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我正在尝试在一张照片上构建静态增强现实场景,其中平面和图像上的共面点之间有 4 个定义的对应关系。
这是一个分步流程:
我还测量了 iPhone 摄像头相对于 A4 纸中心的位置。所以对于这个镜头,位置是 (0, 14, 42.5),以厘米为单位测量。我的 iPhone 也稍微倾斜到 table 上(5-10 度)
使用此数据,我设置了 SCNCamera
以获得第三张图像上蓝色平面的所需视角:
let camera = SCNCamera()
camera.xFov = 66
camera.zFar = 1000
camera.zNear = 0.01
cameraNode.camera = camera
cameraAngle = -7 * CGFloat.pi / 180
cameraNode.rotation = SCNVector4(x: 1, y: 0, z: 0, w: Float(cameraAngle))
cameraNode.position = SCNVector3(x: 0, y: 14, z: 42.5)
这将给我一个引用,以便与我的结果进行比较。
为了使用 SceneKit 构建 AR,我需要:
H - 单应性; K - 内矩阵; <强>[R | t] - 外部矩阵
我尝试了两种方法来找到相机的变换矩阵:使用 OpenCV 的 solvePnP 和基于 4 个共面点的单应性手动计算。
<强>1。找出单应性
这一步成功完成,因为世界原点的 UV 坐标似乎是正确的。
<强>2。内在矩阵
为了获得 iPhone 6 的固有矩阵,我使用了 this应用程序,从 100 张分辨率为 640*480 的图像中得到以下结果:
假设输入图像的宽高比为 4:3,我可以根据分辨率缩放上述矩阵
我不确定,但感觉这里有一个潜在问题。我使用 cv::calibrationMatrixValues 检查 fovx 计算出的内在矩阵,结果是 ~50°,而它应该接近 60°。
<强>3。相机位姿矩阵
func findCameraPose(homography h: matrix_float3x3, size: CGSize) -> matrix_float4x3? {
guard let intrinsic = intrinsicMatrix(imageSize: size),
let intrinsicInverse = intrinsic.inverse else { return nil }
let l1 = 1.0 / (intrinsicInverse * h.columns.0).norm
let l2 = 1.0 / (intrinsicInverse * h.columns.1).norm
let l3 = (l1+l2)/2
let r1 = l1 * (intrinsicInverse * h.columns.0)
let r2 = l2 * (intrinsicInverse * h.columns.1)
let r3 = cross(r1, r2)
let t = l3 * (intrinsicInverse * h.columns.2)
return matrix_float4x3(columns: (r1, r2, r3, t))
}
结果:
因为我测量了这个特定图像的大致位置和方向,所以我知道变换矩阵,它会给出预期的结果并且它是完全不同的:
我也有点担心引用旋转矩阵的 2-3 个元素,它是 -9.1,而它应该接近于零,因为旋转非常轻微。
有一个solvePnP OpenCV 中的函数可以解决这类问题,所以我尝试使用它而不是重新发明轮子。
Objective-C++ 中的 OpenCV:
typedef struct CameraPose {
SCNVector4 rotationVector;
SCNVector3 translationVector;
} CameraPose;
+ (CameraPose)findCameraPose: (NSArray<NSValue *> *) objectPoints imagePoints: (NSArray<NSValue *> *) imagePoints size: (CGSize) size {
vector<Point3f> cvObjectPoints = [self convertObjectPoints:objectPoints];
vector<Point2f> cvImagePoints = [self convertImagePoints:imagePoints withSize: size];
cv::Mat distCoeffs(4,1,cv::DataType<double>::type, 0.0);
cv::Mat rvec(3,1,cv::DataType<double>::type);
cv::Mat tvec(3,1,cv::DataType<double>::type);
cv::Mat cameraMatrix = [self intrinsicMatrixWithImageSize: size];
cv::solvePnP(cvObjectPoints, cvImagePoints, cameraMatrix, distCoeffs, rvec, tvec);
SCNVector4 rotationVector = SCNVector4Make(rvec.at<double>(0), rvec.at<double>(1), rvec.at<double>(2), norm(rvec));
SCNVector3 translationVector = SCNVector3Make(tvec.at<double>(0), tvec.at<double>(1), tvec.at<double>(2));
CameraPose result = CameraPose{rotationVector, translationVector};
return result;
}
+ (vector<Point2f>) convertImagePoints: (NSArray<NSValue *> *) array withSize: (CGSize) size {
vector<Point2f> points;
for (NSValue * value in array) {
CGPoint point = [value CGPointValue];
points.push_back(Point2f(point.x - size.width/2, point.y - size.height/2));
}
return points;
}
+ (vector<Point3f>) convertObjectPoints: (NSArray<NSValue *> *) array {
vector<Point3f> points;
for (NSValue * value in array) {
CGPoint point = [value CGPointValue];
points.push_back(Point3f(point.x, 0.0, -point.y));
}
return points;
}
+ (cv::Mat) intrinsicMatrixWithImageSize: (CGSize) imageSize {
