What ever that means, triangle is definitely the foundation of this paper. Combining SIFT points into a chain of triangles allows us to use dynamic programming; the DP algorithm works as follows: after finding several triangles, we add each node to one of the triangles that most fit to create a new triangle for each iteration. See figure below.
Since for each node we store the best fit triangle that it can combine, at the next iteration when we want to add the best n5 (see above graph) , we only have to consider the best fit among all n5, all the n4 from last iteration and the n3 which each n4 pick . For a model with m nodes and an image with n nodes to match this is a drop roughly from O(n^m) to O(m*n^2).
The fitness of the triangle is a probability defined by both the surf appearance and there location plus orientation compared to the model.
The paper also provides an unsupervised way to learn the model by DP. ( which is probably the emphasis of the paper )
Some of the paper’s result are shown below.