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陈赣
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///////////////////////////////////////////////////////////////////////////////
// Hungarian.cpp: Implementation file for Class HungarianAlgorithm.
//
// This is a C++ wrapper with slight modification of a hungarian algorithm implementation by Markus Buehren.
// The original implementation is a few mex-functions for use in MATLAB, found here:
// http://www.mathworks.com/matlabcentral/fileexchange/6543-functions-for-the-rectangular-assignment-problem
//
// Both this code and the orignal code are published under the BSD license.
// by Cong Ma, 2016
//
#include "Hungarian.h"
#include <cmath>
#include <cfloat>
HungarianAlgorithm::HungarianAlgorithm(){}
HungarianAlgorithm::~HungarianAlgorithm(){}
//********************************************************//
// A single function wrapper for solving assignment problem.
//********************************************************//
double HungarianAlgorithm::Solve(vector<vector<double>>& DistMatrix, vector<int>& Assignment)
{
unsigned int nRows = DistMatrix.size();
unsigned int nCols = DistMatrix[0].size();
double *distMatrixIn = new double[nRows * nCols];
int *assignment = new int[nRows];
double cost = 0.0;
// Fill in the distMatrixIn. Mind the index is "i + nRows * j".
// Here the cost matrix of size MxN is defined as a double precision array of N*M elements.
// In the solving functions matrices are seen to be saved MATLAB-internally in row-order.
// (i.e. the matrix [1 2; 3 4] will be stored as a vector [1 3 2 4], NOT [1 2 3 4]).
for (unsigned int i = 0; i < nRows; i++)
for (unsigned int j = 0; j < nCols; j++)
distMatrixIn[i + nRows * j] = DistMatrix[i][j];
// call solving function
assignmentoptimal(assignment, &cost, distMatrixIn, nRows, nCols);
Assignment.clear();
for (unsigned int r = 0; r < nRows; r++)
Assignment.push_back(assignment[r]);
delete[] distMatrixIn;
delete[] assignment;
return cost;
}
//********************************************************//
// Solve optimal solution for assignment problem using Munkres algorithm, also known as Hungarian Algorithm.
//********************************************************//
void HungarianAlgorithm::assignmentoptimal(int *assignment, double *cost, double *distMatrixIn, int nOfRows, int nOfColumns)
{
double *distMatrix, *distMatrixTemp, *distMatrixEnd, *columnEnd, value, minValue;
bool *coveredColumns, *coveredRows, *starMatrix, *newStarMatrix, *primeMatrix;
int nOfElements, minDim, row, col;
/* initialization */
*cost = 0;
for (row = 0; row<nOfRows; row++)
assignment[row] = -1;
/* generate working copy of distance Matrix */
/* check if all matrix elements are positive */
nOfElements = nOfRows * nOfColumns;
distMatrix = (double *)malloc(nOfElements * sizeof(double));
distMatrixEnd = distMatrix + nOfElements;
for (row = 0; row<nOfElements; row++)
{
value = distMatrixIn[row];
if (value < 0)
cerr << "All matrix elements have to be non-negative." << endl;
distMatrix[row] = value;
}
/* memory allocation */
coveredColumns = (bool *)calloc(nOfColumns, sizeof(bool));
coveredRows = (bool *)calloc(nOfRows, sizeof(bool));
starMatrix = (bool *)calloc(nOfElements, sizeof(bool));
primeMatrix = (bool *)calloc(nOfElements, sizeof(bool));
newStarMatrix = (bool *)calloc(nOfElements, sizeof(bool)); /* used in step4 */
/* preliminary steps */
if (nOfRows <= nOfColumns)
{
minDim = nOfRows;
for (row = 0; row<nOfRows; row++)
{
/* find the smallest element in the row */
distMatrixTemp = distMatrix + row;
minValue = *distMatrixTemp;
distMatrixTemp += nOfRows;
while (distMatrixTemp < distMatrixEnd)
{
value = *distMatrixTemp;
if (value < minValue)
minValue = value;
distMatrixTemp += nOfRows;
}
/* subtract the smallest element from each element of the row */
distMatrixTemp = distMatrix + row;
while (distMatrixTemp < distMatrixEnd)
{
*distMatrixTemp -= minValue;
