915 lines
37 KiB
C
915 lines
37 KiB
C
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//----------------------------------------------------------------------
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// File: ANN.h
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// Programmer: Sunil Arya and David Mount
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// Last modified: 05/03/05 (Release 1.1)
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// Description: Basic include file for approximate nearest
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// neighbor searching.
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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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// Revision 1.0 04/01/05
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// Added copyright and revision information
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// Added ANNcoordPrec for coordinate precision.
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// Added methods theDim, nPoints, maxPoints, thePoints to ANNpointSet.
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// Cleaned up C++ structure for modern compilers
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// Revision 1.1 05/03/05
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// Added fixed-radius k-NN searching
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//----------------------------------------------------------------------
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//----------------------------------------------------------------------
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// ANN - approximate nearest neighbor searching
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// ANN is a library for approximate nearest neighbor searching,
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// based on the use of standard and priority search in kd-trees
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// and balanced box-decomposition (bbd) trees. Here are some
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// references to the main algorithmic techniques used here:
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//
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// kd-trees:
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// Friedman, Bentley, and Finkel, ``An algorithm for finding
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// best matches in logarithmic expected time,'' ACM
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// Transactions on Mathematical Software, 3(3):209-226, 1977.
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//
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// Priority search in kd-trees:
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// Arya and Mount, ``Algorithms for fast vector quantization,''
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// Proc. of DCC '93: Data Compression Conference, eds. J. A.
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// Storer and M. Cohn, IEEE Press, 1993, 381-390.
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//
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// Approximate nearest neighbor search and bbd-trees:
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// Arya, Mount, Netanyahu, Silverman, and Wu, ``An optimal
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// algorithm for approximate nearest neighbor searching,''
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// 5th Ann. ACM-SIAM Symposium on Discrete Algorithms,
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// 1994, 573-582.
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//----------------------------------------------------------------------
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#ifndef ANN_H
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#define ANN_H
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#ifdef WIN32
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//----------------------------------------------------------------------
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// For Microsoft Visual C++, externally accessible symbols must be
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// explicitly indicated with DLL_API, which is somewhat like "extern."
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//
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// The following ifdef block is the standard way of creating macros
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// which make exporting from a DLL simpler. All files within this DLL
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// are compiled with the DLL_EXPORTS preprocessor symbol defined on the
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// command line. In contrast, projects that use (or import) the DLL
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// objects do not define the DLL_EXPORTS symbol. This way any other
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// project whose source files include this file see DLL_API functions as
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// being imported from a DLL, wheras this DLL sees symbols defined with
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// this macro as being exported.
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//----------------------------------------------------------------------
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#ifdef DLL_EXPORTS
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#define DLL_API __declspec(dllexport)
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#else
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#define DLL_API __declspec(dllimport)
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#endif
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//----------------------------------------------------------------------
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// DLL_API is ignored for all other systems
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//----------------------------------------------------------------------
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#else
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#define DLL_API
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#endif
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//----------------------------------------------------------------------
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// basic includes
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//----------------------------------------------------------------------
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#include <cmath> // math includes
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#include <iostream> // I/O streams
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#include <iomanip> // I/O manipulators
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//----------------------------------------------------------------------
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// Limits
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// There are a number of places where we use the maximum double value as
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// default initializers (and others may be used, depending on the
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// data/distance representation). These can usually be found in limits.h
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// (as LONG_MAX, INT_MAX) or in float.h (as DBL_MAX, FLT_MAX).
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//
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// Not all systems have these files. If you are using such a system,
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// you should set the preprocessor symbol ANN_NO_LIMITS_H when
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// compiling, and modify the statements below to generate the
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// appropriate value. For practical purposes, this does not need to be
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// the maximum double value. It is sufficient that it be at least as
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// large than the maximum squared distance between between any two
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// points.
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//----------------------------------------------------------------------
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#ifdef ANN_NO_LIMITS_H // limits.h unavailable
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#include <cvalues> // replacement for limits.h
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const double ANN_DBL_MAX = MAXDOUBLE; // insert maximum double
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#else
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#include <climits>
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#include <cfloat>
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const double ANN_DBL_MAX = DBL_MAX;
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#endif
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#define ANNversion "1.1.1" // ANN version and information
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#define ANNversionCmt ""
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#define ANNcopyright "David M. Mount and Sunil Arya"
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#define ANNlatestRev "Aug 4, 2006"
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//----------------------------------------------------------------------
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// ANNbool
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// This is a simple boolean type. Although ANSI C++ is supposed
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// to support the type bool, some compilers do not have it.
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//----------------------------------------------------------------------
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enum ANNbool {ANNfalse = 0, ANNtrue = 1}; // ANN boolean type (non ANSI C++)
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//----------------------------------------------------------------------
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// ANNcoord, ANNdist
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// ANNcoord and ANNdist are the types used for representing
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// point coordinates and distances. They can be modified by the
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// user, with some care. It is assumed that they are both numeric
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// types, and that ANNdist is generally of an equal or higher type
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// from ANNcoord. A variable of type ANNdist should be large
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// enough to store the sum of squared components of a variable
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// of type ANNcoord for the number of dimensions needed in the
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// application. For example, the following combinations are
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// legal:
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//
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// ANNcoord ANNdist
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// --------- -------------------------------
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// short short, int, long, float, double
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// int int, long, float, double
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// long long, float, double
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// float float, double
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// double double
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//
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// It is the user's responsibility to make sure that overflow does
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// not occur in distance calculation.
