This paper describes a fast feature-based algorithm for accurately estimating the absolute location of a surgical tool (a laser), pointed at the curved human retina, from a series of image frames. The method is capable of a 91% success rate with just a third of the feature extraction computation, taking 37 ms overall per image on a 900MHz Pentium III. The success rate approaches 100% when the feature extraction is allowed to run to completion. The median error is 0.92 pixels with 512x512 8-bit image frames. Making a significant break from prior incremental tracking-based efforts, we propose a framework that involves extensive off-line precomputation to build a "spatial map" and high-speed on-line "spatial referencing" to rapidly register each surgical image with this spatial map. The spatial referencing technique is designed around the idea of quasi-invariant indexing. Similarity invariants, locally valid despite the curved nature of the retina, are computed from constellations of vascular landmarks. These are detected using a high-speed algorithm that recursively traces the blood vessel structure. Invariant indexing establishes initial correspondences between landmarks from the on-line image and landmarks stored in the spatial map. Alignment and verification steps gradually extend the similarity transformation computed from these initial correspondences to a global, high-order transformation. The spatial map is pre-computed to contain mosaics, distance maps and an invariant database, all designed to make these spatial referencing computations extremely fast.