distMatrixTemp += nOfRows;
}
}
/* Steps 1 and 2a */
for (row = 0; row<nOfRows; row++)
for (col = 0; col<nOfColumns; col++)
if (fabs(distMatrix[row + nOfRows*col]) < DBL_EPSILON)
if (!coveredColumns[col])
{
starMatrix[row + nOfRows*col] = true;
coveredColumns[col] = true;
break;
}
}
else /* if(nOfRows > nOfColumns) */
{
minDim = nOfColumns;
for (col = 0; col<nOfColumns; col++)
{
/* find the smallest element in the column */
distMatrixTemp = distMatrix + nOfRows*col;
columnEnd = distMatrixTemp + nOfRows;
minValue = *distMatrixTemp++;
while (distMatrixTemp < columnEnd)
{
value = *distMatrixTemp++;
if (value < minValue)
minValue = value;
}
/* subtract the smallest element from each element of the column */
distMatrixTemp = distMatrix + nOfRows*col;
while (distMatrixTemp < columnEnd)
*distMatrixTemp++ -= minValue;
}
/* Steps 1 and 2a */
for (col = 0; col<nOfColumns; col++)
for (row = 0; row<nOfRows; row++)
if (fabs(distMatrix[row + nOfRows*col]) < DBL_EPSILON)
if (!coveredRows[row])
{
starMatrix[row + nOfRows*col] = true;
coveredColumns[col] = true;
coveredRows[row] = true;
break;
}
for (row = 0; row<nOfRows; row++)
coveredRows[row] = false;
}
/* move to step 2b */
step2b(assignment, distMatrix, starMatrix, newStarMatrix, primeMatrix, coveredColumns, coveredRows, nOfRows, nOfColumns, minDim);
/* compute cost and remove invalid assignments */
computeassignmentcost(assignment, cost, distMatrixIn, nOfRows);
/* free allocated memory */
free(distMatrix);
free(coveredColumns);
free(coveredRows);
free(starMatrix);
free(primeMatrix);
free(newStarMatrix);
return;
}
/********************************************************/
void HungarianAlgorithm::buildassignmentvector(int *assignment, bool *starMatrix, int nOfRows, int nOfColumns)
{
int row, col;
for (row = 0; row<nOfRows; row++)
for (col = 0; col<nOfColumns; col++)
if (starMatrix[row + nOfRows*col])
{
#ifdef ONE_INDEXING
assignment[row] = col + 1; /* MATLAB-Indexing */
#else
assignment[row] = col;
#endif
break;
}
}
/********************************************************/
void HungarianAlgorithm::computeassignmentcost(int *assignment, double *cost, double *distMatrix, int nOfRows)
{
int row, col;
for (row = 0; row<nOfRows; row++)
{
col = assignment[row];
if (col >= 0)
*cost += distMatrix[row + nOfRows*col];
}
}
/********************************************************/
void HungarianAlgorithm::step2a(int *assignment, double *distMatrix, bool *starMatrix, bool *newStarMatrix, bool *primeMatrix, bool *coveredColumns, bool *coveredRows, int nOfRows, int nOfColumns, int minDim)
{
bool *starMatrixTemp, *columnEnd;
int col;
/* cover every column containing a starred zero */
for (col = 0; col<nOfColumns; col++)
{
starMatrixTemp = starMatrix + nOfRows*col;
columnEnd = starMatrixTemp + nOfRows;
while (starMatrixTemp < columnEnd){
if (*starMatrixTemp++)
{
coveredColumns[col] = true;
break;
}
}
}
/* move to step 3 */
step2b(assignment, distMatrix, starMatrix, newStarMatrix, primeMatrix, coveredColumns, coveredRows, nOfRows, nOfColumns, minDim);
}
/********************************************************/
void HungarianAlgorithm::step2b(int *assignment, double *distMatrix, bool *starMatrix, bool *newStarMatrix, bool *primeMatrix, bool *coveredColumns, bool *coveredRows, int nOfRows, int nOfColumns, int minDim)
{
int col, nOfCoveredColumns;
/* count covered columns */
nOfCoveredColumns = 0;
for (col = 0; col<nOfColumns; col++)
if (coveredColumns[col])
nOfCoveredColumns++;
if (nOfCoveredColumns == minDim)
{
/* algorithm finished */
buildassignmentvector(assignment, starMatrix, nOfRows, nOfColumns);
}
else
{
/* move to step 3 */
step3(assignment, distMatrix, starMatrix, newStarMatrix, primeMatrix, coveredColumns, coveredRows, nOfRows, nOfColumns, minDim);
}
}
/********************************************************/
