This paper presents a generalized Gray Level Co-occurrence Matrix (GLCM) framework that extends traditional formulations to a continuous, differentiable spatial domain. By replacing discrete pixel displacements with continuous vectors of constant L2-norm, the method achieves rotational invariance and improved robustness across varying resolutions. A radius-based neighborhood criterion ensures consistent spatial coverage, while flexible directional sampling—uniform or random—enhances texture representation. The differentiable formulation supports integration with gradient-based optimization and learning frameworks. Experimental results demonstrate that the proposed GLCM generalization offers greater stability and accuracy, with broad applicability in medical imaging, materials analysis, and texture-driven segmentation.