Bounds for Haralick features in synthetic images with sinusoidal gradients

IF 1.3 Q3 ENGINEERING, ELECTRICAL & ELECTRONIC Frontiers in signal processing Pub Date : 2023-11-23 DOI:10.3389/frsip.2023.1271769
A. Oprisan, S. Oprisan
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Abstract

Introduction: The gray-level co-occurrence matrix (GLCM) reduces the dimension of an image to a square matrix determined by the number of gray-level intensities present in that image. Since GLCM only measures the co-occurrence frequency of pairs of gray levels at a given distance from each other, it also stores information regarding the gradients of gray-level intensities in the original image.Methods: The GLCM is a second-order statical method of encoding image information and dimensionality reduction. Image features are scalars that reduce GLCM dimensionality and allow fast texture classification. We used Haralick features to extract information regarding image gradients based on the GLCM.Results: We demonstrate that a gradient of k gray levels per pixel in an image generates GLCM entries on the kth parallel line to the main diagonal. We find that, for synthetic sinusoidal periodic gradients with different wavelengths, the number of gray levels due to intensity quantization follows a power law that also transpires in some Haralick features. We estimate bounds for four of the most often used Haralick features: energy, contrast, correlation, and entropy. We find good agreement between our analytically predicted values of Haralick features and the numerical results from synthetic images of sinusoidal periodic gradients.Discussion: This study opens the possibility of deriving bounds for Haralick features for targeted textures and provides a better selection mechanism for optimal features in texture analysis applications.
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正弦梯度合成图像中哈拉利克特征的界限
简介灰度级共现矩阵(GLCM)将图像的维度缩减为由图像中灰度级强度数量决定的正方形矩阵。由于 GLCM 只测量在给定距离内灰度级对的共现频率,因此它还存储了原始图像中灰度级强度的梯度信息:GLCM 是一种对图像信息进行编码和降维的二阶静态方法。图像特征是一种标量,可降低 GLCM 的维度并实现快速纹理分类。我们使用 Haralick 特征来提取基于 GLCM 的图像梯度信息:我们证明,图像中每个像素 k 个灰度级的梯度会在主对角线的第 k 条平行线上生成 GLCM 条目。我们发现,对于不同波长的合成正弦周期梯度,由于强度量化而产生的灰度级数遵循幂律,这在某些 Haralick 特征中也有体现。我们估算了四个最常用的哈拉利克特征的边界:能量、对比度、相关性和熵。我们发现,分析预测的哈里克特征值与正弦周期梯度合成图像的数值结果非常吻合:讨论:这项研究为推导目标纹理的 Haralick 特征边界提供了可能性,并为纹理分析应用中的最佳特征提供了更好的选择机制。
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