Question

我通过协方差矩阵生成了连通分量区域的椭圆：

    //initialize distribution of points
    int num = blob.size();
    float arr[num][2];
    for(int i=0; i<num; i++)
    {
        arr[i][1] = blob[i].first; //row index, y
        arr[i][0] = blob[i].second; //column index, x
    }
    //calculate covariance matrix
    cv::Mat mat = cv::Mat(num, 2, CV_32FC1, &arr);
    cv::Mat cov, mean;
    cv::calcCovarMatrix( mat, cov, mean, CV_COVAR_NORMAL | CV_COVAR_ROWS);
    cov = cov / (mat.rows - 1);
    //calculate eigen problem
    cv::Mat eigVec = cv::Mat(2, 2, CV_32FC1);
    cv::Mat eigVal = cv::Mat(1, 2, CV_32FC1);
    cv::eigen( cov, eigVal, eigVec);
    // cout << eigVec << endl;
    //calculate the major and minor axes
    float alpha = sqrt( eigVal.at<double>(0,0) ) * sqrt(chisquare_val);
    float beta = sqrt( eigVal.at<double>(0,1) ) * sqrt(chisquare_val);
    //calcualte the angle.
    double angle = atan2( eigVec.at<double>(0,1), eigVec.at<double>(0,0) ) * 180 / M_PI;

    return cv::RotatedRect( cv::Point2f(mean.at<double>(0,0), mean.at<double>(0,1)), 
        cv::Size2f(alpha, beta), angle);

现在，我需要通过以下公式计算每个像素到椭圆的距离：

X = cos（θ）（x-xc）+ sin（θ）（y-yc）

Y = -sin（θ）（x-xc）+ cos（θ）（y-yc）

dist =（X /α）^ 2 +（Y /β）^ 2

其中θ是旋转角度，xc，yc是中心坐标， α是半长轴（始终是最大轴），β是半短轴

这是我的实施：

    double distance(cv::RotatedRect &ellipse, cv::Point &point)
{
    double center_x = ellipse.center.x;
    double center_y = ellipse.center.y;
    double alpha = ellipse.size.width / 2; //semi-major axes
    double beta = ellipse.size.height / 2; //semi-minor axes
    double angle = ellipse.angle; //rotation angle

    double p_x = point.x;
    double p_y = point.y;

    double new_x = (p_x - center_x) * cos(angle) + (p_y - center_y) * sin(angle);
    double new_y = (p_x - center_x) * (-sin(angle)) + (p_y - center_y) * cos(angle);

    double result = (pow(new_x, 2.0) / pow(alpha, 2.0)) + (pow( new_y, 2.0) / pow(beta, 2.0));
    return result;
}

我用图像测试了这段代码。它适用于水平椭圆，如： the grey area covers the points that within the ellipse

但代码在垂直椭圆上失败，输出如下：the gray area should cover the ellipse perfectly

那么，有人可以告诉我问题是什么以及为什么用垂直椭圆计算距离失败了？

查找椭圆内的像素（由协方差矩阵生成）

0 个答案: