Question

我在iOS应用程序中遇到问题，我尝试使用solvePnP获取视图矩阵并使用现代OpenGL渲染3d立方体。当我的代码尝试直接在检测到的标记之上渲染一个3d立方体时，它似乎与标记有一定的偏移（例如，参见视频）

https://www.youtube.com/watch?v=HhP5Qr3YyGI&feature=youtu.be

（在图像的右下角，您可以看到跟踪器标记周围的单应性的opencv渲染。屏幕的其余部分是相机输入框的opengl渲染和位置处的3d立方体（0,0， 0）。

每当我移动标记时，立方体都会旋转并正确平移，尽管它非常有说明翻译的规模存在一些差异（IE，如果我在现实世界中移动我的标记5cm，它几乎不会移动1cm屏幕）

这些是我认为错误可能来自的代码的相关部分：

从单应性中提取视图矩阵：

AVCaptureDevice *deviceInput = [AVCaptureDevice defaultDeviceWithMediaType:AVMediaTypeVideo];
AVCaptureDeviceFormat *format = deviceInput.activeFormat;
CMFormatDescriptionRef fDesc = format.formatDescription;
CGSize dim = CMVideoFormatDescriptionGetPresentationDimensions(fDesc, true, true);

const float cx = float(dim.width) / 2.0;
const float cy = float(dim.height) / 2.0;

const float HFOV = format.videoFieldOfView;
const float VFOV = ((HFOV)/cx)*cy;

const float fx = abs(float(dim.width) / (2 * tan(HFOV / 180 * float(M_PI) / 2)));
const float fy = abs(float(dim.height) / (2 * tan(VFOV / 180 * float(M_PI) / 2)));


Mat camIntrinsic = Mat::zeros(3, 3, CV_64F);
camIntrinsic.at<double>(0, 0) = fx;
camIntrinsic.at<double>(0, 2) = cx;
camIntrinsic.at<double>(1, 1) = fy;
camIntrinsic.at<double>(1, 2) = cy;
camIntrinsic.at<double>(2, 2) = 1.0;

std::vector<cv::Point3f> object3dPoints;
object3dPoints.push_back(cv::Point3f(-0.5f,-0.5f,0));
object3dPoints.push_back(cv::Point3f(+0.5f,-0.5f,0));
object3dPoints.push_back(cv::Point3f(+0.5f,+0.5f,0));
object3dPoints.push_back(cv::Point3f(-0.5f,+0.5f,0));


cv::Mat raux,taux;
cv::Mat Rvec, Tvec;
cv::solvePnP(object3dPoints, mNewImageBounds, camIntrinsic, Mat(),raux,taux); //mNewImageBounds are the 4 corner of the homography detected by perspectiveTransform (the green outline seen in the image)
raux.convertTo(Rvec,CV_32F);
taux.convertTo(Tvec ,CV_64F);

Mat Rot(3,3,CV_32FC1);
Rodrigues(Rvec, Rot);

// [R | t] matrix
Mat_<double> para = Mat_<double>::eye(4,4);
Rot.convertTo(para(cv::Rect(0,0,3,3)),CV_64F);
Tvec.copyTo(para(cv::Rect(3,0,1,3)));

Mat cvToGl = Mat::zeros(4, 4, CV_64F);
cvToGl.at<double>(0, 0) = 1.0f;
cvToGl.at<double>(1, 1) = -1.0f; // Invert the y axis
cvToGl.at<double>(2, 2) = -1.0f; // invert the z axis
cvToGl.at<double>(3, 3) = 1.0f;

para = cvToGl * para;

Mat_<double> modelview_matrix;
Mat(para.t()).copyTo(modelview_matrix); // transpose to col-major for OpenGL
glm::mat4 openGLViewMatrix;
for(int col = 0; col < modelview_matrix.cols; col++)
{
    for(int row = 0; row < modelview_matrix.rows; row++)
    {
        openGLViewMatrix[col][row] = modelview_matrix.at<double>(col,row);
    }
}

我确保相机内在矩阵包含正确的值，将opencv Mat转换为opengl视图矩阵的部分我认为正确，因为立方体平移并向正确方向旋转。

一旦计算了视图矩阵，我就用它来绘制立方体，如下所示：

_projectionMatrix = glm::perspective<float>(radians(60.0f), fabs(view.bounds.size.width / view.bounds.size.height), 0.1f, 100.0f);
_cube_ModelMatrix = glm::translate(glm::vec3(0,0,0));
const mat4 MVP = _projectionMatrix * openGLViewMatrix * _cube_ModelMatrix;
glUniformMatrix4fv(glGetUniformLocation(_cube_program, "ModelMatrix"), 1, GL_FALSE, value_ptr(MVP));

glDrawElements(GL_TRIANGLES, 36, GL_UNSIGNED_INT, BUFFER_OFFSET(0));

是否有人能够发现我的错误？

Answer 1

您应该按照此处的说明创建透视矩阵：http://ksimek.github.io/2013/06/03/calibrated_cameras_in_opengl

这是快速代码：

const float fx = intrinsicParams(0, 0); // Focal length in x axis
const float fy = intrinsicParams(1, 1); // Focal length in y axis
const float cx = intrinsicParams(0, 2); // Primary point x
const float cy = intrinsicParams(1, 2); // Primary point y

projectionMatrix(0, 0) = 2.0f * fx;
projectionMatrix(0, 1) = 0.0f;
projectionMatrix(0, 2) = 0.0f;
projectionMatrix(0, 3) = 0.0f;

projectionMatrix(1, 0) = 0.0f;
projectionMatrix(1, 1) = 2.0f * fy;
projectionMatrix(1, 2) = 0.0f;
projectionMatrix(1, 3) = 0.0f;

projectionMatrix(2, 0) = 2.0f * cx - 1.0f;
projectionMatrix(2, 1) = 2.0f * cy - 1.0f;
projectionMatrix(2, 2) = -(far + near) / (far - near);
projectionMatrix(2, 3) = -1.0f;

projectionMatrix(3, 0) = 0.0f;
projectionMatrix(3, 1) = 0.0f;
projectionMatrix(3, 2) = -2.0f * far * near / (far - near);
projectionMatrix(3, 3) = 0.0f;

有关内在矩阵的更多信息：http://ksimek.github.io/2013/08/13/intrinsic

OpenCV + OpenGL使用solvePnP相机姿势 - 对象与检测到的标记偏移

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