We present a method for densely computing local rotation invariant image descriptors in volumetric images. The descriptors are based on a transformation to the harmonic domain, which we compute very efficiently via differential operators. We show that this fast voxel-wise computation is restricted to a family of basis functions that have certain differential relationships. Building upon this finding, we propose local descriptors based on the Gaussian Laguerre and spherical Gabor basis functions and show how the coefficients can be computed efficiently by recursive differentiation. We exemplarily demonstrate the effectiveness of such dense descriptors in a detection and classification task on biological 3D images. In a direct comparison to existing volumetric features, among them 3D-SIFT, our descriptors reveal superior performance.