void HungarianAlgorithm::step3(int *assignment, double *distMatrix, bool *starMatrix, bool *newStarMatrix, bool *primeMatrix, bool *coveredColumns, bool *coveredRows, int nOfRows, int nOfColumns, int minDim)
{
bool zerosFound;
int row, col, starCol;
zerosFound = true;
while (zerosFound)
{
zerosFound = false;
for (col = 0; col<nOfColumns; col++)
if (!coveredColumns[col])
for (row = 0; row<nOfRows; row++)
if ((!coveredRows[row]) && (fabs(distMatrix[row + nOfRows*col]) < DBL_EPSILON))
{
/* prime zero */
primeMatrix[row + nOfRows*col] = true;
/* find starred zero in current row */
for (starCol = 0; starCol<nOfColumns; starCol++)
if (starMatrix[row + nOfRows*starCol])
break;
if (starCol == nOfColumns) /* no starred zero found */
{
/* move to step 4 */
step4(assignment, distMatrix, starMatrix, newStarMatrix, primeMatrix, coveredColumns, coveredRows, nOfRows, nOfColumns, minDim, row, col);
return;
}
else
{
coveredRows[row] = true;
coveredColumns[starCol] = false;
zerosFound = true;
break;
}
}
}
/* move to step 5 */
step5(assignment, distMatrix, starMatrix, newStarMatrix, primeMatrix, coveredColumns, coveredRows, nOfRows, nOfColumns, minDim);
}
/********************************************************/
void HungarianAlgorithm::step4(int *assignment, double *distMatrix, bool *starMatrix, bool *newStarMatrix, bool *primeMatrix, bool *coveredColumns, bool *coveredRows, int nOfRows, int nOfColumns, int minDim, int row, int col)
{
int n, starRow, starCol, primeRow, primeCol;
int nOfElements = nOfRows*nOfColumns;
/* generate temporary copy of starMatrix */
for (n = 0; n<nOfElements; n++)
newStarMatrix[n] = starMatrix[n];
/* star current zero */
newStarMatrix[row + nOfRows*col] = true;
/* find starred zero in current column */
starCol = col;
for (starRow = 0; starRow<nOfRows; starRow++)
if (starMatrix[starRow + nOfRows*starCol])
break;
while (starRow<nOfRows)
{
/* unstar the starred zero */
newStarMatrix[starRow + nOfRows*starCol] = false;
/* find primed zero in current row */
primeRow = starRow;
for (primeCol = 0; primeCol<nOfColumns; primeCol++)
if (primeMatrix[primeRow + nOfRows*primeCol])
break;
/* star the primed zero */
newStarMatrix[primeRow + nOfRows*primeCol] = true;
/* find starred zero in current column */
starCol = primeCol;
for (starRow = 0; starRow<nOfRows; starRow++)
if (starMatrix[starRow + nOfRows*starCol])
break;
}
/* use temporary copy as new starMatrix */
/* delete all primes, uncover all rows */
for (n = 0; n<nOfElements; n++)
{
primeMatrix[n] = false;
starMatrix[n] = newStarMatrix[n];
}
for (n = 0; n<nOfRows; n++)
coveredRows[n] = false;
/* move to step 2a */
step2a(assignment, distMatrix, starMatrix, newStarMatrix, primeMatrix, coveredColumns, coveredRows, nOfRows, nOfColumns, minDim);
}
/********************************************************/
void HungarianAlgorithm::step5(int *assignment, double *distMatrix, bool *starMatrix, bool *newStarMatrix, bool *primeMatrix, bool *coveredColumns, bool *coveredRows, int nOfRows, int nOfColumns, int minDim)
{
double h, value;
int row, col;
/* find smallest uncovered element h */
h = DBL_MAX;
for (row = 0; row<nOfRows; row++)
if (!coveredRows[row])
for (col = 0; col<nOfColumns; col++)
if (!coveredColumns[col])
{
value = distMatrix[row + nOfRows*col];
if (value < h)
h = value;
}
/* add h to each covered row */
for (row = 0; row<nOfRows; row++)
if (coveredRows[row])
for (col = 0; col<nOfColumns; col++)
distMatrix[row + nOfRows*col] += h;
/* subtract h from each uncovered column */
for (col = 0; col<nOfColumns; col++)
if (!coveredColumns[col])
for (row = 0; row<nOfRows; row++)
distMatrix[row + nOfRows*col] -= h;
/* move to step 3 */
step3(assignment, distMatrix, starMatrix, newStarMatrix, primeMatrix, coveredColumns, coveredRows, nOfRows, nOfColumns, minDim);
}

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///////////////////////////////////////////////////////////////////////////////
// Hungarian.h: Header file for Class HungarianAlgorithm.