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//----------------------------------------------------------------------
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typedef double ANNcoord; // coordinate data type
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typedef double ANNdist; // distance data type
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//----------------------------------------------------------------------
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// ANNidx
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// ANNidx is a point index. When the data structure is built, the
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// points are given as an array. Nearest neighbor results are
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// returned as an integer index into this array. To make it
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// clearer when this is happening, we define the integer type
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// ANNidx. Indexing starts from 0.
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//
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// For fixed-radius near neighbor searching, it is possible that
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// there are not k nearest neighbors within the search radius. To
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// indicate this, the algorithm returns ANN_NULL_IDX as its result.
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// It should be distinguishable from any valid array index.
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//----------------------------------------------------------------------
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typedef int ANNidx; // point index
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const ANNidx ANN_NULL_IDX = -1; // a NULL point index
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//----------------------------------------------------------------------
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// Infinite distance:
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// The code assumes that there is an "infinite distance" which it
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// uses to initialize distances before performing nearest neighbor
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// searches. It should be as larger or larger than any legitimate
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// nearest neighbor distance.
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//
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// On most systems, these should be found in the standard include
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// file <limits.h> or possibly <float.h>. If you do not have these
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// file, some suggested values are listed below, assuming 64-bit
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// long, 32-bit int and 16-bit short.
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//
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// ANNdist ANN_DIST_INF Values (see <limits.h> or <float.h>)
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// ------- ------------ ------------------------------------
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// double DBL_MAX 1.79769313486231570e+308
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// float FLT_MAX 3.40282346638528860e+38
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// long LONG_MAX 0x7fffffffffffffff
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// int INT_MAX 0x7fffffff
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// short SHRT_MAX 0x7fff
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//----------------------------------------------------------------------
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const ANNdist ANN_DIST_INF = ANN_DBL_MAX;
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//----------------------------------------------------------------------
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// Significant digits for tree dumps:
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// When floating point coordinates are used, the routine that dumps
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// a tree needs to know roughly how many significant digits there
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// are in a ANNcoord, so it can output points to full precision.
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// This is defined to be ANNcoordPrec. On most systems these
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// values can be found in the standard include files <limits.h> or
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// <float.h>. For integer types, the value is essentially ignored.
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//
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// ANNcoord ANNcoordPrec Values (see <limits.h> or <float.h>)
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// -------- ------------ ------------------------------------
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// double DBL_DIG 15
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// float FLT_DIG 6
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// long doesn't matter 19
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// int doesn't matter 10
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// short doesn't matter 5
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//----------------------------------------------------------------------
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#ifdef DBL_DIG // number of sig. bits in ANNcoord
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const int ANNcoordPrec = DBL_DIG;
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#else
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const int ANNcoordPrec = 15; // default precision
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#endif
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//----------------------------------------------------------------------
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// Self match?
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// In some applications, the nearest neighbor of a point is not
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// allowed to be the point itself. This occurs, for example, when
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// computing all nearest neighbors in a set. By setting the
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// parameter ANN_ALLOW_SELF_MATCH to ANNfalse, the nearest neighbor
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// is the closest point whose distance from the query point is
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// strictly positive.
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//----------------------------------------------------------------------
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const ANNbool ANN_ALLOW_SELF_MATCH = ANNtrue;
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//----------------------------------------------------------------------
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// Norms and metrics:
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// ANN supports any Minkowski norm for defining distance. In
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// particular, for any p >= 1, the L_p Minkowski norm defines the
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// length of a d-vector (v0, v1, ..., v(d-1)) to be
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//
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// (|v0|^p + |v1|^p + ... + |v(d-1)|^p)^(1/p),
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//
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// (where ^ denotes exponentiation, and |.| denotes absolute
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// value). The distance between two points is defined to be the
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// norm of the vector joining them. Some common distance metrics
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// include
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//
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// Euclidean metric p = 2
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// Manhattan metric p = 1
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// Max metric p = infinity
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//
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// In the case of the max metric, the norm is computed by taking
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// the maxima of the absolute values of the components. ANN is
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// highly "coordinate-based" and does not support general distances
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// functions (e.g. those obeying just the triangle inequality). It
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// also does not support distance functions based on
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// inner-products.
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//
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// For the purpose of computing nearest neighbors, it is not
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// necessary to compute the final power (1/p). Thus the only
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// component that is used by the program is |v(i)|^p.
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//
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// ANN parameterizes the distance computation through the following
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// macros. (Macros are used rather than procedures for
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// efficiency.) Recall that the distance between two points is
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// given by the length of the vector joining them, and the length
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// or norm of a vector v is given by formula:
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//
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// |v| = ROOT(POW(v0) # POW(v1) # ... # POW(v(d-1)))
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//
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// where ROOT, POW are unary functions and # is an associative and
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// commutative binary operator mapping the following types:
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//
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// ** POW: ANNcoord --> ANNdist
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// ** #: ANNdist x ANNdist --> ANNdist
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// ** ROOT: ANNdist (>0) --> double
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//
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// For early termination in distance calculation (partial distance
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// calculation) we assume that POW and # together are monotonically
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// increasing on sequences of arguments, meaning that for all
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// v0..vk and y:
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//
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// POW(v0) #...# POW(vk) <= (POW(v0) #...# POW(vk)) # POW(y).
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//
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// Incremental Distance Calculation:
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// The program uses an optimized method of computing distances for
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// kd-trees and bd-trees, called incremental distance calculation.
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// It is used when distances are to be updated when only a single
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// coordinate of a point has been changed. In order to use this,
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// we assume that there is an incremental update function DIFF(x,y)
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// for #, such that if:
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//
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// s = x0 # ... # xi # ... # xk
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//
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// then if s' is equal to s but with xi replaced by y, that is,
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//
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// s' = x0 # ... # y # ... # xk
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//
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// then the length of s' can be computed by:
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//
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// |s'| = |s| # DIFF(xi,y).
