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Motivated by the problem of retinal image registration, this paper introduces and analyzes a new registration algorithm called Dual-Bootstrap Iterative Closest Point (Dual-Bootstrap ICP). The approach is to start from one or more initial, low-order estimates that are only accurate in small image regions, called bootstrap regions. In each bootstrap region, the algorithm iteratively: 1) refines the transformation estimate using constraints only from within the bootstrap region; 2) expands the bootstrap region; and 3) tests to see if a higher order transformation model can be used, stopping when the region expands to cover the overlap between images. Steps 1): and 3), the bootstrap steps, are governed by the covariance matrix of the estimated transformation. Estimation refinement [Step 2)] uses a novel robust version of the ICP algorithm. In registering retinal image pairs, Dual-Bootstrap ICP is initialized by automatically matching individual vascular landmarks, and it aligns images based on detected blood vessel centerlines. The resulting quadratic transformations are accurate to less than a pixel. On tests involving approximately 6000 image pairs, it successfully registered 99.5% of the pairs containing at least one common landmark, and 100% of the pairs containing at least one common landmark and at least 35% image overlap.