Perceptual hash algorithms for images
vp-trees is an implementation of vantage point tree data structure in Common Lisp. It allows to perform fast (O(log N) in the best case) fixed-radius near neighbors searches in some set of a metric space.
Look at the following example. Let's choose the space ℝ²[0, 1] and generate some points belonging to this space:
(defun gen-point () (vector (random 1.0) (random 1.0))) (defun gen-points (n) (loop repeat n collect (gen-point)))
Then introduce a metric on this space (usual Euclidean metric):
(defun dist (a b) (sqrt (reduce #'+ (map 'vector (lambda (x y) (expt (- x y) 2)) a b))))
Build a tree consisting of 1000000 elements in ℝ²[0, 1]:
(defparameter *tree* (vp-trees:make-vp-tree (gen-points 1000000) #'dist))
Now return points which are closer than 0.1 to the origin:
(vp-trees:search-close *tree* #(0.0 0.0) 0.1 #'dist)
The advantage of VP trees is that you don't have to stick to Euclidean metric: you may choose whatever metric you want as long as four metric axioms hold. For example, VP trees can be used for multidimensional spaces.