SceneKit 3D Marker Augmented Reality iOS - ios

Last couple of weeks I've been working on developing a simple proof-of-concept application in which a 3D model is projected over a specific Augmented Reality marker (in my case I am using Aruco markers) in IOS (with Swift and Objective-C)
I calibrated an Ipad Camera with a specific fixed lens position and used that to estimate the pose of the AR marker (which from my debug analysis seem pretty accurate). The problem seems (surprise, surprise) when I try to use SceneKit scene to project a model over the marker.
I am aware that the axis in opencv and SceneKit are different (Y and Z) and already done this correction as well as the row order/column order difference between the two libraries.
After constructing the projection matrix, I apply that same transform to the 3D model and from my debug analysis the object seems to be translated to the desired position and with the desired rotation. The problem is that it never does overlap the specific image pixel position of the marker. I am using a AVCapturePreviewVideoLayer as to put the video in background that has the same bounds as my SceneKit View.
Has anyone has a clue why this happens? I tried to play with cameras FOV's but with no real impact in the results.
Thank you all for your time.
EDIT1: I Will post some of the code here to reveal what I am currently doing.
I have two subviews inside the main view, one which is a background AVCaptureVideoPreviewLayer and another which is a SceneKitView. Both have the same bounds as the main view.
At each frame I use an opencv wrapper which outputs the pose of each marker:
std::vector<int> ids;
std::vector<std::vector<cv::Point2f>> corners, rejected;
cv::aruco::detectMarkers(frame, _dictionary, corners, ids, _detectorParams, rejected);
if (ids.size() > 0 ){
cv::aruco::drawDetectedMarkers(frame, corners, ids);
cv::Mat rvecs, tvecs;
cv::aruco::estimatePoseSingleMarkers(corners, 2.6, _intrinsicMatrix, _distCoeffs, rvecs, tvecs);
// Let's protect ourselves agains multiple markers
if (rvecs.total() > 1)
return;
_markerFound = true;
cv::Rodrigues(rvecs, _currentR);
_currentT = tvecs;
for (int row = 0; row < _currentR.rows; row++){
for (int col = 0; col < _currentR.cols; col++){
_currentExtrinsics.at<double>(row, col) = _currentR.at<double>(row, col);
}
_currentExtrinsics.at<double>(row, 3) = _currentT.at<double>(row);
}
_currentExtrinsics.at<double>(3,3) = 1;
std::cout << tvecs << std::endl;
// Convert coordinate systems of opencv to openGL (SceneKit)
// Note that in openCV z goes away the camera (in openGL goes into the camera)
// and y points down and on openGL point up
// Another note: openCV has a column order matrix representation, while SceneKit
// has a row order matrix, but we'll take care of it later.
cv::Mat cvToGl = cv::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;
_currentExtrinsics = cvToGl * _currentExtrinsics;
cv::aruco::drawAxis(frame, _intrinsicMatrix, _distCoeffs, rvecs, tvecs, 5);
Then in each frame I convert the opencv matrix for a SCN4Matrix:
- (SCNMatrix4) transformToSceneKit:(cv::Mat&) openCVTransformation{
SCNMatrix4 mat = SCNMatrix4Identity;
// Transpose
openCVTransformation = openCVTransformation.t();
// copy the rotationRows
mat.m11 = (float) openCVTransformation.at<double>(0, 0);
mat.m12 = (float) openCVTransformation.at<double>(0, 1);
mat.m13 = (float) openCVTransformation.at<double>(0, 2);
mat.m14 = (float) openCVTransformation.at<double>(0, 3);
mat.m21 = (float)openCVTransformation.at<double>(1, 0);
mat.m22 = (float)openCVTransformation.at<double>(1, 1);
mat.m23 = (float)openCVTransformation.at<double>(1, 2);
mat.m24 = (float)openCVTransformation.at<double>(1, 3);
mat.m31 = (float)openCVTransformation.at<double>(2, 0);
mat.m32 = (float)openCVTransformation.at<double>(2, 1);
mat.m33 = (float)openCVTransformation.at<double>(2, 2);
mat.m34 = (float)openCVTransformation.at<double>(2, 3);
//copy the translation row
mat.m41 = (float)openCVTransformation.at<double>(3, 0);
mat.m42 = (float)openCVTransformation.at<double>(3, 1)+2.5;
mat.m43 = (float)openCVTransformation.at<double>(3, 2);
mat.m44 = (float)openCVTransformation.at<double>(3, 3);
return mat;
}
At each frame in which the AR marker is found I add a box to the scene and apply the transformation to the object node:
SCNBox *box = [SCNBox boxWithWidth:5.0 height:5.0 length:5.0 chamferRadius:0.0];
_boxNode = [SCNNode nodeWithGeometry:box];
if (found){
[self.delegate returnExtrinsicsMat:extrinsicMatrixOfTheMarker];
Mat R, T;
[self.delegate returnRotationMat:R];
[self.delegate returnTranslationMat:T];
SCNMatrix4 Transformation;
Transformation = [self transformToSceneKit:extrinsicMatrixOfTheMarker];
//_cameraNode.transform = SCNMatrix4Invert(Transformation);
[_sceneKitScene.rootNode addChildNode:_cameraNode];
//_cameraNode.camera.projectionTransform = SCNMatrix4Identity;
//_cameraNode.camera.zNear = 0.0;
_sceneKitView.pointOfView = _cameraNode;
_boxNode.transform = Transformation;
[_sceneKitScene.rootNode addChildNode:_boxNode];
//_boxNode.position = SCNVector3Make(Transformation.m41, Transformation.m42, Transformation.m43);
std::cout << (_boxNode.position.x) << " " << (_boxNode.position.y) << " " << (_boxNode.position.z) << std::endl << std::endl;
}
For example if the translation vector is (-1, 5, 20) the object appears in the scene in position (-1, -5, -20) in the scene, and the rotation is correct also. The problem is that it never appears in the correct position in the background image. I will add some images to show the result.
Does anyone know why this is happening?