//
// This is a C++ wrapper with slight modification of a hungarian algorithm implementation by Markus Buehren.
// The original implementation is a few mex-functions for use in MATLAB, found here:
// http://www.mathworks.com/matlabcentral/fileexchange/6543-functions-for-the-rectangular-assignment-problem
//
// Both this code and the orignal code are published under the BSD license.
// by Cong Ma, 2016
//
#include <iostream>
#include <vector>
using namespace std;
class HungarianAlgorithm
{
public:
HungarianAlgorithm();
~HungarianAlgorithm();
double Solve(vector<vector<double>>& DistMatrix, vector<int>& Assignment);
private:
void assignmentoptimal(int *assignment, double *cost, double *distMatrix, int nOfRows, int nOfColumns);
void buildassignmentvector(int *assignment, bool *starMatrix, int nOfRows, int nOfColumns);
void computeassignmentcost(int *assignment, double *cost, double *distMatrix, int nOfRows);
void step2a(int *assignment, double *distMatrix, bool *starMatrix, bool *newStarMatrix, bool *primeMatrix, bool *coveredColumns, bool *coveredRows, int nOfRows, int nOfColumns, int minDim);
void step2b(int *assignment, double *distMatrix, bool *starMatrix, bool *newStarMatrix, bool *primeMatrix, bool *coveredColumns, bool *coveredRows, int nOfRows, int nOfColumns, int minDim);
void step3(int *assignment, double *distMatrix, bool *starMatrix, bool *newStarMatrix, bool *primeMatrix, bool *coveredColumns, bool *coveredRows, int nOfRows, int nOfColumns, int minDim);
void step4(int *assignment, double *distMatrix, bool *starMatrix, bool *newStarMatrix, bool *primeMatrix, bool *coveredColumns, bool *coveredRows, int nOfRows, int nOfColumns, int minDim, int row, int col);
void step5(int *assignment, double *distMatrix, bool *starMatrix, bool *newStarMatrix, bool *primeMatrix, bool *coveredColumns, bool *coveredRows, int nOfRows, int nOfColumns, int minDim);
};

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///////////////////////////////////////////////////////////////////////////////
// KalmanTracker.cpp: KalmanTracker Class Implementation Declaration
#include "KalmanTracker.h"
int KalmanTracker::kf_count = 0;
// initialize Kalman filter
void KalmanTracker::init_kf(StateType stateMat)
{
int stateNum = 7;
int measureNum = 4;
kf = KalmanFilter(stateNum, measureNum, 0);
measurement = cv::Mat::zeros(measureNum, 1, CV_32F);
kf.transitionMatrix = (cv::Mat_<float>(stateNum, stateNum) << 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1);
setIdentity(kf.measurementMatrix);
setIdentity(kf.processNoiseCov, Scalar::all(1e-2));
setIdentity(kf.measurementNoiseCov, Scalar::all(1e-1));
setIdentity(kf.errorCovPost, Scalar::all(1));
// initialize state vector with bounding box in [cx,cy,s,r] style
kf.statePost.at<float>(0, 0) = stateMat.x + stateMat.width / 2;
kf.statePost.at<float>(1, 0) = stateMat.y + stateMat.height / 2;
kf.statePost.at<float>(2, 0) = stateMat.area();
kf.statePost.at<float>(3, 0) = stateMat.width / stateMat.height;
}
// Predict the estimated bounding box.
StateType KalmanTracker::predict()
{
// predict
Mat p = kf.predict();
m_age += 1;
if (m_time_since_update > 0)
m_hit_streak = 0;
m_time_since_update += 1;
StateType predictBox = get_rect_xysr(p.at<float>(0, 0), p.at<float>(1, 0), p.at<float>(2, 0), p.at<float>(3, 0));
m_history.push_back(predictBox);
return m_history.back();
}
// Update the state vector with observed bounding box.
void KalmanTracker::update(StateType stateMat)
{
m_time_since_update = 0;
m_history.clear();
m_hits += 1;
m_hit_streak += 1;
// measurement
measurement.at<float>(0, 0) = stateMat.x + stateMat.width / 2;
measurement.at<float>(1, 0) = stateMat.y + stateMat.height / 2;
measurement.at<float>(2, 0) = stateMat.area();
measurement.at<float>(3, 0) = stateMat.width / stateMat.height;
// update
kf.correct(measurement);
}
// Return the current state vector
StateType KalmanTracker::get_state()
{
Mat s = kf.statePost;
return get_rect_xysr(s.at<float>(0, 0), s.at<float>(1, 0), s.at<float>(2, 0), s.at<float>(3, 0));
}
// Convert bounding box from [cx,cy,s,r] to [x,y,w,h] style.
