广东哪里有卖南天竹种子的?

小说:广东哪里有卖南天竹种子的?作者:通建更新时间:2019-05-26字数:21055

就此王小民在枫叶派安顿下来,每天都会有消息,通过他的渠道传递出去。

春天紫藤什么时候发芽?

正自不安间,暗处却有人走了出来,春静儿定神看去,却见那是一个她认识的女人。她诧异地问:“青耕夫人,您怎么会在这里?”
在丹凤门一角,裴?F正在和颜真卿谈话,两人都穿着三品朝服,手中执象牙朝笏,两人昨天都去城外迎接了李庆安,也亲眼目睹了长安民众的狂热欢迎,尽管他们相信李庆安能将大唐带入中兴,但他们仍然为不能在李庆安登基前和他好好谈一谈而感到遗憾。

“你踢完了,该我踢了”叶扬露出一副洁白的牙齿,身体突然动了,飞快的来到了金炳南的身前,然后便是一脚踢去。

  上一篇博客中讲到了goodFeatureToTrack()这个API函数能够获取图像中的强角点。但是获取的角点坐标是整数,但是通常情况下,角点的真实位置并不一定在整数像素位置,因此为了获取更为精确的角点位置坐标,需要角点坐标达到亚像素(subPixel)精度。

1. 求取亚像素精度的原理

  找到一篇讲述原理非常清楚的文档

https://xueyayang.github.io/pdf_posts/%E4%BA%9A%E5%83%8F%E7%B4%A0%E8%A7%92%E7%82%B9%E7%9A%84%E6%B1%82%E6%B3%95.pdf,贴上来,如下:

 2. OpenCV源代码分析

  OpenCV中有cornerSubPixel()这个API函数用来针对初始的整数角点坐标进行亚像素精度的优化,该函数原型如下:

void cv::cornerSubPix( InputArray _image, InputOutputArray _corners,
                       Size win, Size zeroZone, TermCriteria criteria )

  _image为输入的单通道图像;_corners为提取的初始整数角点(比如用goodFeatureToTrack提取的强角点);win为求取亚像素角点的窗口大小,比如设置Size(11,11),需要注意的是11为半径,则窗口大小为23x23;zeroZone是设置的“零区域”,在搜索窗口内,设置的“零区域”内的值不会被累加,权重值为0。如果设置为Size(-1,-1),则表示没有这样的区域;critteria是条件阈值,包括迭代次数阈值和误差精度阈值,一旦其中一项条件满足设置的阈值,则停止迭代,获得亚像素角点。

  这个API通过下面示例的语句进行调用:

cv::cornerSubPix(grayImg, pts, cv::Size(11, 11), cv::Size(-1, -1), cv::TermCriteria(CV_TERMCRIT_EPS + CV_TERMCRIT_ITER, 30, 0.1));

   首先看criteria包含的两个条件阈值在代码中是怎么设置的。如下所示,最大迭代次数为100次,误差精度为eps*eps,也就是0.1*0.1。

    const int MAX_ITERS = 100;
    int win_w = win.width * 2 + 1, win_h = win.height * 2 + 1;
    int i, j, k;
    int max_iters = (criteria.type & CV_TERMCRIT_ITER) ? MIN(MAX(criteria.maxCount, 1), MAX_ITERS) : MAX_ITERS;
    double eps = (criteria.type & CV_TERMCRIT_EPS) ? MAX(criteria.epsilon, 0.) : 0;
    eps *= eps; // use square of error in comparsion operations

  然后是高斯权重的计算,如下所示,窗口中心附近权重高,越往窗口边界权重越小。如果设置的有“零区域”,则权重值设置为0。计算出的权重分布如下图:

Mat maskm(win_h, win_w, CV_32F), subpix_buf(win_h+2, win_w+2, CV_32F);
    float* mask = maskm.ptr<float>();

    for( i = 0; i < win_h; i++ )
    {
        float y = (float)(i - win.height)/win.height;
        float vy = std::exp(-y*y);
        for( j = 0; j < win_w; j++ )
        {
            float x = (float)(j - win.width)/win.width;
            mask[i * win_w + j] = (float)(vy*std::exp(-x*x));
        }
    }

