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This paper presents an accurate, computationally efficient, fast and fully-automated algorithm for the alignment of 2D serially acquired sections forming a 3D volume. The method accounts for the main shortcomings of 3D image alignment: corrupted data (cuts and tears), dissimilarities or discontinuities between slices and missing slices. The approach relies on the determination of inter-slice correspondences. The features used for correspondence are extracted by a 2D physics-based deformable model parameterizing the object shape. Correspondence affinities and global constraints render the method efficient and reliable. The method has been evaluated on real images and the experimental results demonstrate its accuracy, as reconstruction errors are smaller than 1 degree in rotation and smaller than 1 pixel in translation.