//----------------------------------------------------------------------
// File: kd_search.cpp
// Programmer: Sunil Arya and David Mount
// Description: Standard kd-tree search
// Last modified: 01/04/05 (Version 1.0)
//----------------------------------------------------------------------
// Copyright (c) 1997-2005 University of Maryland and Sunil Arya and
// David Mount. All Rights Reserved.
//
// This software and related documentation is part of the Approximate
// Nearest Neighbor Library (ANN). This software is provided under
// the provisions of the Lesser GNU Public License (LGPL). See the
// file ../ReadMe.txt for further information.
//
// The University of Maryland (U.M.) and the authors make no
// representations about the suitability or fitness of this software for
// any purpose. It is provided "as is" without express or implied
// warranty.
//----------------------------------------------------------------------
// History:
// Revision 0.1 03/04/98
// Initial release
// Revision 1.0 04/01/05
// Changed names LO, HI to ANN_LO, ANN_HI
//----------------------------------------------------------------------
#include "kd_search.h" // kd-search declarations
//----------------------------------------------------------------------
// Approximate nearest neighbor searching by kd-tree search
// The kd-tree is searched for an approximate nearest neighbor.
// The point is returned through one of the arguments, and the
// distance returned is the squared distance to this point.
//
// The method used for searching the kd-tree is an approximate
// adaptation of the search algorithm described by Friedman,
// Bentley, and Finkel, ``An algorithm for finding best matches
// in logarithmic expected time,'' ACM Transactions on Mathematical
// Software, 3(3):209-226, 1977).
//
// The algorithm operates recursively. When first encountering a
// node of the kd-tree we first visit the child which is closest to
// the query point. On return, we decide whether we want to visit
// the other child. If the box containing the other child exceeds
// 1/(1+eps) times the current best distance, then we skip it (since
// any point found in this child cannot be closer to the query point
// by more than this factor.) Otherwise, we visit it recursively.
// The distance between a box and the query point is computed exactly
// (not approximated as is often done in kd-tree), using incremental
// distance updates, as described by Arya and Mount in ``Algorithms
// for fast vector quantization,'' Proc. of DCC '93: Data Compression
// Conference, eds. J. A. Storer and M. Cohn, IEEE Press, 1993,
// 381-390.
//
// The main entry points is annkSearch() which sets things up and
// then call the recursive routine ann_search(). This is a recursive
// routine which performs the processing for one node in the kd-tree.
// There are two versions of this virtual procedure, one for splitting
// nodes and one for leaves. When a splitting node is visited, we
// determine which child to visit first (the closer one), and visit
// the other child on return. When a leaf is visited, we compute
// the distances to the points in the buckets, and update information
// on the closest points.
//
// Some trickery is used to incrementally update the distance from
// a kd-tree rectangle to the query point. This comes about from
// the fact that which each successive split, only one component
// (along the dimension that is split) of the squared distance to
// the child rectangle is different from the squared distance to
// the parent rectangle.
//----------------------------------------------------------------------
//----------------------------------------------------------------------
// To keep argument lists short, a number of global variables
// are maintained which are common to all the recursive calls.
// These are given below.
//----------------------------------------------------------------------
int ANNkdDim; // dimension of space
ANNpoint ANNkdQ; // query point
double ANNkdMaxErr; // max tolerable squared error
ANNpointArray ANNkdPts; // the points
ANNmin_k *ANNkdPointMK; // set of k closest points
//----------------------------------------------------------------------
// annkSearch - search for the k nearest neighbors
//----------------------------------------------------------------------
void ANNkd_tree::annkSearch(
ANNpoint q, // the query point
int k, // number of near neighbors to return
ANNidxArray nn_idx, // nearest neighbor indices (returned)
ANNdistArray dd, // the approximate nearest neighbor
double eps) // the error bound
{
ANNkdDim = dim; // copy arguments to static equivs
ANNkdQ = q;
ANNkdPts = pts;
ANNptsVisited = 0; // initialize count of points visited
if (k > n_pts) { // too many near neighbors?
