kd_search.cpp

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//----------------------------------------------------------------------
// 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
}