Object detection is a main task in computer vision. Template matching is the reference method for detecting objects with arbitrary templates. However, template matching computational complexity depends on the rotation accuracy, being a limiting factor for large 3D images (tomograms). Here, we implement a new algorithm called tensorial template matching, based on a mathematical framework that represents all rotations of a template with a tensor field. Contrary to standard template matching, the computational complexity of the presented algorithm is independent of the rotation accuracy. Using both, synthetic and real data from tomography, we demonstrate that tensorial template matching is much faster than template matching and has the potential to improve its accuracy.