2D/3D Keypoints

Photo Tourism aka Photosynth detects similarities in photographs and computes 3D structure from that. The three underlying algorithms can be used in many different settings:

Keypoint detection: SIFT
Pre-computed data structures for accelerated search for nearest neighbors (in 2D, one could use a Voronoi diagram; with dozens of dimensions, the problem gets much harder)
Finding good data among outliers: RANSAC