Found out the solution. Instead of applying the transform to the node of the object I applied the inverted transformation matrix to the camera node. Then for the camera perspective transform matrix I applied the following matrix:
projection = SCNMatrix4Identity
projection.m11 = (2 * (float)(cameraMatrix[0])) / -(ImageWidth*0.5)
projection.m12 = (-2 * (float)(cameraMatrix[1])) / (ImageWidth*0.5)
projection.m13 = (width - (2 * Float(cameraMatrix[2]))) / (ImageWidth*0.5)
projection.m22 = (2 * (float)(cameraMatrix[4])) / (ImageHeight*0.5)
projection.m23 = (-height + (2 * (float)(cameraMatrix[5]))) / (ImageHeight*0.5)
projection.m33 = (-far - near) / (far - near)
projection.m34 = (-2 * far * near) / (far - near)
projection.m43 = -1
projection.m44 = 0
being far and near the z clipping planes.
I also had to correct the box initial position to center it on the marker.

Related

Pose Estimation - cv::SolvePnP with Scenekit - Coordinate System Question

I have been working on Pose Estimation (rectifying key points on a 3D model with 2D points on an image to match pose) via OpenCV's cv::solvePNP, using features / key points from Apples Vision framework.
TL-DR:
My scene kit model is being translated and the units look correct when introspecting the translation and rotation vectors from solvePnP (ie, they are the right order of magnitude), but the coordinate system of the translation appears off:
I am trying to understand the coordinate system requirements with solvePnP wrt to Metal / OpenGL coordinate system and my camera projection matrix.
What 'projectionMatrix' does my SCNCamera require to match image based coordinate system passed into solvePnP?
Some things ive read / believe I am taking into account.
OpenCV vs OpenGL (thus Metal) have row major vs column major differences.
OpenCV's coordinate system for 3D is different than OpenGL (thus Metal).
Longer with code:
My workflow is as such:
Step 1 - use a 3D model tool to introspect points on my 3D model and get the objects vertex positions for the major key points in the 2D detected features. I am using left pupil, right pupil, tip of nose, tip of chin, left outer lip corner, right outer lip corner.
Step 2 - Run a vision request and extract a list of points in image space (converting for OpenCV's top left coordinate system) and extract the same ordered list of 2D points.
Step 3 - Construct a camera matrix by using the size of the input image.
Step 4 - run cv::solvePnP, and then use cv::Rodrigues to convert the rotation vector to a matrix
Step 5 - Convert the coordinate system of the resulting transforms into something appropriate for the GPU - invert the y and z axis and combine the translation and rotation to a single 4x4 Matrix, and then transpose it for the appropriate major ness of OpenGL / Metal
Step 6 - apply the resulting transform to Scenekit via:
let faceNodeTransform = openCVWrapper.transform(for: landmarks, imageSize: size)
self.destinationView.pointOfView?.transform = SCNMatrix4Invert(faceNodeTransform)
Below is my Obj-C++ OpenCV Wrapper which takes in a subset of Vision Landmarks and the true pixel size of the image being looked at:
/ https://answers.opencv.org/question/23089/opencv-opengl-proper-camera-pose-using-solvepnp/
- (SCNMatrix4) transformFor:(VNFaceLandmarks2D*)landmarks imageSize:(CGSize)imageSize
{
// 1 convert landmarks to image points in image space (pixels) to vector of cv::Point2f's :