    // make zero_zone
    if( zeroZone.width >= 0 && zeroZone.height >= 0 &&
        zeroZone.width * 2 + 1 < win_w && zeroZone.height * 2 + 1 < win_h )
    {
        for( i = win.height - zeroZone.height; i <= win.height + zeroZone.height; i++ )
        {
            for( j = win.width - zeroZone.width; j <= win.width + zeroZone.width; j++ )
            {
                mask[i * win_w + j] = 0;
            }
        }
    }

  接下来就是针对每个初始角点,按照上述公式,逐个进行迭代求取亚像素角点,代码如下。

  ① 代码中CI2为本次迭代获取的亚像素角点位置,CI为上次迭代获取的亚像素角点位置,CT是初始的整数角点位置。

  ② 每次迭代结束计算CI与CI2之间的欧式距离err,如果两者之间的欧式距离err小于设定的阈值,或者迭代次数达到设定的阈值,则停止迭代。

  ③停止迭代后,需要再次判断最终的亚像素角点位置和初始整数角点之间的差异,如果差值大于设定窗口尺寸的一半,则说明最小二乘计算中收敛性不好,丢弃计算得到的亚像素角点,仍然使用初始的整数角点。

// do optimization loop for all the points
    for( int pt_i = 0; pt_i < count; pt_i++ )
    {
        Point2f cT = corners[pt_i], cI = cT;
        int iter = 0;
        double err = 0;

        do
        {
            Point2f cI2;
            double a = 0, b = 0, c = 0, bb1 = 0, bb2 = 0;

            getRectSubPix(src, Size(win_w+2, win_h+2), cI, subpix_buf, subpix_buf.type());
            const float* subpix = &subpix_buf.at<float>(1,1);

            // process gradient
            for( i = 0, k = 0; i < win_h; i++, subpix += win_w + 2 )
            {
                double py = i - win.height;

                for( j = 0; j < win_w; j++, k++ )
                {
                    double m = mask[k];
                    double tgx = subpix[j+1] - subpix[j-1];
                    double tgy = subpix[j+win_w+2] - subpix[j-win_w-2];
                    double gxx = tgx * tgx * m;
                    double gxy = tgx * tgy * m;
                    double gyy = tgy * tgy * m;
                    double px = j - win.width;

                    a += gxx;
                    b += gxy;
                    c += gyy;

                    bb1 += gxx * px + gxy * py;
                    bb2 += gxy * px + gyy * py;
                }
            }

            double det=a*c-b*b;
            if( fabs( det ) <= DBL_EPSILON*DBL_EPSILON )
                break;

            // 2x2 matrix inversion
            double scale=1.0/det;
            cI2.x = (float)(cI.x + c*scale*bb1 - b*scale*bb2);
            cI2.y = (float)(cI.y - b*scale*bb1 + a*scale*bb2);
            err = (cI2.x - cI.x) * (cI2.x - cI.x) + (cI2.y - cI.y) * (cI2.y - cI.y);
            cI = cI2;
            if( cI.x < 0 || cI.x >= src.cols || cI.y < 0 || cI.y >= src.rows )
                break;
        }
        while( ++iter < max_iters && err > eps );

        // if new point is too far from initial, it means poor convergence.
        // leave initial point as the result
        if( fabs( cI.x - cT.x ) > win.width || fabs( cI.y - cT.y ) > win.height )
            cI = cT;

        corners[pt_i] = cI;
    }

  


 

  自己参照OpenCV源代码写了一个myCornerSubPix()接口函数以便加深理解,如下,仅供参考:

