterion involve two or more random variables. They all ignore a constraint that the random variables involved in the overall entropy calculation of a random system should be independent of each other, which directly affects their segmentation accuracy and application scope. In this paper, an automatic threshold selection method guided by maximizing single Tsallis entropy under bidirectional sparse probability distribution is proposed, and it can naturally circumvent the constraint that multiple random variables should be independent of each other. On two images derived from a multi-scale convolution transformation, the proposed method first constructs a two-dimensional random variable with bidirectional sparse probability distribution, then a two-dimensional Tsallis entropy is defined on the basis of the two-dimensional random variable. After simplifying the calculation of two-dimensional Tsallis entropy to only involve the marginal probability distribution of the two-dimensional random variables, the corresponding threshold when the single Tsallis entropy takes maximal value is selected as the final segmentation threshold. The proposed method is compared with an interactive thresholding method, 4 automatic thresholding methods, and an automatic clustering method on 44 synthetic images and 44 real-world images, and the gray level histograms of these test images are unimodal, bimodal, multimodal or peakless. The experimental results show that the proposed method is not superior to these 5 automatic methods in computational efficiency, but it has a significant enhancement in the adaptability and accuracy of segmentation.

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邹耀斌,张进玉,臧兆祥,夏平,王俊英,龚国强,孙水发.概率分布双向稀疏化下的单一Tsallis熵阈值选取方法.软件学报,,():0

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  • 收稿日期:2020-02-17
  • 最后修改日期:2020-05-18
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  • 在线发布日期: 2021-11-24
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