// Note that this translates the point coordinate system to be top left oriented for OpenCV's image coordinates:
std::vector<cv::Point2f > imagePoints = [self imagePointsForLandmarks:landmarks imageSize:imageSize];
// 2 Load Model Points
std::vector<cv::Point3f > modelPoints = [self modelPoints];
// 3 create our camera extrinsic matrix
// TODO - see if this is sane?
double max_d = fmax(imageSize.width, imageSize.height);
cv::Mat cameraMatrix = (cv::Mat_<double>(3,3) << max_d, 0, imageSize.width/2.0,
0, max_d, imageSize.height/2.0,
0, 0, 1.0);
// 4 Run solvePnP
double distanceCoef[] = {0,0,0,0};
cv::Mat distanceCoefMat = cv::Mat(1 ,4 ,CV_64FC1,distanceCoef);
// Output Matrixes
std::vector<double> rv(3);
cv::Mat rotationOut = cv::Mat(rv);
std::vector<double> tv(3);
cv::Mat translationOut = cv::Mat(tv);
cv::solvePnP(modelPoints, imagePoints, cameraMatrix, distanceCoefMat, rotationOut, translationOut, false, cv::SOLVEPNP_EPNP);
// 5 Convert rotation matrix (actually a vector)
// To a real 4x4 rotation matrix:
cv::Mat viewMatrix = cv::Mat::zeros(4, 4, CV_64FC1);
cv::Mat rotation;
cv::Rodrigues(rotationOut, rotation);
// Append our transforms to our matrix and set final to identity:
for(unsigned int row=0; row<3; ++row)
{
for(unsigned int col=0; col<3; ++col)
{
viewMatrix.at<double>(row, col) = rotation.at<double>(row, col);
}
viewMatrix.at<double>(row, 3) = translationOut.at<double>(row, 0);
}
viewMatrix.at<double>(3, 3) = 1.0f;
// Transpose OpenCV to OpenGL coords
cv::Mat cvToGl = cv::Mat::zeros(4, 4, CV_64FC1);
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;
viewMatrix = cvToGl * viewMatrix;
// Finally transpose to get correct SCN / OpenGL Matrix :
cv::Mat glViewMatrix = cv::Mat::zeros(4, 4, CV_64FC1);
cv::transpose(viewMatrix , glViewMatrix);
return [self convertCVMatToMatrix4:glViewMatrix];
}
- (SCNMatrix4) convertCVMatToMatrix4:(cv::Mat)matrix
{
SCNMatrix4 scnMatrix = SCNMatrix4Identity;
scnMatrix.m11 = matrix.at<double>(0, 0);
scnMatrix.m12 = matrix.at<double>(0, 1);
scnMatrix.m13 = matrix.at<double>(0, 2);
scnMatrix.m14 = matrix.at<double>(0, 3);
scnMatrix.m21 = matrix.at<double>(1, 0);
scnMatrix.m22 = matrix.at<double>(1, 1);
scnMatrix.m23 = matrix.at<double>(1, 2);
scnMatrix.m24 = matrix.at<double>(1, 3);
scnMatrix.m31 = matrix.at<double>(2, 0);
scnMatrix.m32 = matrix.at<double>(2, 1);
scnMatrix.m33 = matrix.at<double>(2, 2);
scnMatrix.m34 = matrix.at<double>(2, 3);
scnMatrix.m41 = matrix.at<double>(3, 0);
scnMatrix.m42 = matrix.at<double>(3, 1);
scnMatrix.m43 = matrix.at<double>(3, 2);
scnMatrix.m44 = matrix.at<double>(3, 3);
return (scnMatrix);
}
Some questions:
An SCNNode has no modelViewMatrix (just as I understand it, a transform, which is the modelMatrix) to just throw a matrix at - so I've read the inverse of the transform from SolvePNP process can be used to pose the camera instead, which appears to get me the closes result. I want to ensure this approach is correct.
If I have the modelViewMatrix, and the projectionMatrix, I should be able to calculate the appropriate modelMatrix? Is this the approach I should be taking?
Its unclear to me what projectionMatrix I should be using for my SceneKit Scene and If that has any bearing on my results. Do I need a pixel for pixel exact match of my viewport to the image size, and how do I properly configure my SCNCamera to ensure coordinate system agreeance for SolvePnP?
Thank you very much!

