kalman 滤波 演示与opencv代码

在机器视觉中追踪时常会用到预测算法，kalman是你一定知道的。它可以用来预测各种状态，比如说位置，速度等。关于它的理论有很多很好的文献可以参考。opencv给出了kalman filter的一个实现，而且有范例，但估计不少人对它的使用并不清楚，因为我也是其中一个。本文的应用是对二维坐标进行预测和平滑

使用方法：

1、初始化

const int stateNum=4;//状态数，包括（x，y，dx，dy）坐标及速度（每次移动的距离）

const int measureNum=2;//观测量，能看到的是坐标值，当然也可以自己计算速度，但没必要

Kalman* kalman = cvCreateKalman( stateNum, measureNum, 0 );//state(x,y,detaX,detaY)

转移矩阵或者说增益矩阵的值好像有点莫名其妙

[cpp]
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float A[stateNum][stateNum] ={//transition matrix
1,0,1,0,
0,1,0,1,
0,0,1,0,
0,0,0,1
};

[cpp]
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float A[stateNum][stateNum] ={//transition matrix

1,0,0,1,0,0,
0,1,0,0,1,0,
0,0,1,0,0,1,
0,0,0,1,0,0,
0,0,0,0,1,0,
0,0,0,0,0,1
};

float A[stateNum][stateNum] ={//transition matrix
1,0,0,1,0,0,
0,1,0,0,1,0,
0,0,1,0,0,1,
0,0,0,1,0,0,
0,0,0,0,1,0,
0,0,0,0,0,1
};

当然并不一定得是1和0

2.预测cvKalmanPredict，然后读出自己需要的值

3.更新观测矩阵

4.更新CvKalman

只有第一步麻烦些。上述这几步跟代码中的序号对应

如果你在做tracking，下面的例子或许更有用些。

[cpp]
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#include <cv.h>
#include <cxcore.h>
#include <highgui.h>

#include <cmath>
#include <vector>
#include <iostream>

using namespace std;

const int winHeight=600;
const int winWidth=800;

CvPoint mousePosition=cvPoint(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=cvPoint(x,y);
}
}

int main (void)
{
//1.kalman filter setup
const int stateNum=4;
const int measureNum=2;
CvKalman* kalman = cvCreateKalman( stateNum, measureNum, 0 );//state(x,y,detaX,detaY)

CvMat* process_noise = cvCreateMat( stateNum, 1, CV_32FC1 );
CvMat* measurement = cvCreateMat( measureNum, 1, CV_32FC1 );//measurement(x,y)

CvRNG rng = cvRNG(-1);
float A[stateNum][stateNum] ={//transition matrix

1,0,1,0,
0,1,0,1,
0,0,1,0,
0,0,0,1
};

memcpy( kalman->transition_matrix->data.fl,A,sizeof(A));
cvSetIdentity(kalman->measurement_matrix,cvRealScalar(1) );
cvSetIdentity(kalman->process_noise_cov,cvRealScalar(1e-5));
cvSetIdentity(kalman->measurement_noise_cov,cvRealScalar(1e-1));
cvSetIdentity(kalman->error_cov_post,cvRealScalar(1));
//initialize post state of kalman filter at random

cvRandArr(&rng,kalman->state_post,CV_RAND_UNI,cvRealScalar(0),cvRealScalar(winHeight>winWidth?winWidth:winHeight));

CvFont font;
cvInitFont(&font,CV_FONT_HERSHEY_SCRIPT_COMPLEX,1,1);

cvNamedWindow("kalman");
cvSetMouseCallback("kalman",mouseEvent);
IplImage* img=cvCreateImage(cvSize(winWidth,winHeight),8,3);
while (1){
//2.kalman prediction

const CvMat* prediction=cvKalmanPredict(kalman,0);
CvPoint predict_pt=cvPoint((int)prediction->data.fl[0],(int)prediction->data.fl[1]);

//3.update measurement

measurement->data.fl[0]=(float)mousePosition.x;
measurement->data.fl[1]=(float)mousePosition.y;

//4.update
cvKalmanCorrect( kalman, measurement );

