Large electron microscopy image datasets for connectomics are typically composed of thousands to millions of partially overlapping two-dimensional images (tiles), which must be registered into a coherent volume prior to further analysis. A common registration strategy is to find matching features between neighboring and overlapping image pairs, followed by a numerical estimation of optimal image deformation using a so-called solver program... Existing solvers are inadequate for large data volumes, and inefficient for small-scale image registration. In this work, an efficient and accurate matrix-based solver method is presented. A linear system is constructed that combines minimization of feature-pair square distances with explicit constraints in a regularization term. In absence of reliable priors for regularization, we show how to construct a rigid-model approximation to use as prior. The linear system is solved using available computer programs, whose performance on typical registration tasks we briefly compare, and to which future scale-up is delegated. Our method is applied to the joint alignment of 2.67 million images, with more than 200 million point-pairs and has been used for successfully aligning the first full adult fruit fly brain. (read more)