Using android data to stitch multiple images

I am using gyroscope data from android phone to stitch two images. The image are placed as if they are flipped.
rotation matrix of camera from gyroscope-
double thetaOverTwo = gyroscopeRotationVelocity * dT / 2.0f;
double sinThetaOverTwo = Math.sin(thetaOverTwo);
double cosThetaOverTwo = Math.cos(thetaOverTwo);
deltaQuaternion.setY((float) (sinThetaOverTwo * axisX));
deltaQuaternion.setX(-(float) (sinThetaOverTwo * axisY));
deltaQuaternion.setZ((float) (sinThetaOverTwo * axisZ));
deltaQuaternion.setW(-(float) cosThetaOverTwo);
Matrix.setRotateM(mRotationMatrix, 0, (-(float) (2.0f * Math.acos(q.getW()) * 180.0f / Math.PI)), q.getX(), q.getY(), q.getZ());
Note: Above set of equation is used because android phone is always used in landscape mode.
Each time I click an image, rotation matrix calculated from above code is pushed to rot_mat vector;
Now I am using the same matrix as camera rotation matrix, but the output is as if images are flipped.
Mat ref_matg = rot_mat[mid]; // mid is index of reference image
for (size_t i = 0; i < num_images; ++i){
Mat R = rot_mat[i]*ref_matg.inv();
R.convertTo(R, CV_32F);
cameras[i].R = R;
cameras[i].focal = focal;
cameras[i].ppx = ppx;
cameras[i].ppy = ppy;
cameras[i].aspect = aspect;
}
However if I use the same code, by initially flipping all the images, the output is correct.
Can anyone give me reason behind this.