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//
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// Thus, if # is + then DIFF(xi,y) is (yi-x). For the L_infinity
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// norm we make use of the fact that in the program this function
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// is only invoked when y > xi, and hence DIFF(xi,y)=y.
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//
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// Finally, for approximate nearest neighbor queries we assume
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// that POW and ROOT are related such that
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//
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// v*ROOT(x) = ROOT(POW(v)*x)
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//
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// Here are the values for the various Minkowski norms:
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//
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// L_p: p even: p odd:
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// ------------------------- ------------------------
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// POW(v) = v^p POW(v) = |v|^p
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// ROOT(x) = x^(1/p) ROOT(x) = x^(1/p)
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// # = + # = +
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// DIFF(x,y) = y - x DIFF(x,y) = y - x
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//
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// L_inf:
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// POW(v) = |v|
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// ROOT(x) = x
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// # = max
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// DIFF(x,y) = y
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//
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// By default the Euclidean norm is assumed. To change the norm,
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// uncomment the appropriate set of macros below.
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//----------------------------------------------------------------------
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//----------------------------------------------------------------------
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// Use the following for the Euclidean norm
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//----------------------------------------------------------------------
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#define ANN_POW(v) ((v)*(v))
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#define ANN_ROOT(x) sqrt(x)
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#define ANN_SUM(x,y) ((x) + (y))
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#define ANN_DIFF(x,y) ((y) - (x))
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//----------------------------------------------------------------------
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// Use the following for the L_1 (Manhattan) norm
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//----------------------------------------------------------------------
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// #define ANN_POW(v) fabs(v)
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// #define ANN_ROOT(x) (x)
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// #define ANN_SUM(x,y) ((x) + (y))
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// #define ANN_DIFF(x,y) ((y) - (x))
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//----------------------------------------------------------------------
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// Use the following for a general L_p norm
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//----------------------------------------------------------------------
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// #define ANN_POW(v) pow(fabs(v),p)
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// #define ANN_ROOT(x) pow(fabs(x),1/p)
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// #define ANN_SUM(x,y) ((x) + (y))
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// #define ANN_DIFF(x,y) ((y) - (x))
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//----------------------------------------------------------------------
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// Use the following for the L_infinity (Max) norm
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//----------------------------------------------------------------------
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// #define ANN_POW(v) fabs(v)
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||
|
|
// #define ANN_ROOT(x) (x)
|
||
|
|
// #define ANN_SUM(x,y) ((x) > (y) ? (x) : (y))
|
||
|
|
// #define ANN_DIFF(x,y) (y)
|
||
|
|
|
||
|
|
//----------------------------------------------------------------------
|
||
|
|
// Array types
|
||
|
|
// The following array types are of basic interest. A point is
|
||
|
|
// just a dimensionless array of coordinates, a point array is a
|
||
|
|
// dimensionless array of points. A distance array is a
|
||
|
|
// dimensionless array of distances and an index array is a
|
||
|
|
// dimensionless array of point indices. The latter two are used
|
||
|
|
// when returning the results of k-nearest neighbor queries.
|
||
|
|
//----------------------------------------------------------------------
|
||
|
|
|
||
|
|
typedef ANNcoord* ANNpoint; // a point
|
||
|
|
typedef ANNpoint* ANNpointArray; // an array of points
|
||
|
|
typedef ANNdist* ANNdistArray; // an array of distances
|
||
|
|
typedef ANNidx* ANNidxArray; // an array of point indices
|
||
|
|
|
||
|
|
//----------------------------------------------------------------------
|
||
|
|
// Basic point and array utilities:
|
||
|
|
// The following procedures are useful supplements to ANN's nearest
|
||
|
|
// neighbor capabilities.
|
||
|
|
//
|
||
|
|
// annDist():
|
||
|
|
// Computes the (squared) distance between a pair of points.
|
||
|
|
// Note that this routine is not used internally by ANN for
|
||
|
|
// computing distance calculations. For reasons of efficiency
|
||
|
|
// this is done using incremental distance calculation. Thus,
|
||
|
|
// this routine cannot be modified as a method of changing the
|
||
|
|
// metric.
|
||
|
|
//
|
||
|
|
// Because points (somewhat like strings in C) are stored as
|
||
|
|
// pointers. Consequently, creating and destroying copies of
|
||
|
|
// points may require storage allocation. These procedures do
|
||
|
|
// this.
|
||
|
|
//
|
||
|
|
// annAllocPt() and annDeallocPt():
|
||
|
|
// Allocate a deallocate storage for a single point, and
|
||
|
|
// return a pointer to it. The argument to AllocPt() is
|
||
|
|
// used to initialize all components.
|
||
|
|
//
|
||
|
|
// annAllocPts() and annDeallocPts():
|
||
|
|
// Allocate and deallocate an array of points as well a
|
||
|
|
// place to store their coordinates, and initializes the
|
||
|
|
// points to point to their respective coordinates. It
|
||
|
|
// allocates point storage in a contiguous block large
|
||
|
|
// enough to store all the points. It performs no
|
||
|
|
// initialization.
|
||
|
|
//
|
||
|
|
// annCopyPt():
|
||
|
|
// Creates a copy of a given point, allocating space for
|
||
|
|
// the new point. It returns a pointer to the newly
|
||
|
|
// allocated copy.
