220 lines
8.7 KiB
Text
220 lines
8.7 KiB
Text
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//----------------------------------------------------------------------
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// File: kd_pr_search.cpp
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// Programmer: Sunil Arya and David Mount
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// Description: Priority search for kd-trees
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// Last modified: 01/04/05 (Version 1.0)
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//----------------------------------------------------------------------
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// Copyright (c) 1997-2005 University of Maryland and Sunil Arya and
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// David Mount. All Rights Reserved.
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//
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// This software and related documentation is part of the Approximate
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// Nearest Neighbor Library (ANN). This software is provided under
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// the provisions of the Lesser GNU Public License (LGPL). See the
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// file ../ReadMe.txt for further information.
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//
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// The University of Maryland (U.M.) and the authors make no
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// representations about the suitability or fitness of this software for
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// any purpose. It is provided "as is" without express or implied
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// warranty.
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//----------------------------------------------------------------------
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// History:
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// Revision 0.1 03/04/98
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// Initial release
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//----------------------------------------------------------------------
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#include "kd_pr_search.h" // kd priority search declarations
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//----------------------------------------------------------------------
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// Approximate nearest neighbor searching by priority search.
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// The kd-tree is searched for an approximate nearest neighbor.
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// The point is returned through one of the arguments, and the
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// distance returned is the SQUARED distance to this point.
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//
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// The method used for searching the kd-tree is called priority
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// search. (It is described in Arya and Mount, ``Algorithms for
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// fast vector quantization,'' Proc. of DCC '93: Data Compression
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// Conference}, eds. J. A. Storer and M. Cohn, IEEE Press, 1993,
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// 381--390.)
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//
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// The cell of the kd-tree containing the query point is located,
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// and cells are visited in increasing order of distance from the
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// query point. This is done by placing each subtree which has
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// NOT been visited in a priority queue, according to the closest
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// distance of the corresponding enclosing rectangle from the
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// query point. The search stops when the distance to the nearest
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// remaining rectangle exceeds the distance to the nearest point
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// seen by a factor of more than 1/(1+eps). (Implying that any
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// point found subsequently in the search cannot be closer by more
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// than this factor.)
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//
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// The main entry point is annkPriSearch() which sets things up and
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// then call the recursive routine ann_pri_search(). This is a
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// recursive routine which performs the processing for one node in
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// the kd-tree. There are two versions of this virtual procedure,
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// one for splitting nodes and one for leaves. When a splitting node
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// is visited, we determine which child to continue the search on
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// (the closer one), and insert the other child into the priority
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// queue. When a leaf is visited, we compute the distances to the
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// points in the buckets, and update information on the closest
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// points.
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//
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// Some trickery is used to incrementally update the distance from
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// a kd-tree rectangle to the query point. This comes about from
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// the fact that which each successive split, only one component
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// (along the dimension that is split) of the squared distance to
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// the child rectangle is different from the squared distance to
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// the parent rectangle.
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//----------------------------------------------------------------------
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//----------------------------------------------------------------------
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// To keep argument lists short, a number of global variables
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// are maintained which are common to all the recursive calls.
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// These are given below.
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//----------------------------------------------------------------------
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double ANNprEps; // the error bound
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int ANNprDim; // dimension of space
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ANNpoint ANNprQ; // query point
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double ANNprMaxErr; // max tolerable squared error
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ANNpointArray ANNprPts; // the points
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ANNpr_queue *ANNprBoxPQ; // priority queue for boxes
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ANNmin_k *ANNprPointMK; // set of k closest points
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//----------------------------------------------------------------------
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// annkPriSearch - priority search for k nearest neighbors
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//----------------------------------------------------------------------
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void ANNkd_tree::annkPriSearch(
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ANNpoint q, // query point
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int k, // number of near neighbors to return
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ANNidxArray nn_idx, // nearest neighbor indices (returned)
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ANNdistArray dd, // dist to near neighbors (returned)
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double eps) // error bound (ignored)
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{
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// max tolerable squared error
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ANNprMaxErr = ANN_POW(1.0 + eps);
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ANN_FLOP(2) // increment floating ops
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ANNprDim = dim; // copy arguments to static equivs
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ANNprQ = q;
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ANNprPts = pts;
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ANNptsVisited = 0; // initialize count of points visited
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ANNprPointMK = new ANNmin_k(k); // create set for closest k points
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// distance to root box
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ANNdist box_dist = annBoxDistance(q,
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bnd_box_lo, bnd_box_hi, dim);
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ANNprBoxPQ = new ANNpr_queue(n_pts);// create priority queue for boxes
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ANNprBoxPQ->insert(box_dist, root); // insert root in priority queue
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while (ANNprBoxPQ->non_empty() &&
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(!(ANNmaxPtsVisited != 0 && ANNptsVisited > ANNmaxPtsVisited))) {
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ANNkd_ptr np; // next box from prior queue
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// extract closest box from queue
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ANNprBoxPQ->extr_min(box_dist, (void *&) np);
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ANN_FLOP(2) // increment floating ops
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if (box_dist*ANNprMaxErr >= ANNprPointMK->max_key())
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break;
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np->ann_pri_search(box_dist); // search this subtree.