//draw
cvSet(img,cvScalar(255,255,255,0));
cvCircle(img,predict_pt,5,CV_RGB(0,255,0),3);//predicted point with green

cvCircle(img,mousePosition,5,CV_RGB(255,0,0),3);//current position with red

char buf[256];
sprintf_s(buf,256,"predicted position:(%3d,%3d)",predict_pt.x,predict_pt.y);
cvPutText(img,buf,cvPoint(10,30),&font,CV_RGB(0,0,0));
sprintf_s(buf,256,"current position :(%3d,%3d)",mousePosition.x,mousePosition.y);
cvPutText(img,buf,cvPoint(10,60),&font,CV_RGB(0,0,0));

cvShowImage("kalman", img);
int key=cvWaitKey(3);
if (key==27){//esc

break;
}
}

cvReleaseImage(&img);
cvReleaseKalman(&kalman);
return 0;
}

#include <cv.h>
#include <cxcore.h>
#include <highgui.h>

#include <cmath>
#include <vector>
#include <iostream>
using namespace std;

const int winHeight=600;
const int winWidth=800;

CvPoint mousePosition=cvPoint(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=cvPoint(x,y);
}
}

int main (void)
{
//1.kalman filter setup
const int stateNum=4;
const int measureNum=2;
CvKalman* kalman = cvCreateKalman( stateNum, measureNum, 0 );//state(x,y,detaX,detaY)
CvMat* process_noise = cvCreateMat( stateNum, 1, CV_32FC1 );
CvMat* measurement = cvCreateMat( measureNum, 1, CV_32FC1 );//measurement(x,y)
CvRNG rng = cvRNG(-1);
float A[stateNum][stateNum] ={//transition matrix
1,0,1,0,
0,1,0,1,
0,0,1,0,
0,0,0,1
};

memcpy( kalman->transition_matrix->data.fl,A,sizeof(A));
cvSetIdentity(kalman->measurement_matrix,cvRealScalar(1) );
cvSetIdentity(kalman->process_noise_cov,cvRealScalar(1e-5));
cvSetIdentity(kalman->measurement_noise_cov,cvRealScalar(1e-1));
cvSetIdentity(kalman->error_cov_post,cvRealScalar(1));
//initialize post state of kalman filter at random
cvRandArr(&rng,kalman->state_post,CV_RAND_UNI,cvRealScalar(0),cvRealScalar(winHeight>winWidth?winWidth:winHeight));

CvFont font;
cvInitFont(&font,CV_FONT_HERSHEY_SCRIPT_COMPLEX,1,1);

cvNamedWindow("kalman");
cvSetMouseCallback("kalman",mouseEvent);
IplImage* img=cvCreateImage(cvSize(winWidth,winHeight),8,3);
while (1){
//2.kalman prediction
const CvMat* prediction=cvKalmanPredict(kalman,0);
CvPoint predict_pt=cvPoint((int)prediction->data.fl[0],(int)prediction->data.fl[1]);

//3.update measurement
measurement->data.fl[0]=(float)mousePosition.x;
measurement->data.fl[1]=(float)mousePosition.y;

//4.update
cvKalmanCorrect( kalman, measurement );

//draw
cvSet(img,cvScalar(255,255,255,0));
cvCircle(img,predict_pt,5,CV_RGB(0,255,0),3);//predicted point with green
cvCircle(img,mousePosition,5,CV_RGB(255,0,0),3);//current position with red
char buf[256];
sprintf_s(buf,256,"predicted position:(%3d,%3d)",predict_pt.x,predict_pt.y);
cvPutText(img,buf,cvPoint(10,30),&font,CV_RGB(0,0,0));
sprintf_s(buf,256,"current position :(%3d,%3d)",mousePosition.x,mousePosition.y);
cvPutText(img,buf,cvPoint(10,60),&font,CV_RGB(0,0,0));

cvShowImage("kalman", img);
int key=cvWaitKey(3);
if (key==27){//esc
break;
}
}

cvReleaseImage(&img);
cvReleaseKalman(&kalman);
return 0;
}

kalman filter 视频演示：

http://v.youku.com/v_show/id_XMjU4MzEyODky.html

demo snapshot：