Augmented Reality iOS application tracking issue

I am able to detect markers, identify markers and initialise OpenGL objects on screen. The issue I'm having is overlaying them on top of the markers position in the camera world. My camera is calibrated best I can using this method Iphone 6 camera calibration for OpenCV. I feel there is an issue with my cameras projection matrix, I create it as follows:
-(void)buildProjectionMatrix:
(Matrix33)cameraMatrix:
(int)screen_width:
(int)screen_height:
(Matrix44&) projectionMatrix
{
float near = 0.01; // Near clipping distance
float far = 100; // Far clipping distance
// Camera parameters
float f_x = cameraMatrix.data[0]; // Focal length in x axis
float f_y = cameraMatrix.data[4]; // Focal length in y axis
float c_x = cameraMatrix.data[2]; // Camera primary point x
float c_y = cameraMatrix.data[5]; // Camera primary point y
std::cout<<"fx "<<f_x<<" fy "<<f_y<<" cx "<<c_x<<" cy "<<c_y<<std::endl;
std::cout<<"width "<<screen_width<<" height "<<screen_height<<std::endl;
projectionMatrix.data[0] = - 2.0 * f_x / screen_width;
projectionMatrix.data[1] = 0.0;
projectionMatrix.data[2] = 0.0;
projectionMatrix.data[3] = 0.0;
projectionMatrix.data[4] = 0.0;
projectionMatrix.data[5] = 2.0 * f_y / screen_height;
projectionMatrix.data[6] = 0.0;
projectionMatrix.data[7] = 0.0;
projectionMatrix.data[8] = 2.0 * c_x / screen_width - 1.0;
projectionMatrix.data[9] = 2.0 * c_y / screen_height - 1.0;
projectionMatrix.data[10] = -( far+near ) / ( far - near );
projectionMatrix.data[11] = -1.0;
projectionMatrix.data[12] = 0.0;
projectionMatrix.data[13] = 0.0;
projectionMatrix.data[14] = -2.0 * far * near / ( far - near );
projectionMatrix.data[15] = 0.0;
}
This is the method to estimate the position of the marker:
void MarkerDetector::estimatePosition(std::vector<Marker>& detectedMarkers)
{
for (size_t i=0; i<detectedMarkers.size(); i++)
{
Marker& m = detectedMarkers[i];
cv::Mat Rvec;
cv::Mat_<float> Tvec;
cv::Mat raux,taux;
cv::solvePnP(m_markerCorners3d, m.points, camMatrix, distCoeff,raux,taux);
raux.convertTo(Rvec,CV_32F);
taux.convertTo(Tvec ,CV_32F);
cv::Mat_<float> rotMat(3,3);
cv::Rodrigues(Rvec, rotMat);
// Copy to transformation matrix
for (int col=0; col<3; col++)
{
for (int row=0; row<3; row++)
{
m.transformation.r().mat[row][col] = rotMat(row,col); // Copy rotation component
}
m.transformation.t().data[col] = Tvec(col); // Copy translation component
}
// Since solvePnP finds camera location, w.r.t to marker pose, to get marker pose w.r.t to the camera we invert it.
m.transformation = m.transformation.getInverted();
}
}
The OpenGL shape is able to track and account for size and roation, but something is going wrong with the translation. If the camera is turned 90 degrees, the opengl shape swings around 90 degrees about the centre of the marker. Its almost as if I am translating before rotating, but I am not.
See video for issue:
https://vid.me/fLvX
I guess you can have some problem with projecting the 3-D modelpoints. Essentially, solvePnP gives a transformation that brings points from the model coordinate system to the camera coordinate system and this is composed of a rotation and translation vector (output of solvePnP):
cv::Mat rvec, tvec;
cv::solvePnP(objectPoints, imagePoints, cameraMatrix, distCoeffs, rvec, tvec)
At this point you are able to project model points onto the image plane
std::vector<cv::Vec2d> imagePointsRP; // Reprojected image points
cv::projectPoints(objectPoints, rvec, tvec, cameraMatrix, distCoeffs, imagePointsRP);
Now, you should only draw the points of imagePointsRP over the incoming image and if the pose estimation was correct then you'll see the reprojected corners over the corners of the marker
Anyway, the matrices of model TO camera and camera TO model direction can be composed as below:
cv::Mat rmat
cv::Rodrigues(rvec, rmat); // mRmat is 3x3
cv::Mat modelToCam = cv::Mat::eye(4, 4, CV_64FC1);
modelToCam(cv::Range(0, 3), cv::Range(0, 3)) = rmat * 1.0;
modelToCam(cv::Range(0, 3), cv::Range(3, 4)) = tvec * 1.0;
cv::Mat camToModel = cv::Mat::eye(4, 4, CV_64FC1);
cv::Mat rmatinv = rmat.t(); // rotation of inverse
cv::Mat tvecinv = -rmatinv * tvec; // translation of inverse
camToModel(cv::Range(0, 3), cv::Range(0, 3)) = rmatinv * 1.0;
camToModel(cv::Range(0, 3), cv::Range(3, 4)) = tvecinv * 1.0;
In any case, it's also useful to estimate reprojection error and discard the poses with high error (remember, the PnP problem has only unique solution if n=4 and these points are coplanar):
double totalErr = 0.0;
for (size_t i = 0; i < imagePoints.size(); i++)
{
double err = cv::norm(cv::Mat(imagePoints[i]), cv::Mat(imagePointsRP[i]), cv::NORM_L2);
totalErr += err*err;
}
totalErr = std::sqrt(totalErr / imagePoints.size());

