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Semi-implicit schemes have been recently shown to speed up nonlinear diffusion in hyperspectral images while increasing the accuracy of subsequent classifiers in thematic mapping. Here, we show how semi-implicit schemes can be used to implement a truly anisotropic diffusion method for hyperspectral images, and we test the performance of different implementations in terms of computational overhead, speed, numerical accuracy, and thematic mapping performance. In addition, truly anisotropic trace-based diffusion formulations, besides a more precise steering of the diffusion processes, also allow implementation by means of local oriented Gaussian masks. We show how the implementations with the highest numerical accuracy can be also the simplest and fastest while still increasing the classification performance.