Up to the present, an enormous number of advanced techniques have been developed to enhance and extract the spatially semantic information in hyperspectral image processing and analysis. However, locally semantic change, such as scene composition, relative position between objects, spectral variability caused by illumination, atmospheric effects, and material mixture, has been less frequently investigated in modeling spatial information. As a consequence, identifying the same materials from spatially different scenes or positions can be difficult. In this paper, we propose a solution to address this issue by locally extracting invariant features from hyperspectral imagery (HSI) in both spatial and frequency domains, using a method called invariant attribute profiles (IAPs). IAPs extract the spatial invariant features by exploiting isotropic filter banks or convolutional kernels on HSI and spatial aggregation techniques (e.g., superpixel segmentation) in the Cartesian coordinate system. Furthermore, they model invariant behaviors (e.g., shift, rotation) by the means of a continuous histogram of oriented gradients constructed in a Fourier polar coordinate. This yields a combinatorial representation of spatial-frequency invariant features with application to HSI classification. Extensive experiments conducted on three promising hyperspectral datasets (Houston2013 and Houston2018) demonstrate the superiority and effectiveness of the proposed IAP method in comparison with several state-of-the-art profile-related techniques. The codes will be available from the website: https://sites.google.com/view/danfeng-hong/data-code.
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