double f = 0.84 * max(imageSize.width, imageSize.height);
Mat result(3,3,cv::DataType<double>::type);
cv::setIdentity(result);
result.at<double>(0) = f;
result.at<double>(4) = f;
return result;
}
在 Swift 中的用法:
func testSolvePnP() {
let source = modelPoints().map { NSValue(cgPoint: $0) }
let destination = perspectivePicker.currentPerspective.map { NSValue(cgPoint: $0)}
let cameraPose = CameraPoseDetector.findCameraPose(source, imagePoints: destination, size: backgroundImageView.size);
cameraNode.rotation = cameraPose.rotationVector
cameraNode.position = cameraPose.translationVector
}
输出:
结果更好,但与我的预期相去甚远。
我还尝试过一些其他的东西:
我真的被这个问题困住了,所以非常感谢任何帮助。
最佳答案
实际上,我距离使用 OpenCV 的工作解决方案只有一步之遥。
第二种方法的问题是我忘记将 solvePnP
的输出转换回 SpriteKit 的坐标系。
请注意,输入(图像和世界点)实际上已正确转换为 OpenCV 坐标系(convertObjectPoints:
和 convertImagePoints:withSize:
方法)
所以这是一个固定的 findCameraPose
方法,其中打印了一些注释和中间结果:
+ (CameraPose)findCameraPose: (NSArray<NSValue *> *) objectPoints imagePoints: (NSArray<NSValue *> *) imagePoints size: (CGSize) size {
vector<Point3f> cvObjectPoints = [self convertObjectPoints:objectPoints];
vector<Point2f> cvImagePoints = [self convertImagePoints:imagePoints withSize: size];
std::cout << "object points: " << cvObjectPoints << std::endl;
std::cout << "image points: " << cvImagePoints << std::endl;
cv::Mat distCoeffs(4,1,cv::DataType<double>::type, 0.0);
cv::Mat rvec(3,1,cv::DataType<double>::type);
cv::Mat tvec(3,1,cv::DataType<double>::type);
cv::Mat cameraMatrix = [self intrinsicMatrixWithImageSize: size];
cv::solvePnP(cvObjectPoints, cvImagePoints, cameraMatrix, distCoeffs, rvec, tvec);
std::cout << "rvec: " << rvec << std::endl;
std::cout << "tvec: " << tvec << std::endl;
std::vector<cv::Point2f> projectedPoints;
cvObjectPoints.push_back(Point3f(0.0, 0.0, 0.0));
cv::projectPoints(cvObjectPoints, rvec, tvec, cameraMatrix, distCoeffs, projectedPoints);
for(unsigned int i = 0; i < projectedPoints.size(); ++i) {
std::cout << "Image point: " << cvImagePoints[i] << " Projected to " << projectedPoints[i] << std::endl;
}
cv::Mat RotX(3, 3, cv::DataType<double>::type);
cv::setIdentity(RotX);
RotX.at<double>(4) = -1; //cos(180) = -1
RotX.at<double>(8) = -1;
cv::Mat R;
cv::Rodrigues(rvec, R);
R = R.t(); // rotation of inverse
Mat rvecConverted;
Rodrigues(R, rvecConverted); //
std::cout << "rvec in world coords:\n" << rvecConverted << std::endl;
rvecConverted = RotX * rvecConverted;
std::cout << "rvec scenekit :\n" << rvecConverted << std::endl;
Mat tvecConverted = -R * tvec;
std::cout << "tvec in world coords:\n" << tvecConverted << std::endl;
tvecConverted = RotX * tvecConverted;
std::cout << "tvec scenekit :\n" << tvecConverted << std::endl;
SCNVector4 rotationVector = SCNVector4Make(rvecConverted.at<double>(0), rvecConverted.at<double>(1), rvecConverted.at<double>(2), norm(rvecConverted));
SCNVector3 translationVector = SCNVector3Make(tvecConverted.at<double>(0), tvecConverted.at<double>(1), tvecConverted.at<double>(2));
return CameraPose{rotationVector, translationVector};
}
注意事项:
关于ios - 从单应性或使用 solvePnP() 函数估计相机姿态,我们在Stack Overflow上找到一个类似的问题: https://stackoverflow.com/questions/44008003/
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