As an important feature of images, the structure tensor (ST) provides properties of the local image intensities. However, it is a challenging task to analyse images directly using STs since STs are 2nd-order symmetric positive semi-definite matrices. In this paper, we define a robust intrinsic feature of images using ST. In addition, using our feature, we propose an improved image similarity measure. By converting the ST into a symmetric positive definite (called tensor) matrix, we define our feature using the extended geodesic distance of tensors calculated in a Riemannian manifold. Our feature shows the essential natural properties of ST and images as tensors are analysed on the tensor manifold. Moreover, defined by the global embedded geometry of the structure tensor, our feature provides a stable intrinsic property of images. The experiments show that our feature performs well in representing the essential attributes of images, especially the edges and important structures. It also shows that our image similarity measure can accurately detect similar images or patches.

作为图像的一个重要特征，结构张量（ST）提供了局部图像强度的属性。然而，直接使用 ST 分析图像是一项具有挑战性的任务，因为 ST 是二阶对称半正定矩阵。在本文中，我们使用 ST 定义了图像的稳健内在特征。此外，利用我们的特征，我们提出了一种改进的图像相似度度量。通过将 ST 转换为对称正定（称为张量）矩阵，我们使用在黎曼流形中计算的张量的扩展测地距离来定义我们的特征。我们的特征显示了在张量流形上分析张量时 ST 和图像的基本自然属性。此外，由结构张量的全局嵌入几何定义，我们的特征提供了图像的稳定内在属性。实验表明，我们的特征在表示图像的基本属性方面表现良好，尤其是边缘和重要结构。它还表明我们的图像相似度测量可以准确地检测到相似的图像或补丁。