>Why are we transforming the triangles to equilateral triangles?
This is so that the extracted image fragments/triangles are always very similar and so have an extremely similar hash. If I didn't transform the triangles then, for example, a fragment of a query image might be stretched compared with the matching fragment in the database. Intuitively it makes sense that it would be easier to match image fragments if they have the same scale/aren't stretched versions of each other. The transformation to equilateral triangles is what makes the algorithm 2D affine-invariant.
>what if you use ASIFT (Affine SIFT) which is Affine transformation friendly
I only discovered ASIFT while reading this thread, it looks very interesting and useful but I'll need to look into it more. I did test out SIFT as a keypoint finder and it performed really poorly for what I wanted to do but I didn't do a lot of testing. My current method of finding keypoints is a load of crap that I threw together for this demo, a better one would seriously improve the accuracy and speed.
>like if too many keypoints are within some 2D window/I propose that let us do Delaunay Triangulation
I looked into both Delaunay Triangulation and a 2D window as a way to decrease the number of proposals/triangles generated, but had problems with both. I will still try later to implement a 2D window. As for Delaunay Triangulation, if you play around with it on paper you can see that it's not 2D affine invariant, it might still work well for small transformations but there are affine transformations where it fails. Still I think it would be worth looking into more.
This is so that the extracted image fragments/triangles are always very similar and so have an extremely similar hash. If I didn't transform the triangles then, for example, a fragment of a query image might be stretched compared with the matching fragment in the database. Intuitively it makes sense that it would be easier to match image fragments if they have the same scale/aren't stretched versions of each other. The transformation to equilateral triangles is what makes the algorithm 2D affine-invariant.
>what if you use ASIFT (Affine SIFT) which is Affine transformation friendly
I only discovered ASIFT while reading this thread, it looks very interesting and useful but I'll need to look into it more. I did test out SIFT as a keypoint finder and it performed really poorly for what I wanted to do but I didn't do a lot of testing. My current method of finding keypoints is a load of crap that I threw together for this demo, a better one would seriously improve the accuracy and speed.
>like if too many keypoints are within some 2D window/I propose that let us do Delaunay Triangulation
I looked into both Delaunay Triangulation and a 2D window as a way to decrease the number of proposals/triangles generated, but had problems with both. I will still try later to implement a 2D window. As for Delaunay Triangulation, if you play around with it on paper you can see that it's not 2D affine invariant, it might still work well for small transformations but there are affine transformations where it fails. Still I think it would be worth looking into more.