The structures of many helical protein filaments can be derived from electron micrographs of their suspensions in thin films of vitrified aqueous solutions. The most successful and generally-applicable approach treats short segments of these filaments as independent "single particles", yielding near-atomic resolution for rigid and well-ordered filaments. The single-particle approach can also accommodate filament deformations, yielding sub-nanometer resolution for more flexible filaments. However, in the case of thin and flexible filaments, such as some amyloid-beta (A beta) fibrils, the single-particle approach may fail because helical segments can be curved or otherwise distorted and their alignment can be inaccurate due to low contrast in the micrographs. We developed new software called Frealix that allows the use of arbitrarily short filament segments during alignment to approximate even high curvatures. All segments in a filament are aligned simultaneously with constraints that ensure that they connect to each other in space to form a continuous helical structure. In this paper, we describe the algorithm and benchmark it against datasets of A beta(1-40) fibrils and tobacco mosaic virus (TMV), both analyzed in earlier work. In the case of TMV, our algorithm achieves similar results to single-particle analysis. In the case of A beta(1-40) fibrils, we match the previously-obtained resolution but we are also able to obtain reliable alignments and similar to 8-angstrom reconstructions from curved filaments. Our algorithm also offers a detailed characterization of filament deformations in three dimensions and enables a critical evaluation of the worm-like chain model for biological filaments. (C) 2014 Elsevier Inc. All rights reserved.