Abid Muqaddas, Hitam Muhammad Suzuri, Ali Rozniza, Azami Hamed, Humeau-Heurtier Anne
Faculty of Computer Science and Mathematics, Universiti Malaysia Terengganu, Kuala Terengganu 21030, Malaysia.
Centre for Addiction and Mental Health, University of Toronto, Toronto, ON M6J 1H1, Canada.
Entropy (Basel). 2025 Jan 17;27(1):80. doi: 10.3390/e27010080.
Entropy algorithms are widely applied in signal analysis to quantify the irregularity of data. In the realm of two-dimensional data, their two-dimensional forms play a crucial role in analyzing images. Previous works have demonstrated the effectiveness of one-dimensional increment entropy in detecting abrupt changes in signals. Leveraging these advantages, we introduce a novel concept, two-dimensional increment entropy (IncrEn2D), tailored for analyzing image textures. In our proposed method, increments are translated into two-letter words, encoding both the size (magnitude) and direction (sign) of the increments calculated from an image. We validate the effectiveness of this new entropy measure by applying it to MIX() processes and synthetic textures. Experimental validation spans diverse datasets, including the Kylberg dataset for real textures and medical images featuring colon cancer characteristics. To further validate our results, we employ a support vector machine model, utilizing multiscale entropy values as feature inputs. A comparative analysis with well-known bidimensional sample entropy (SampEn) and bidimensional dispersion entropy (DispEn) reveals that IncrEn achieves an average classification accuracy surpassing that of other methods. In summary, IncrEn emerges as an innovative and potent tool for image analysis and texture characterization, offering superior performance compared to existing bidimensional entropy measures.
熵算法在信号分析中被广泛应用于量化数据的不规则性。在二维数据领域，其二维形式在图像分析中起着至关重要的作用。先前的研究已经证明了一维增量熵在检测信号突变方面的有效性。利用这些优势，我们引入了一个新颖的概念，即二维增量熵（IncrEn2D），专门用于分析图像纹理。在我们提出的方法中，增量被转换为双字母单词，对从图像计算出的增量的大小（幅度）和方向（符号）进行编码。我们通过将其应用于MIX()过程和合成纹理来验证这种新熵度量的有效性。实验验证涵盖了各种数据集，包括用于真实纹理的基尔伯格数据集以及具有结肠癌特征的医学图像。为了进一步验证我们的结果，我们采用支持向量机模型，将多尺度熵值用作特征输入。与著名的二维样本熵（SampEn）和二维离散熵（DispEn）的比较分析表明，IncrEn实现了超过其他方法的平均分类准确率。总之，IncrEn成为图像分析和纹理表征的一种创新且强大的工具，与现有的二维熵度量相比具有卓越的性能。