|
||
|
|
//----------------------------------------------------------------------
|
||
|
|
|
||
|
|
DLL_API ANNdist annDist(
|
||
|
|
int dim, // dimension of space
|
||
|
|
ANNpoint p, // points
|
||
|
|
ANNpoint q);
|
||
|
|
|
||
|
|
DLL_API ANNpoint annAllocPt(
|
||
|
|
int dim, // dimension
|
||
|
|
ANNcoord c = 0); // coordinate value (all equal)
|
||
|
|
|
||
|
|
DLL_API ANNpointArray annAllocPts(
|
||
|
|
int n, // number of points
|
||
|
|
int dim); // dimension
|
||
|
|
|
||
|
|
DLL_API void annDeallocPt(
|
||
|
|
ANNpoint &p); // deallocate 1 point
|
||
|
|
|
||
|
|
DLL_API void annDeallocPts(
|
||
|
|
ANNpointArray &pa); // point array
|
||
|
|
|
||
|
|
DLL_API ANNpoint annCopyPt(
|
||
|
|
int dim, // dimension
|
||
|
|
ANNpoint source); // point to copy
|
||
|
|
|
||
|
|
//----------------------------------------------------------------------
|
||
|
|
//Overall structure: ANN supports a number of different data structures
|
||
|
|
//for approximate and exact nearest neighbor searching. These are:
|
||
|
|
//
|
||
|
|
// ANNbruteForce A simple brute-force search structure.
|
||
|
|
// ANNkd_tree A kd-tree tree search structure. ANNbd_tree
|
||
|
|
// A bd-tree tree search structure (a kd-tree with shrink
|
||
|
|
// capabilities).
|
||
|
|
//
|
||
|
|
// At a minimum, each of these data structures support k-nearest
|
||
|
|
// neighbor queries. The nearest neighbor query, annkSearch,
|
||
|
|
// returns an integer identifier and the distance to the nearest
|
||
|
|
// neighbor(s) and annRangeSearch returns the nearest points that
|
||
|
|
// lie within a given query ball.
|
||
|
|
//
|
||
|
|
// Each structure is built by invoking the appropriate constructor
|
||
|
|
// and passing it (at a minimum) the array of points, the total
|
||
|
|
// number of points and the dimension of the space. Each structure
|
||
|
|
// is also assumed to support a destructor and member functions
|
||
|
|
// that return basic information about the point set.
|
||
|
|
//
|
||
|
|
// Note that the array of points is not copied by the data
|
||
|
|
// structure (for reasons of space efficiency), and it is assumed
|
||
|
|
// to be constant throughout the lifetime of the search structure.
|
||
|
|
//
|
||
|
|
// The search algorithm, annkSearch, is given the query point (q),
|
||
|
|
// and the desired number of nearest neighbors to report (k), and
|
||
|
|
// the error bound (eps) (whose default value is 0, implying exact
|
||
|
|
// nearest neighbors). It returns two arrays which are assumed to
|
||
|
|
// contain at least k elements: one (nn_idx) contains the indices
|
||
|
|
// (within the point array) of the nearest neighbors and the other
|
||
|
|
// (dd) contains the squared distances to these nearest neighbors.
|
||
|
|
//
|
||
|
|
// The search algorithm, annkFRSearch, is a fixed-radius kNN
|
||
|
|
// search. In addition to a query point, it is given a (squared)
|
||
|
|
// radius bound. (This is done for consistency, because the search
|
||
|
|
// returns distances as squared quantities.) It does two things.
|
||
|
|
// First, it computes the k nearest neighbors within the radius
|
||
|
|
// bound, and second, it returns the total number of points lying
|
||
|
|
// within the radius bound. It is permitted to set k = 0, in which
|
||
|
|
// case it effectively answers a range counting query. If the
|
||
|
|
// error bound epsilon is positive, then the search is approximate
|
||
|
|
// in the sense that it is free to ignore any point that lies
|
||
|
|
// outside a ball of radius r/(1+epsilon), where r is the given
|
||
|
|
// (unsquared) radius bound.
|
||
|
|
//
|
||
|
|
// The generic object from which all the search structures are
|
||
|
|
// dervied is given below. It is a virtual object, and is useless
|
||
|
|
// by itself.
|
||
|
|
//----------------------------------------------------------------------
|
||
|
|
|
||
|
|
class DLL_API ANNpointSet {
|
||
|
|
public:
|
||
|
|
virtual ~ANNpointSet() {} // virtual distructor
|
||
|
|
|
||
|
|
virtual void annkSearch( // approx k near neighbor search
|
||
|
|
ANNpoint q, // query point
|
||
|
|
int k, // number of near neighbors to return
|
||
|
|
ANNidxArray nn_idx, // nearest neighbor array (modified)
|
||
|
|
ANNdistArray dd, // dist to near neighbors (modified)
|
||
|
|
double eps=0.0 // error bound
|
||
|
|
) = 0; // pure virtual (defined elsewhere)
|
||
|
|
|
||
|
|
virtual int annkFRSearch( // approx fixed-radius kNN search
|
||
|
|
ANNpoint q, // query point
|
||
|
|
ANNdist sqRad, // squared radius
|
||
|
|
int k = 0, // number of near neighbors to return
|
||
|
|
ANNidxArray nn_idx = NULL, // nearest neighbor array (modified)
|
||
|
|
ANNdistArray dd = NULL, // dist to near neighbors (modified)
|
||
|
|
double eps=0.0 // error bound
|
||
|
|
) = 0; // pure virtual (defined elsewhere)
|
||
|
|
|
||
|
|
virtual int theDim() = 0; // return dimension of space
|
||
|
|
virtual int nPoints() = 0; // return number of points
|
||
|
|
// return pointer to points
|
||
|
|
virtual ANNpointArray thePoints() = 0;
|
||
|
|
};
|
||
|
|
|
||
|
|
//----------------------------------------------------------------------
|
||
|
|
// Brute-force nearest neighbor search:
|
||
|
|
// The brute-force search structure is very simple but inefficient.
