We describe an approach to the computation of the planar or volumetric maximal directional derivative (gradient) of a multispectral or hyperspectral image. We show that the planar multispectral case has an immediate solution. For the non-planar (volumetric or multitemporal) case we demonstrate that an iterative optimization technique (downhill simplex) exploiting image coherency is faster than the conventional eigendecomposition. Finally, we show that the iterative technique, based on matrix norms, has extensions not meaningful in the eigendecomposition method.
Greenshields, I. R. (1999). Coherent computation of the multispectral maximal directional derivative. Image and Vision Computing, 18(1), 1–7. https://doi.org/10.1016/S0262-8856(99)00008-6