Fast and accurate motion estimation is an important tool in biomedical imaging applications such as motion compensation and image registration. In this paper, we present a novel algorithm to estimate motion in volumetric images based on the recently developed Local All-Pass (LAP) optical flow framework. The framework is built upon the idea that any motion can be regarded as a local rigid displacement and is hence equivalent to all-pass filtering. Accordingly, our algorithm aims to relate two images, on a local level, using a 3D all-pass filter and then extract the local motion flow from the filter. As this process is based on filtering, it can be efficiently repeated over the whole image volume allowing fast estimation of a dense 3D motion. We demonstrate the effectiveness of this algorithm on both synthetic motion flows and in-vivo MRI data involving respiratory motion. In particular, the algorithm obtains greater accuracy for significantly reduced computation time when compared to competing approaches. Further images illustrating the performance of the 3D LAP can be found at https://sites.google.com/site/cwsgilliam/3D-LAP .