StateType KalmanTracker::get_rect_xysr(float cx, float cy, float s, float r)
{
float w = sqrt(s * r);
float h = s / w;
float x = (cx - w / 2);
float y = (cy - h / 2);
if (x < 0 && cx > 0)
x = 0;
if (y < 0 && cy > 0)
y = 0;
return StateType(x, y, w, h);
}
/*
// --------------------------------------------------------------------
// Kalman Filter Demonstrating, a 2-d ball demo
// --------------------------------------------------------------------
const int winHeight = 600;
const int winWidth = 800;
Point mousePosition = Point(winWidth >> 1, winHeight >> 1);
// mouse event callback
void mouseEvent(int event, int x, int y, int flags, void *param)
{
if (event == CV_EVENT_MOUSEMOVE) {
mousePosition = Point(x, y);
}
}
void TestKF();
void main()
{
TestKF();
}
void TestKF()
{
int stateNum = 4;
int measureNum = 2;
KalmanFilter kf = KalmanFilter(stateNum, measureNum, 0);
// initialization
Mat processNoise(stateNum, 1, CV_32F);
Mat measurement = Mat::zeros(measureNum, 1, CV_32F);
kf.transitionMatrix = *(Mat_<float>(stateNum, stateNum) <<
1, 0, 1, 0,
0, 1, 0, 1,
0, 0, 1, 0,
0, 0, 0, 1);
setIdentity(kf.measurementMatrix);
setIdentity(kf.processNoiseCov, Scalar::all(1e-2));
setIdentity(kf.measurementNoiseCov, Scalar::all(1e-1));
setIdentity(kf.errorCovPost, Scalar::all(1));
randn(kf.statePost, Scalar::all(0), Scalar::all(winHeight));
namedWindow("Kalman");
setMouseCallback("Kalman", mouseEvent);
Mat img(winHeight, winWidth, CV_8UC3);
while (1)
{
// predict
Mat prediction = kf.predict();
Point predictPt = Point(prediction.at<float>(0, 0), prediction.at<float>(1, 0));
// generate measurement
Point statePt = mousePosition;
measurement.at<float>(0, 0) = statePt.x;
measurement.at<float>(1, 0) = statePt.y;
// update
kf.correct(measurement);
// visualization
img.setTo(Scalar(255, 255, 255));
circle(img, predictPt, 8, CV_RGB(0, 255, 0), -1); // predicted point as green
circle(img, statePt, 8, CV_RGB(255, 0, 0), -1); // current position as red
imshow("Kalman", img);
char code = (char)waitKey(100);
if (code == 27 || code == 'q' || code == 'Q')
break;
}
destroyWindow("Kalman");
}
*/

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///////////////////////////////////////////////////////////////////////////////
// KalmanTracker.h: KalmanTracker Class Declaration
#ifndef KALMAN_H
#define KALMAN_H 2
#include "opencv2/video/tracking.hpp"
#include "opencv2/highgui/highgui.hpp"
using namespace std;
using namespace cv;
#define StateType Rect_<float>
// This class represents the internel state of individual tracked objects observed as bounding box.
class KalmanTracker
{
public:
KalmanTracker()
{
init_kf(StateType());
m_time_since_update = 0;
m_hits = 0;
m_hit_streak = 0;
m_age = 0;
m_id = kf_count;
//kf_count++;
}
KalmanTracker(StateType initRect)
{
init_kf(initRect);
m_time_since_update = 0;
m_hits = 0;
m_hit_streak = 0;
m_age = 0;
m_id = kf_count;
kf_count++;
}
~KalmanTracker()
{
m_history.clear();
}
StateType predict();
void update(StateType stateMat);
StateType get_state();
StateType get_rect_xysr(float cx, float cy, float s, float r);
static int kf_count;
int m_time_since_update;
int m_hits;
int m_hit_streak;
int m_age;
int m_id;
private:
void init_kf(StateType stateMat);
cv::KalmanFilter kf;
cv::Mat measurement;
std::vector<StateType> m_history;
};
#endif

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summary
-----------
sort algorithm for tracking