|
||
|
|
// It has been provided primarily for the sake of comparison with
|
||
|
|
// and validation of the more complex search structures.
|
||
|
|
//
|
||
|
|
// Query processing is the same as described above, but the value
|
||
|
|
// of epsilon is ignored, since all distance calculations are
|
||
|
|
// performed exactly.
|
||
|
|
//
|
||
|
|
// WARNING: This data structure is very slow, and should not be
|
||
|
|
// used unless the number of points is very small.
|
||
|
|
//
|
||
|
|
// Internal information:
|
||
|
|
// ---------------------
|
||
|
|
// This data structure bascially consists of the array of points
|
||
|
|
// (each a pointer to an array of coordinates). The search is
|
||
|
|
// performed by a simple linear scan of all the points.
|
||
|
|
//----------------------------------------------------------------------
|
||
|
|
|
||
|
|
class DLL_API ANNbruteForce: public ANNpointSet {
|
||
|
|
int dim; // dimension
|
||
|
|
int n_pts; // number of points
|
||
|
|
ANNpointArray pts; // point array
|
||
|
|
public:
|
||
|
|
ANNbruteForce( // constructor from point array
|
||
|
|
ANNpointArray pa, // point array
|
||
|
|
int n, // number of points
|
||
|
|
int dd); // dimension
|
||
|
|
|
||
|
|
~ANNbruteForce(); // destructor
|
||
|
|
|
||
|
|
void annkSearch( // approx k near neighbor search
|
||
|
|
ANNpoint q, // query point
|
||
|
|
int k, // number of near neighbors to return
|
||
|
|
ANNidxArray nn_idx, // nearest neighbor array (modified)
|
||
|
|
ANNdistArray dd, // dist to near neighbors (modified)
|
||
|
|
double eps=0.0); // error bound
|
||
|
|
|
||
|
|
int annkFRSearch( // approx fixed-radius kNN search
|
||
|
|
ANNpoint q, // query point
|
||
|
|
ANNdist sqRad, // squared radius
|
||
|
|
int k = 0, // number of near neighbors to return
|
||
|
|
ANNidxArray nn_idx = NULL, // nearest neighbor array (modified)
|
||
|
|
ANNdistArray dd = NULL, // dist to near neighbors (modified)
|
||
|
|
double eps=0.0); // error bound
|
||
|
|
|
||
|
|
int theDim() // return dimension of space
|
||
|
|
{ return dim; }
|
||
|
|
|
||
|
|
int nPoints() // return number of points
|
||
|
|
{ return n_pts; }
|
||
|
|
|
||
|
|
ANNpointArray thePoints() // return pointer to points
|
||
|
|
{ return pts; }
|
||
|
|
};
|
||
|
|
|
||
|
|
//----------------------------------------------------------------------
|
||
|
|
// kd- and bd-tree splitting and shrinking rules
|
||
|
|
// kd-trees supports a collection of different splitting rules.
|
||
|
|
// In addition to the standard kd-tree splitting rule proposed
|
||
|
|
// by Friedman, Bentley, and Finkel, we have introduced a
|
||
|
|
// number of other splitting rules, which seem to perform
|
||
|
|
// as well or better (for the distributions we have tested).
|
||
|
|
//
|
||
|
|
// The splitting methods given below allow the user to tailor
|
||
|
|
// the data structure to the particular data set. They are
|
||
|
|
// are described in greater details in the kd_split.cc source
|
||
|
|
// file. The method ANN_KD_SUGGEST is the method chosen (rather
|
||
|
|
// subjectively) by the implementors as the one giving the
|
||
|
|
// fastest performance, and is the default splitting method.
|
||
|
|
//
|
||
|
|
// As with splitting rules, there are a number of different
|
||
|
|
// shrinking rules. The shrinking rule ANN_BD_NONE does no
|
||
|
|
// shrinking (and hence produces a kd-tree tree). The rule
|
||
|
|
// ANN_BD_SUGGEST uses the implementors favorite rule.
|
||
|
|
//----------------------------------------------------------------------
|
||
|
|
|
||
|
|
enum ANNsplitRule {
|
||
|
|
ANN_KD_STD = 0, // the optimized kd-splitting rule
|
||
|
|
ANN_KD_MIDPT = 1, // midpoint split
|
||
|
|
ANN_KD_FAIR = 2, // fair split
|
||
|
|
ANN_KD_SL_MIDPT = 3, // sliding midpoint splitting method
|
||
|
|
ANN_KD_SL_FAIR = 4, // sliding fair split method
|
||
|
|
ANN_KD_SUGGEST = 5}; // the authors' suggestion for best
|
||
|
|
const int ANN_N_SPLIT_RULES = 6; // number of split rules
|
||
|
|
|
||
|
|
enum ANNshrinkRule {
|
||
|
|
ANN_BD_NONE = 0, // no shrinking at all (just kd-tree)
|
||
|
|
ANN_BD_SIMPLE = 1, // simple splitting
|
||
|
|
ANN_BD_CENTROID = 2, // centroid splitting
|
||
|
|
ANN_BD_SUGGEST = 3}; // the authors' suggested choice
|
||
|
|
const int ANN_N_SHRINK_RULES = 4; // number of shrink rules
|
||
|
|
|
||
|
|
//----------------------------------------------------------------------
|
||
|
|
// kd-tree:
|
||
|
|
// The main search data structure supported by ANN is a kd-tree.
