In this paper, we propose a novel method for automatic, feature-based alignment of transmission electron microscope images that is needed for computing 3D reconstructions in electron tomography. The proposed method, termed as trifocal alignment, is more accurate than the previous markerless methods. The key components of this work are (1) a reliable multiresolution algorithm for matching feature points between images, (2) a robust, maximumlikelihood- based estimator for determining the trifocal constraint, needed for validating the correctness of the matches, (3) a robust, large scale optimisation framework to compute the alignment parameters from hundreds of thousands of feature point measurements from a couple of hundred images. The experiments show for the first time that by the proposed feature-based alignment approach the accuracy level of the fiducial marker alignment can be achieved.