Oprisan Sorinel A, Oprisan Ana
Physics and Astronomy, College of Charleston, Charleston, SC, United States.
PeerJ Comput Sci. 2025 Apr 30;11:e2856. doi: 10.7717/peerj-cs.2856. eCollection 2025.
This study presents a novel analytical framework for understanding the relationship between the image gradients and the symmetries of the Gray Level Co-occurrence Matrix (GLCM). Analytical expression for four key features-sum average (SA), sum variance (SV), difference variance (DV), and entropy-were derived to capture their dependence on image's gray-level quantization (N), the gradient magnitude (∇), and the displacement vector (d) through the corresponding GLCM. Scaling laws obtained from the exact analytical dependencies of Haralick features on N, ∇ and |d| show that SA and DV scale linearly with N, SV scales quadratically, and entropy follows a logarithmic trend. The scaling laws allow a consistent derivation of normalization factors that make Haralick features independent of the quantization scheme N. Numerical simulations using synthetic one-dimensional gradients validated our theoretical predictions. This theoretical framework establishes a foundation for consistent derivation of analytic expressions and scaling laws for Haralick features. Such an approach would streamline texture analysis across datasets and imaging modalities, enhancing the portability and interpretability of Haralick features in machine learning and medical imaging applications.
本研究提出了一种新颖的分析框架，用于理解图像梯度与灰度共生矩阵（GLCM）对称性之间的关系。通过相应的GLCM，推导了四个关键特征——和均值（SA）、和方差（SV）、差方差（DV）和熵的解析表达式，以捕捉它们对图像灰度量化（N）、梯度幅值（∇）和位移矢量（d）的依赖性。从哈拉里克特征对N、∇和|d|的精确解析依赖性中获得的缩放定律表明，SA和DV与N呈线性缩放，SV呈二次方缩放，熵呈对数趋势。这些缩放定律允许一致地推导归一化因子，使哈拉里克特征与量化方案N无关。使用合成一维梯度的数值模拟验证了我们的理论预测。该理论框架为一致推导哈拉里克特征的解析表达式和缩放定律奠定了基础。这种方法将简化跨数据集和成像模态的纹理分析，提高哈拉里克特征在机器学习和医学成像应用中的可移植性和可解释性。