|
||
|
|
// The main constructor is given a set of points and a choice of
|
||
|
|
// splitting method to use in building the tree.
|
||
|
|
//
|
||
|
|
// Construction:
|
||
|
|
// -------------
|
||
|
|
// The constructor is given the point array, number of points,
|
||
|
|
// dimension, bucket size (default = 1), and the splitting rule
|
||
|
|
// (default = ANN_KD_SUGGEST). The point array is not copied, and
|
||
|
|
// is assumed to be kept constant throughout the lifetime of the
|
||
|
|
// search structure. There is also a "load" constructor that
|
||
|
|
// builds a tree from a file description that was created by the
|
||
|
|
// Dump operation.
|
||
|
|
//
|
||
|
|
// Search:
|
||
|
|
// -------
|
||
|
|
// There are two search methods:
|
||
|
|
//
|
||
|
|
// Standard search (annkSearch()):
|
||
|
|
// Searches nodes in tree-traversal order, always visiting
|
||
|
|
// the closer child first.
|
||
|
|
// Priority search (annkPriSearch()):
|
||
|
|
// Searches nodes in order of increasing distance of the
|
||
|
|
// associated cell from the query point. For many
|
||
|
|
// distributions the standard search seems to work just
|
||
|
|
// fine, but priority search is safer for worst-case
|
||
|
|
// performance.
|
||
|
|
//
|
||
|
|
// Printing:
|
||
|
|
// ---------
|
||
|
|
// There are two methods provided for printing the tree. Print()
|
||
|
|
// is used to produce a "human-readable" display of the tree, with
|
||
|
|
// indenation, which is handy for debugging. Dump() produces a
|
||
|
|
// format that is suitable reading by another program. There is a
|
||
|
|
// "load" constructor, which constructs a tree which is assumed to
|
||
|
|
// have been saved by the Dump() procedure.
|
||
|
|
//
|
||
|
|
// Performance and Structure Statistics:
|
||
|
|
// -------------------------------------
|
||
|
|
// The procedure getStats() collects statistics information on the
|
||
|
|
// tree (its size, height, etc.) See ANNperf.h for information on
|
||
|
|
// the stats structure it returns.
|
||
|
|
//
|
||
|
|
// Internal information:
|
||
|
|
// ---------------------
|
||
|
|
// The data structure consists of three major chunks of storage.
|
||
|
|
// The first (implicit) storage are the points themselves (pts),
|
||
|
|
// which have been provided by the users as an argument to the
|
||
|
|
// constructor, or are allocated dynamically if the tree is built
|
||
|
|
// using the load constructor). These should not be changed during
|
||
|
|
// the lifetime of the search structure. It is the user's
|
||
|
|
// responsibility to delete these after the tree is destroyed.
|
||
|
|
//
|
||
|
|
// The second is the tree itself (which is dynamically allocated in
|
||
|
|
// the constructor) and is given as a pointer to its root node
|
||
|
|
// (root). These nodes are automatically deallocated when the tree
|
||
|
|
// is deleted. See the file src/kd_tree.h for further information
|
||
|
|
// on the structure of the tree nodes.
|
||
|
|
//
|
||
|
|
// Each leaf of the tree does not contain a pointer directly to a
|
||
|
|
// point, but rather contains a pointer to a "bucket", which is an
|
||
|
|
// array consisting of point indices. The third major chunk of
|
||
|
|
// storage is an array (pidx), which is a large array in which all
|
||
|
|
// these bucket subarrays reside. (The reason for storing them
|
||
|
|
// separately is the buckets are typically small, but of varying
|
||
|
|
// sizes. This was done to avoid fragmentation.) This array is
|
||
|
|
// also deallocated when the tree is deleted.
|
||
|
|
//
|
||
|
|
// In addition to this, the tree consists of a number of other
|
||
|
|
// pieces of information which are used in searching and for
|
||
|
|
// subsequent tree operations. These consist of the following:
|
||
|
|
//
|
||
|
|
// dim Dimension of space
|
||
|
|
// n_pts Number of points currently in the tree
|
||
|
|
// n_max Maximum number of points that are allowed
|
||
|
|
// in the tree
|
||
|
|
// bkt_size Maximum bucket size (no. of points per leaf)
|
||
|
|
// bnd_box_lo Bounding box low point
|
||
|
|
// bnd_box_hi Bounding box high point
|
||
|
|
// splitRule Splitting method used
|
||
|
|
//
|
||
|
|
//----------------------------------------------------------------------
|
||
|
|
|
||
|
|
|
||
|
|
//----------------------------------------------------------------------
|
||
|
|
// Orthogonal (axis aligned) rectangle
|
||
|
|
// Orthogonal rectangles are represented by two points, one
|
||
|
|
// for the lower left corner (min coordinates) and the other
|
||
|
|
// for the upper right corner (max coordinates).
|
||
|
|
//
|
||
|
|
// The constructor initializes from either a pair of coordinates,
|
||
|
|
// pair of points, or another rectangle. Note that all constructors
|
||
|
|
// allocate new point storage. The destructor deallocates this
|
||
|
|
// storage.
|
||
|
|
//
|
||
|
|
// BEWARE: Orthogonal rectangles should be passed ONLY BY REFERENCE.
|
||
|
|
// (C++'s default copy constructor will not allocate new point
|
||
|
|
// storage, then on return the destructor free's storage, and then
|
||
|
|
// you get into big trouble in the calling procedure.)