annError("Requesting more near neighbors than data points", ANNabort);
}
ANNkdMaxErr = ANN_POW(1.0 + eps);
ANN_FLOP(2) // increment floating op count
ANNkdPointMK = new ANNmin_k(k); // create set for closest k points
// search starting at the root
root->ann_search(annBoxDistance(q, bnd_box_lo, bnd_box_hi, dim));
for (int i = 0; i < k; i++) { // extract the k-th closest points
dd[i] = ANNkdPointMK->ith_smallest_key(i);
nn_idx[i] = ANNkdPointMK->ith_smallest_info(i);
}
delete ANNkdPointMK; // deallocate closest point set
}
//----------------------------------------------------------------------
// kd_split::ann_search - search a splitting node
//----------------------------------------------------------------------
void ANNkd_split::ann_search(ANNdist box_dist)
{
// check dist calc term condition
if (ANNmaxPtsVisited != 0 && ANNptsVisited > ANNmaxPtsVisited) return;
// distance to cutting plane
ANNcoord cut_diff = ANNkdQ[cut_dim] - cut_val;
if (cut_diff < 0) { // left of cutting plane
child[ANN_LO]->ann_search(box_dist);// visit closer child first
ANNcoord box_diff = cd_bnds[ANN_LO] - ANNkdQ[cut_dim];
if (box_diff < 0) // within bounds - ignore
box_diff = 0;
// distance to further box
box_dist = (ANNdist) ANN_SUM(box_dist,
ANN_DIFF(ANN_POW(box_diff), ANN_POW(cut_diff)));
// visit further child if close enough
if (box_dist * ANNkdMaxErr < ANNkdPointMK->max_key())
child[ANN_HI]->ann_search(box_dist);
}
else { // right of cutting plane
child[ANN_HI]->ann_search(box_dist);// visit closer child first
ANNcoord box_diff = ANNkdQ[cut_dim] - cd_bnds[ANN_HI];
if (box_diff < 0) // within bounds - ignore
box_diff = 0;
// distance to further box
box_dist = (ANNdist) ANN_SUM(box_dist,
ANN_DIFF(ANN_POW(box_diff), ANN_POW(cut_diff)));
// visit further child if close enough
if (box_dist * ANNkdMaxErr < ANNkdPointMK->max_key())
child[ANN_LO]->ann_search(box_dist);
}
ANN_FLOP(10) // increment floating ops
ANN_SPL(1) // one more splitting node visited
}
//----------------------------------------------------------------------
// kd_leaf::ann_search - search points in a leaf node
// Note: The unreadability of this code is the result of
// some fine tuning to replace indexing by pointer operations.
//----------------------------------------------------------------------
void ANNkd_leaf::ann_search(ANNdist box_dist)
{
register ANNdist dist; // distance to data point
register ANNcoord* pp; // data coordinate pointer
register ANNcoord* qq; // query coordinate pointer
register ANNdist min_dist; // distance to k-th closest point
register ANNcoord t;
register int d;
min_dist = ANNkdPointMK->max_key(); // k-th smallest distance so far
for (int i = 0; i < n_pts; i++) { // check points in bucket
pp = ANNkdPts[bkt[i]]; // first coord of next data point
qq = ANNkdQ; // first coord of query point
dist = 0;
for(d = 0; d < ANNkdDim; d++) {
ANN_COORD(1) // one more coordinate hit
ANN_FLOP(4) // increment floating ops
t = *(qq++) - *(pp++); // compute length and adv coordinate
// exceeds dist to k-th smallest?
if( (dist = ANN_SUM(dist, ANN_POW(t))) > min_dist) {
break;
}
}
if (d >= ANNkdDim && // among the k best?
(ANN_ALLOW_SELF_MATCH || dist!=0)) { // and no self-match problem
// add it to the list
ANNkdPointMK->insert(dist, bkt[i]);
min_dist = ANNkdPointMK->max_key();
}
}
ANN_LEAF(1) // one more leaf node visited
ANN_PTS(n_pts) // increment points visited
ANNptsVisited += n_pts; // increment number of points visited
}