OpenCV + OpenGL: proper camera pose using solvePnP

I've got problem with obtaining proper camera pose from iPad camera using OpenCV.
I'm using custom made 2D marker (based on AruCo library ) - I want to render 3D cube over that marker using OpenGL.
In order to recieve camera pose I'm using solvePnP function from OpenCV.
According to THIS LINK I'm doing it like this:
cv::solvePnP(markerObjectPoints, imagePoints, [self currentCameraMatrix], _userDefaultsManager.distCoeffs, rvec, tvec);
tvec.at<double>(0, 0) *= -1; // I don't know why I have to do it, but translation in X axis is inverted
cv::Mat R;
cv::Rodrigues(rvec, R); // R is 3x3
R = R.t(); // rotation of inverse
tvec = -R * tvec; // translation of inverse
cv::Mat T(4, 4, R.type()); // T is 4x4
T(cv::Range(0, 3), cv::Range(0, 3)) = R * 1; // copies R into T
T(cv::Range(0, 3), cv::Range(3, 4)) = tvec * 1; // copies tvec into T
double *p = T.ptr<double>(3);
p[0] = p[1] = p[2] = 0;
p[3] = 1;
camera matrix & dist coefficients are coming from findChessboardCorners function, imagePoints are manually detected corners of marker (you can see them as green square in the video posted below), and markerObjectPoints are manually hardcoded points that represents marker corners:
markerObjectPoints.push_back(cv::Point3d(-6, -6, 0));
markerObjectPoints.push_back(cv::Point3d(6, -6, 0));
markerObjectPoints.push_back(cv::Point3d(6, 6, 0));
markerObjectPoints.push_back(cv::Point3d(-6, 6, 0));
Because marker is 12 cm long in real world, I've chosed the same size in the for easier debugging.
As a result I'm recieving 4x4 matrix T, that I'll use as ModelView matrix in OpenCV.
Using GLKit drawing function looks more or less like this:
- (void)glkView:(GLKView *)view drawInRect:(CGRect)rect {
// preparations
glClearColor(0.0, 0.0, 0.0, 0.0);
glClear(GL_COLOR_BUFFER_BIT | GL_DEPTH_BUFFER_BIT);
float aspect = fabsf(self.bounds.size.width / self.bounds.size.height);
effect.transform.projectionMatrix = GLKMatrix4MakePerspective(GLKMathDegreesToRadians(39), aspect, 0.1f, 1000.0f);
// set modelViewMatrix
float mat[16] = generateOpenGLMatFromFromOpenCVMat(T);
currentModelMatrix = GLKMatrix4MakeWithArrayAndTranspose(mat);
effect.transform.modelviewMatrix = currentModelMatrix;
[effect prepareToDraw];
glDrawArrays(GL_TRIANGLES, 0, 36); // draw previously prepared cube
}
I'm not rotating everything for 180 degrees around X axis (as it was mentioned in previously linked article), because I doesn't look as necessary.
The problem is that it doesn't work! Translation vector looks OK, but X and Y rotations are messed up :(
I've recorded a video presenting that issue:
http://www.youtube.com/watch?v=EMNBT5H7-os
I've tried almost everything (including inverting all axises one by one), but nothing actually works.
What should I do? How should I properly display that 3D cube? Translation / rotation vectors that come from solvePnP are looking reasonable, so I guess that I can't correctly map these vectors to OpenGL matrices.
Thanks to Djo1509 from http://answers.opencv.org/ I've found out that the problem was unnecessary transposed rotation matrix R matrix used as part of matrix T, and unnecessary tvec = -R * tvec operation.
For more info look there