|
||
|
|
//----------------------------------------------------------------------
|
||
|
|
|
||
|
|
class ANNorthRect {
|
||
|
|
public:
|
||
|
|
ANNpoint lo; // rectangle lower bounds
|
||
|
|
ANNpoint hi; // rectangle upper bounds
|
||
|
|
//
|
||
|
|
ANNorthRect( // basic constructor
|
||
|
|
int dd, // dimension of space
|
||
|
|
ANNcoord l=0, // default is empty
|
||
|
|
ANNcoord h=0)
|
||
|
|
{ lo = annAllocPt(dd, l); hi = annAllocPt(dd, h); }
|
||
|
|
|
||
|
|
ANNorthRect( // (almost a) copy constructor
|
||
|
|
int dd, // dimension
|
||
|
|
const ANNorthRect &r) // rectangle to copy
|
||
|
|
{ lo = annCopyPt(dd, r.lo); hi = annCopyPt(dd, r.hi); }
|
||
|
|
|
||
|
|
ANNorthRect( // construct from points
|
||
|
|
int dd, // dimension
|
||
|
|
ANNpoint l, // low point
|
||
|
|
ANNpoint h) // hight point
|
||
|
|
{ lo = annCopyPt(dd, l); hi = annCopyPt(dd, h); }
|
||
|
|
|
||
|
|
~ANNorthRect() // destructor
|
||
|
|
{ annDeallocPt(lo); annDeallocPt(hi); }
|
||
|
|
|
||
|
|
ANNbool inside(int dim, ANNpoint p);// is point p inside rectangle?
|
||
|
|
};
|
||
|
|
|
||
|
|
void annAssignRect( // assign one rect to another
|
||
|
|
int dim, // dimension (both must be same)
|
||
|
|
ANNorthRect &dest, // destination (modified)
|
||
|
|
const ANNorthRect &source); // source
|
||
|
|
|
||
|
|
//----------------------------------------------------------------------
|
||
|
|
// Some types and objects used by kd-tree functions
|
||
|
|
// See src/kd_tree.h and src/kd_tree.cpp for definitions
|
||
|
|
//----------------------------------------------------------------------
|
||
|
|
class ANNkdStats; // stats on kd-tree
|
||
|
|
//class ANNkd_node; // generic node in a kd-tree
|
||
|
|
|
||
|
|
//----------------------------------------------------------------------
|
||
|
|
// Generic kd-tree node
|
||
|
|
//
|
||
|
|
// Nodes in kd-trees are of two types, splitting nodes which contain
|
||
|
|
// splitting information (a splitting hyperplane orthogonal to one
|
||
|
|
// of the coordinate axes) and leaf nodes which contain point
|
||
|
|
// information (an array of points stored in a bucket). This is
|
||
|
|
// handled by making a generic class kd_node, which is essentially an
|
||
|
|
// empty shell, and then deriving the leaf and splitting nodes from
|
||
|
|
// this.
|
||
|
|
//----------------------------------------------------------------------
|
||
|
|
|
||
|
|
class ANNkd_node{ // generic kd-tree node (empty shell)
|
||
|
|
public:
|
||
|
|
virtual ~ANNkd_node() {} // virtual distroyer
|
||
|
|
|
||
|
|
virtual void ann_search(ANNdist) = 0; // tree search
|
||
|
|
virtual void ann_pri_search(ANNdist) = 0; // priority search
|
||
|
|
virtual void ann_FR_search(ANNdist) = 0; // fixed-radius search
|
||
|
|
|
||
|
|
virtual void getStats( // get tree statistics
|
||
|
|
int dim, // dimension of space
|
||
|
|
ANNkdStats &st, // statistics
|
||
|
|
ANNorthRect &bnd_box) = 0; // bounding box
|
||
|
|
// print node
|
||
|
|
virtual void print(int level, std::ostream &out) = 0;
|
||
|
|
virtual void dump(std::ostream &out) = 0; // dump node
|
||
|
|
virtual bool isLeaf() {return false;} //Deyuan Qiu
|
||
|
|
|
||
|
|
friend class ANNkd_tree; // allow kd-tree to access us
|
||
|
|
};
|
||
|
|
|
||
|
|
typedef ANNkd_node* ANNkd_ptr; // pointer to a kd-tree node
|
||
|
|
|
||
|
|
class DLL_API ANNkd_tree: public ANNpointSet {
|
||
|
|
protected:
|
||
|
|
int dim; // dimension of space
|
||
|
|
int n_pts; // number of points in tree
|
||
|
|
int bkt_size; // bucket size
|
||
|
|
ANNpointArray pts; // the points
|
||
|
|
ANNidxArray pidx; // point indices (to pts array)
|
||
|
|
ANNkd_ptr root; // root of kd-tree
|
||
|
|
ANNpoint bnd_box_lo; // bounding box low point
|
||
|
|
ANNpoint bnd_box_hi; // bounding box high point
|
||
|
|
|
||
|
|
void SkeletonTree( // construct skeleton tree
|
||
|
|
int n, // number of points
|
||
|
|
int dd, // dimension
|
||
|
|
int bs, // bucket size
|
||
|
|
ANNpointArray pa = NULL, // point array (optional)
|
||
|
|
ANNidxArray pi = NULL); // point indices (optional)
|
||
|
|
|
||
|
|
public:
|
||
|
|
ANNkd_tree( // build skeleton tree
|
||
|
|
int n = 0, // number of points
|
||
|
|
int dd = 0, // dimension
|
||
|
|
int bs = 1); // bucket size
|
||
|
|
|
||
|
|
ANNkd_tree( // build from point array
|
||
|
|
ANNpointArray pa, // point array
|
||
|
|
int n, // number of points
|
||
