We present a novel algorithm for the registration of 2D image sequences that combines the principles of multiresolution B-spline-based elastic registration and those of bidirectional consistent registration. In our method, consecutive triples of images are iteratively registered to gradually extend the information through the set of images of the entire sequence. The intermediate results are reused for the registration of the following triple. We choose to interpolate the images and model the deformation fields using B-spline multiresolution pyramids. Novel boundary conditions are introduced to better characterize the deformations at the boundaries. In the experimental section, we quantitatively show that our method recovers from barrel/pincushion and fish-eye deformations with subpixel error. Moreover, it is more robust against outliers—occasional strong noise and large rotations—than the state-of-the-art methods. Finally, we show that our method can be used to realign series of histological serial sections, which are often heavily distorted due to folding and tearing of the tissues.