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}
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for (int i = 0; i < k; i++) { // extract the k-th closest points
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dd[i] = ANNprPointMK->ith_smallest_key(i);
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nn_idx[i] = ANNprPointMK->ith_smallest_info(i);
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}
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delete ANNprPointMK; // deallocate closest point set
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delete ANNprBoxPQ; // deallocate priority queue
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}
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//----------------------------------------------------------------------
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// kd_split::ann_pri_search - search a splitting node
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//----------------------------------------------------------------------
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void ANNkd_split::ann_pri_search(ANNdist box_dist)
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{
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ANNdist new_dist; // distance to child visited later
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// distance to cutting plane
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ANNcoord cut_diff = ANNprQ[cut_dim] - cut_val;
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if (cut_diff < 0) { // left of cutting plane
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ANNcoord box_diff = cd_bnds[ANN_LO] - ANNprQ[cut_dim];
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if (box_diff < 0) // within bounds - ignore
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box_diff = 0;
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// distance to further box
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new_dist = (ANNdist) ANN_SUM(box_dist,
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ANN_DIFF(ANN_POW(box_diff), ANN_POW(cut_diff)));
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if (child[ANN_HI] != KD_TRIVIAL)// enqueue if not trivial
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ANNprBoxPQ->insert(new_dist, child[ANN_HI]);
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// continue with closer child
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child[ANN_LO]->ann_pri_search(box_dist);
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}
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else { // right of cutting plane
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ANNcoord box_diff = ANNprQ[cut_dim] - cd_bnds[ANN_HI];
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if (box_diff < 0) // within bounds - ignore
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box_diff = 0;
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// distance to further box
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new_dist = (ANNdist) ANN_SUM(box_dist,
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ANN_DIFF(ANN_POW(box_diff), ANN_POW(cut_diff)));
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if (child[ANN_LO] != KD_TRIVIAL)// enqueue if not trivial
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ANNprBoxPQ->insert(new_dist, child[ANN_LO]);
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// continue with closer child
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child[ANN_HI]->ann_pri_search(box_dist);
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}
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ANN_SPL(1) // one more splitting node visited
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ANN_FLOP(8) // increment floating ops
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}
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//----------------------------------------------------------------------
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// kd_leaf::ann_pri_search - search points in a leaf node
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//
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// This is virtually identical to the ann_search for standard search.
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//----------------------------------------------------------------------
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void ANNkd_leaf::ann_pri_search(ANNdist box_dist)
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{
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register ANNdist dist; // distance to data point
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register ANNcoord* pp; // data coordinate pointer
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register ANNcoord* qq; // query coordinate pointer
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register ANNdist min_dist; // distance to k-th closest point
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register ANNcoord t;
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register int d;
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min_dist = ANNprPointMK->max_key(); // k-th smallest distance so far
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for (int i = 0; i < n_pts; i++) { // check points in bucket
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pp = ANNprPts[bkt[i]]; // first coord of next data point
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qq = ANNprQ; // first coord of query point
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dist = 0;
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for(d = 0; d < ANNprDim; d++) {
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ANN_COORD(1) // one more coordinate hit
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ANN_FLOP(4) // increment floating ops
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t = *(qq++) - *(pp++); // compute length and adv coordinate
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// exceeds dist to k-th smallest?
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if( (dist = ANN_SUM(dist, ANN_POW(t))) > min_dist) {
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break;
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}
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}
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if (d >= ANNprDim && // among the k best?
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(ANN_ALLOW_SELF_MATCH || dist!=0)) { // and no self-match problem
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// add it to the list
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ANNprPointMK->insert(dist, bkt[i]);
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min_dist = ANNprPointMK->max_key();
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}
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}
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ANN_LEAF(1) // one more leaf node visited
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ANN_PTS(n_pts) // increment points visited
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ANNptsVisited += n_pts; // increment number of points visited
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}
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