您的位置:首页 > 运维架构

图像处理中二次曲线拟合

2016-07-16 12:43 351 查看
2016/7/16

 

在一次提取发光管的中心线程序中,由于我们只拍到了断续而弯曲的发光管,所以无法使用光带中心线提取的方法进行提取。

在此背景下,我想到了拟合。之前有学过直线拟合的方法,名为最小二乘法。其基本步骤如下:

(1)    设需要拟合的直线为y=a*x+b。

(2)    首先选取进行拟合的点集,选取方法可以为阈值分割,模板匹配等,设最后选出的点集为。

(3)    求该点集到直线的距离平方和,

(4)    对Sum分别求关于x,y的偏导函数。

(5)    根据偏导求出该距离平方和最小时的a,b值即为拟合的曲线的参数。

为了与之后的二次曲线拟合做对比,我写了下直线拟合的函数,先从源图像中根据阈值分割选取拟合点集(这里我认为灰度值超过45即被选取),再根据上述步骤计算a,b的值。源代码如下:

/*输入为三通道图像*/
/*对图像中的亮点进行直线拟合*/
void cvLineFit1D(IplImage* src_getin)
{
    IplImage*src =cvCloneImage(src_getin);
    IplImage*image_threshold = cvCreateImage(cvGetSize(src),8,1);
    cvCvtColor(src,image_threshold,CV_BGR2GRAY);
    cvThreshold(image_threshold,image_threshold,45,255,CV_THRESH_BINARY);
    cvShowImage("cvLineFit1D[Threshold]",image_threshold);
 
    //设拟合的二次曲线方程为y=ax+b;
    //先求出各点到拟合直线上的距离的平方和;
    //求出使得该平方和最小的a,b的值 ;
    long
long int k1=0;
    long
long int k2=0;
    long
long int k3=0;
    long
long int k4=0;
    long
long int k5=0;
    long
long int k6=0;
    for (inti=0;i<image_threshold->height;i++)
    {
        for (intj=0;j<image_threshold->width;j++)
        {
            if(cvGetReal2D(image_threshold,i,j)==255)
            {
                k1+=2*i*i;
                k2+=2*i;
                k3+=2*i*j;
                k4+=2*i;
                k5+=2;
                k6+=2*j;
            }
        }
    }
 
 
    double a,b;
    a = (double)(k3*k5-k6*k2)/(k1*k5-k4*k2);
    b = (double)(k3-k1*a)/k2;
   
    int bottom = image_threshold->height;
    int top = 0;
    for(int i =0;i<image_threshold->height;i++)
        for(int j =0;j<image_threshold->width;j++)
        {
            if(cvGetReal2D(image_threshold,i,j) == 255)
            {
                if(i>top)
                    top= i;
                if(i<bottom)
                    bottom= i;
            }
        }
 
    for (inti=bottom;i<top;i++)
    {
        int temp_y = a*i+b;
        if(temp_y<src->width&&temp_y>0)
        {
            cvCircle(src,cvPoint(temp_y,i),1,cvScalar(255,255,255));
            //cvSet2D(src,i,temp_y,cvScalar(255,255,255));
        }
        cvShowImage("直线拟合",src);
    }
    cvReleaseImage(&src);
}
拟合效果如下:



 


而曲线拟合,则是在直线拟合的基础上,进行相似的偏导计算,只是设所拟合的曲线方程为y=a*x*x+b*x+c

 

代码如下:

 

/*对图像中的亮点进行二次曲线拟合;*/
void cvCurveFit2D(IplImage* src)
{
 
    IplImage*image_threshold = cvCreateImage(cvGetSize(src),8,1);
    cvCvtColor(src,image_threshold,CV_BGR2GRAY);
 
    cvThreshold(image_threshold,image_threshold,50,255,CV_THRESH_BINARY);
    //cvShowImage("cvCurveFit2D[Threshold]",image_threshold);
      
    //设拟合的二次曲线方程为y=ax2+bx+c;
    //先求出各点到拟合曲线上的距离的平方和;
    //求出使得该平方和最小的a,b,c的值 ;
    double a,b,c;
    long
long int k1=0;
    long
long int k2=0;
    long
long int k3=0;
    long
long int k4=0;
    long
long int k5=0;
    long
long int k6=0;
    long
long int k7=0;
    long
long int k8=0;
    long
long int k9=0;
    long
long int k10=0;
    long
long int k11=0;
    long
long int k12=0;
    for (inti=0;i<image_threshold->height;i+=5)
    {
        for (intj=0;j<image_threshold->width;j+=5)
        {
            if(cvGetReal2D(image_threshold,i,j)==255)
            {
                //cvCircle(src,cvPoint(j,i),1,cvScalar(0,0,0));
                //如果该点为亮点,则将其加入拟合点;
                //cout<<"k1="<<k1<<",i="<<i<<",j="<<j<<endl;
               
                k1= k1+(long
longint)i*i*i*i; //k1==2x^4
                //cout<<"k1="<<k1<<endl;
                //getchar();
                k2= k2 + (long
longint)i*i*i;   //k2==2x^3
                k3= k3 + (long
longint)i*i;     //k3==2x^2
                k4= k4 + (long
longint)i*i*j;   //k4==-2y*x^2
                k5= k5 + (long
longint)i*i*i;
                k6= k6 + (long
longint)i*i;
                k7= k7 + (long
longint)i;
                k8= k8 + (long
longint)i*j;
                k9= k9 + (long
longint)i*i;
                k10= k10 + (long
longint)i;
                k11= k11 + 1;
                k12= k12 + (long
longint)j;
            }
        }
    }
 
    //根据偏导求出a,b,c的值;
 
    long
long int t1 = k1/k3-k5/k7;
    long
long int t2 = k2/k3-k6/k7;
    long
long int t3 = k4/k3-k8/k7;
    long
long int t4 = k1/k3-k9/k11;
    long
long int t5 = k2/k3-k10/k11;
    long
long int t6 = k4/k3-k12/k11;
 
 
    a = (double)(t3*t5-t6*t2)/(t1*t5-t4*t2);
    b = (double)(t3-t1*a)/t2;
    double b1=(double)(t6-t4*a)/t5;
    c = (double)(k4-k1*a-k2*b)/k3;
 
    int bottom = image_threshold->height;
    int top = 0;
    for(int i =0;i<image_threshold->height;i++)
        for(int j =0;j<image_threshold->width;j++)
        {
            if(cvGetReal2D(image_threshold,i,j) == 255)
            {
                if(i>top)
                    top= i;
                if(i<bottom)
                    bottom= i;
            }
        }
 
    for (inti=bottom;i<top;i++)
    {
        int temp_y = a*i*i+b*i+c;
        if(temp_y<src->width&&temp_y>0)

            cvCircle(src,cvPoint(temp_y,i),1,cvScalar(255,255,255));
            //cvSet2D(src,i,temp_y,cvScalar(255,255,255));
        cvShowImage("二次曲线拟合",src);
    }
 }

拟合效果如下:



内容来自用户分享和网络整理,不保证内容的准确性,如有侵权内容,可联系管理员处理 点击这里给我发消息