Binary Image Orientation

I'm trying to find the orientation of a binary image (where orientation is defined to be the axis of least moment of inertia, i.e. least second moment of area). I'm using Dr. Horn's book (MIT) on Robot Vision which can be found here as reference.
Using OpenCV, here is my function, where a, b, and c are the second moments of area as found on page 15 of the pdf above (page 60 of the text):
Point3d findCenterAndOrientation(const Mat& src)
{
Moments m = cv::moments(src, true);
double cen_x = m.m10/m.m00; //Centers are right
double cen_y = m.m01/m.m00;
double a = m.m20-m.m00*cen_x*cen_x;
double b = 2*m.m11-m.m00*(cen_x*cen_x+cen_y*cen_y);
double c = m.m02-m.m00*cen_y*cen_y;
double theta = a==c?0:atan2(b, a-c)/2.0;
return Point3d(cen_x, cen_y, theta);
}
OpenCV calculates the second moments around the origin (0,0) so I have to use the Parallel Axis Theorem to move the axis to the center of the shape, mr^2.
The center looks right when I call
Point3d p = findCenterAndOrientation(src);
rectangle(src, Point(p.x-1,p.y-1), Point(p.x+1, p.y+1), Scalar(0.25), 1);
But when I try to draw the axis with lowest moment of inertia, using this function, it looks completely wrong:
line(src, (Point(p.x,p.y)-Point(100*cos(p.z), 100*sin(p.z))), (Point(p.x, p.y)+Point(100*cos(p.z), 100*sin(p.z))), Scalar(0.5), 1);
Here are some examples of input and output:
(I'd expect it to be vertical)
(I'd expect it to be horizontal)
I worked with the orientation sometimes back and coded the following. It returns me the exact orientation of the object. largest_contour is the shape that is detected.
CvMoments moments1,cenmoments1;
double M00, M01, M10;
cvMoments(largest_contour,&moments1);
M00 = cvGetSpatialMoment(&moments1,0,0);
M10 = cvGetSpatialMoment(&moments1,1,0);
M01 = cvGetSpatialMoment(&moments1,0,1);
posX_Yellow = (int)(M10/M00);
posY_Yellow = (int)(M01/M00);
double theta = 0.5 * atan(
(2 * cvGetCentralMoment(&moments1, 1, 1)) /
(cvGetCentralMoment(&moments1, 2, 0) - cvGetCentralMoment(&moments1, 0, 2)));
theta = (theta / PI) * 180;
// fit an ellipse (and draw it)
if (largest_contour->total >= 6) // can only do an ellipse fit
// if we have > 6 points
{
CvBox2D box = cvFitEllipse2(largest_contour);
if ((box.size.width < imgYellowThresh->width) && (box.size.height < imgYellowThresh->height))
{
cvEllipseBox(imgYellowThresh, box, CV_RGB(255, 255 ,255), 3, 8, 0 );
}
}

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