In this paper, we propose two sensitive contributions to automatically determine the local orientations and centers of short segments of microtubules in cryo-electron microscope images. Indeed, to our knowledge, the methods to determine the local centers of helices are not relevant for non centro-symmetric helices (e.g. 13-protofilament microtubules). The proposed algorithm exploits the helical symmetry of microtubules and the corresponding properties in the Fourier domain, so it can be easily extended to process other helical objects. Experimental results demonstrate that center locations are estimated with an accuracy of lower than one pixel. We applied the algorithm to automatically straighten images of curved microtubules with odd numbers of protofilaments, and to improve 3D reconstructions of microtubules using back-projection methods.