//获取窗口内子图像
bool
getSubImg(cv::Mat srcImg, cv::Point2f currPoint, cv::Mat &subImg) { int subH = subImg.rows; int subW = subImg.cols; int x = int(currPoint.x+0.5f); int y = int(currPoint.y+0.5f); int initx = x - subImg.cols / 2; int inity = y - subImg.rows / 2; if (initx < 0 || inity < 0 || (initx+subW)>=srcImg.cols || (inity+subH)>=srcImg.rows ) return false; cv::Rect imgROI(initx, inity, subW, subH); subImg = srcImg(imgROI).clone(); return true; }
//亚像素角点提取
void myCornerSubPix(cv::Mat srcImg, vector<cv::Point2f> &pts, cv::Size winSize, cv::Size zeroZone, cv::TermCriteria criteria) {
  //搜索窗口大小
int winH = winSize.width * 2 + 1; int winW = winSize.height * 2 + 1; int winCnt = winH*winW;
  //迭代阈值限制
int MAX_ITERS = 100; int max_iters = (criteria.type & CV_TERMCRIT_ITER) ? MIN(MAX(criteria.maxCount, 1), MAX_ITERS) : MAX_ITERS; double eps = (criteria.type & CV_TERMCRIT_EPS) ? MAX(criteria.epsilon, 0.) : 0; eps *= eps; // use square of error in comparsion operations //生成高斯权重 cv::Mat weightMask = cv::Mat(winH, winW, CV_32FC1); for (int i = 0; i < winH; i++) { for (int j = 0; j < winW; j++) { float wx = (float)(j - winSize.width) / winSize.width; float wy = (float)(i - winSize.height) / winSize.height; float vx = exp(-wx*wx); float vy = exp(-wy*wy); weightMask.at<float>(i, j) = (float)(vx*vy); } }   //遍历所有初始角点,依次迭代 for (int k = 0; k < pts.size(); k++) { double a, b, c, bb1, bb2; cv::Mat subImg = cv::Mat::zeros(winH+2, winW+2, CV_8UC1); cv::Point2f currPoint = pts[k]; cv::Point2f iterPoint = currPoint; int iterCnt = 0; double err = 0; //迭代 do { a = b = c = bb1 = bb2 = 0; //提取以当前点为中心的窗口子图像(为了方便求sobel微分,窗口各向四个方向扩展一行(列)像素) if ( !getSubImg(srcImg, iterPoint, subImg)) break; uchar *pSubData = (uchar*)subImg.data+winW+3;
//如下计算参考上述推导公式,窗口内累加
for (int i = 0; i < winH; i ++) { for (int j = 0; j < winW; j++) {
            //读取高斯权重值
double m = weightMask.at<float>(i, j);
//sobel算子求梯度
double sobelx = double(pSubData[i*(winW+2) + j + 1] - pSubData[i*(winW+2) + j - 1]); double sobely = double(pSubData[(i+1)*(winW+2) + j] - pSubData[(i - 1)*(winW+2) + j]); double gxx = sobelx*sobelx*m; double gxy = sobelx*sobely*m; double gyy = sobely*sobely*m; a += gxx; b += gxy; c += gyy; //邻域像素p的位置坐标 double px = j - winSize.width; double py = i - winSize.height; bb1 += gxx*px + gxy*py; bb2 += gxy*px + gyy*py; } } double det = a*c - b*b; if (fabs(det) <= DBL_EPSILON*DBL_EPSILON) break; //求逆矩阵 double invA = c / det; double invC = a / det; double invB = -b / det; //角点新位置 cv::Point2f newPoint; newPoint.x = (float)(iterPoint.x + invA*bb1 + invB*bb2); newPoint.y = (float)(iterPoint.y + invB*bb1 + invC*bb2); //和上一次迭代之间的误差 err = (newPoint.x - iterPoint.x)*(newPoint.x - iterPoint.x) + (newPoint.y - iterPoint.y)*(newPoint.y - iterPoint.y); //更新角点位置 iterPoint = newPoint; iterCnt++; if (iterPoint.x < 0 || iterPoint.x >= srcImg.cols || iterPoint.y < 0 || iterPoint.y >= srcImg.rows) break; } while (err > eps && iterCnt < max_iters); //判断求得的亚像素角点与初始角点之间的差异,即:最小二乘法的收敛性 if (fabs(iterPoint.x - currPoint.x) > winSize.width || fabs(iterPoint.y - currPoint.y) > winSize.height) iterPoint = currPoint;     //保存算出的亚像素角点 pts[k] = iterPoint; } }

  夜已深,结束。

 
  

 

 

 

 

 

   

编辑:文开

发布:2019-05-26 15:52:41

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