|
|
int dd, // dimension
|
||
|
|
int bs = 1, // bucket size
|
||
|
|
ANNsplitRule split = ANN_KD_SUGGEST); // splitting method
|
||
|
|
|
||
|
|
ANNkd_tree( // build from dump file
|
||
|
|
std::istream& in); // input stream for dump file
|
||
|
|
|
||
|
|
~ANNkd_tree(); // tree destructor
|
||
|
|
|
||
|
|
void annkSearch( // approx k near neighbor search
|
||
|
|
ANNpoint q, // query point
|
||
|
|
int k, // number of near neighbors to return
|
||
|
|
ANNidxArray nn_idx, // nearest neighbor array (modified)
|
||
|
|
ANNdistArray dd, // dist to near neighbors (modified)
|
||
|
|
double eps=0.0); // error bound
|
||
|
|
|
||
|
|
void annkPriSearch( // priority k near neighbor search
|
||
|
|
ANNpoint q, // query point
|
||
|
|
int k, // number of near neighbors to return
|
||
|
|
ANNidxArray nn_idx, // nearest neighbor array (modified)
|
||
|
|
ANNdistArray dd, // dist to near neighbors (modified)
|
||
|
|
double eps=0.0); // error bound
|
||
|
|
|
||
|
|
int annkFRSearch( // approx fixed-radius kNN search
|
||
|
|
ANNpoint q, // the query point
|
||
|
|
ANNdist sqRad, // squared radius of query ball
|
||
|
|
int k, // number of neighbors to return
|
||
|
|
ANNidxArray nn_idx = NULL, // nearest neighbor array (modified)
|
||
|
|
ANNdistArray dd = NULL, // dist to near neighbors (modified)
|
||
|
|
double eps=0.0); // error bound
|
||
|
|
|
||
|
|
int theDim() // return dimension of space
|
||
|
|
{ return dim; }
|
||
|
|
|
||
|
|
int nPoints() // return number of points
|
||
|
|
{ return n_pts; }
|
||
|
|
|
||
|
|
ANNpointArray thePoints() // return pointer to points
|
||
|
|
{ return pts; }
|
||
|
|
|
||
|
|
virtual void Print( // print the tree (for debugging)
|
||
|
|
ANNbool with_pts, // print points as well?
|
||
|
|
std::ostream& out); // output stream
|
||
|
|
|
||
|
|
virtual void Dump( // dump entire tree
|
||
|
|
ANNbool with_pts, // print points as well?
|
||
|
|
std::ostream& out); // output stream
|
||
|
|
|
||
|
|
virtual void getStats( // compute tree statistics
|
||
|
|
ANNkdStats& st); // the statistics (modified)
|
||
|
|
|
||
|
|
ANNkd_ptr getRoot() //Deyuan Qiu
|
||
|
|
{ return root; }
|
||
|
|
};
|
||
|
|
|
||
|
|
//----------------------------------------------------------------------
|
||
|
|
// Box decomposition tree (bd-tree)
|
||
|
|
// The bd-tree is inherited from a kd-tree. The main difference
|
||
|
|
// in the bd-tree and the kd-tree is a new type of internal node
|
||
|
|
// called a shrinking node (in the kd-tree there is only one type
|
||
|
|
// of internal node, a splitting node). The shrinking node
|
||
|
|
// makes it possible to generate balanced trees in which the
|
||
|
|
// cells have bounded aspect ratio, by allowing the decomposition
|
||
|
|
// to zoom in on regions of dense point concentration. Although
|
||
|
|
// this is a nice idea in theory, few point distributions are so
|
||
|
|
// densely clustered that this is really needed.
|
||
|
|
//----------------------------------------------------------------------
|
||
|
|
|
||
|
|
class DLL_API ANNbd_tree: public ANNkd_tree {
|
||
|
|
public:
|
||
|
|
ANNbd_tree( // build skeleton tree
|
||
|
|
int n, // number of points
|
||
|
|
int dd, // dimension
|
||
|
|
int bs = 1) // bucket size
|
||
|
|
: ANNkd_tree(n, dd, bs) {} // build base kd-tree
|
||
|
|
|
||
|
|
ANNbd_tree( // build from point array
|
||
|
|
ANNpointArray pa, // point array
|
||
|
|
int n, // number of points
|
||
|
|
int dd, // dimension
|
||
|
|
int bs = 1, // bucket size
|
||
|
|
ANNsplitRule split = ANN_KD_SUGGEST, // splitting rule
|
||
|
|
ANNshrinkRule shrink = ANN_BD_SUGGEST); // shrinking rule
|
||
|
|
|
||
|
|
ANNbd_tree( // build from dump file
|
||
|
|
std::istream& in); // input stream for dump file
|
||
|
|
};
|
||
|
|
|
||
|
|
//----------------------------------------------------------------------
|
||
|
|
// Other functions
|
||
|
|
// annMaxPtsVisit Sets a limit on the maximum number of points
|
||
|
|
// to visit in the search.
|
||
|
|
// annClose Can be called when all use of ANN is finished.
|
||
|
|
// It clears up a minor memory leak.
|
||
|
|
//----------------------------------------------------------------------
|
||
|
|
|
||
|
|
DLL_API void annMaxPtsVisit( // max. pts to visit in search
|
||
|
|
int maxPts); // the limit
|
||
|
|
|
||
|
|
DLL_API void annClose(); // called to end use of ANN
|
||
|
|
|
||
|
|
#endif
|