Hey Tom,
Great work there!
One question - Why are we transforming the triangles to equilateral triangles?
Just throwing out a few ideas and wanted to discuss what potential flaws could they have.
1. For keypoint detection, what if you use ASIFT (Affine SIFT) which is Affine transformation friendly. In that case, you'd probably save time doing the rotations. Given the huge number of proposals we get, we might still need to filter out some keypoint proposals from this may be using a metric like if too many keypoints are within some 2D window, then choose the one which is farthest from all edges of the 2D window (very rough, don't know if there are other ways)
2. With the final set of keypoints, I propose that let us do Delaunay Triangulation in the hope of getting a collection of triangles which cover the complete surface area of the image making it a spatially equidistant breakdown of the image pixels.
3. Hash those triangles (maybe? how?)
4. Now given a query image, perform steps 1-3, and find the triangles which match the triangles from a database image. If the fraction of matches are above a given threshold, then this is a potential candidate for the search result.