Espinosa Ricardo, Bailón Raquel, Laguna Pablo
Department of Biomedical Engineering, Universidad ECCI, Bogotá 111311, Colombia.
Biomedical Signal Interpretation & Computational Simulation (BSICoS) Group, Aragón Institute of Engineering Research (I3A), IIS Aragón, University of Zaragoza, 50018 Zaragoza, Spain.
Entropy (Basel). 2021 Sep 28;23(10):1261. doi: 10.3390/e23101261.
Image processing has played a relevant role in various industries, where the main challenge is to extract specific features from images. Specifically, texture characterizes the phenomenon of the occurrence of a pattern along the spatial distribution, taking into account the intensities of the pixels for which it has been applied in classification and segmentation tasks. Therefore, several feature extraction methods have been proposed in recent decades, but few of them rely on entropy, which is a measure of uncertainty. Moreover, entropy algorithms have been little explored in bidimensional data. Nevertheless, there is a growing interest in developing algorithms to solve current limits, since Shannon Entropy does not consider spatial information, and SampEn2D generates unreliable values in small sizes. We introduce a proposed algorithm, EspEn (Espinosa Entropy), to measure the irregularity present in two-dimensional data, where the calculation requires setting the parameters as follows: (length of square window), (tolerance threshold), and ρ (percentage of similarity). Three experiments were performed; the first two were on simulated images contaminated with different noise levels. The last experiment was with grayscale images from the Normalized Brodatz Texture database (NBT). First, we compared the performance of EspEn against the entropy of Shannon and SampEn2D. Second, we evaluated the dependence of EspEn on variations of the values of the parameters , , and ρ. Third, we evaluated the EspEn algorithm on NBT images. The results revealed that EspEn could discriminate images with different size and degrees of noise. Finally, EspEn provides an alternative algorithm to quantify the irregularity in 2D data; the recommended parameters for better performance are = 3, = 20, and ρ = 0.7.
图像处理在各个行业中都发挥了重要作用，其中主要挑战是从图像中提取特定特征。具体而言，纹理表征了沿空间分布出现的图案现象，在分类和分割任务中考虑了应用纹理的像素强度。因此，近几十年来提出了几种特征提取方法，但其中很少有依赖于熵的，熵是一种不确定性度量。此外，熵算法在二维数据中很少被探索。然而，由于香农熵不考虑空间信息，且二维样本熵在小尺寸数据中会产生不可靠的值，因此人们对开发算法来解决当前的局限性越来越感兴趣。我们引入了一种名为EspEn（埃斯皮诺萨熵）的算法，用于测量二维数据中存在的不规则性，其计算需要设置如下参数：（方形窗口长度）、（容差阈值）和ρ（相似度百分比）。进行了三项实验；前两项实验是针对受不同噪声水平污染的模拟图像。最后一项实验使用的是来自归一化布罗达茨纹理数据库（NBT）的灰度图像。首先，我们将EspEn的性能与香农熵和二维样本熵进行了比较。其次，我们评估了EspEn对参数、和ρ值变化的依赖性。第三，我们在NBT图像上评估了EspEn算法。结果表明，EspEn能够区分不同大小和噪声程度的图像。最后，EspEn提供了一种量化二维数据不规则性的替代算法；为获得更好性能推荐的参数是 = 3、 = 20和ρ = 0.7。
