What I have
I'm generating images using the standard perspective camera in unity. The camera is aiming to the ground plane (in unity it's the xz-plane), see image. From this I need to remove the perspective so all crop rows are parallel to each other.
Methode
The warpPerspective() function from openCV can be used to remove perspective from an image. All information is known such as, field of view, rotation, position, ... and thus I know how a 3D point maps on the 2D plane and visa versa. The problem is OpenCV uses an other system. In openCV should be a 3X3 matrix and the transformation matrix from unit is a 4X4 matrix. Is there a conversion between the two? Or should I think of another strategy?
EDIT
I can not use the orthographic camera in unity.
Fixed
Solved the issue by constructing a ray from the camera origin through each pixel and looking for an intersection with the ground plane. After this I discretised the ground plane in a grid with the same resolution of the original image. Points that map to the same cell are accumulated
I you cannot use the unity's orthographic camera, what I would try to imitate the c++ code from the examples from your link in open CV documentation. Another approach can be to try to obtain the projection matrix of the points you want the projection to be removed by multiplying by the inverse matrix (the inverse of the transformation matrix of that point). A matrix multiplied by its inverse is the identitiy so the projection transformation would be removed. I think that should be possible, you can dig on that you can obtain/change the projection matrix checking this. The point would be to undo the projection transformation. Then you would need to obtain the according othographic projection matrix and apply it to obtain the positions you're after. That should be the same thing that the unity's orthographic camera does.
To understand the projection matrix to the lowest level this source is awesome.
I think that In the camera component you just need to change the projection from prespective to orthographic:
Related
I have a real/physical stick with an IR camera attached to it and some IR LED that forms a pattern that I'm using in order to make a virtual stick move in the same way as the physical one.
For that, I'm using OpenCV in Python and send a rotation and translation vector calculated by solvePnP to Unity.
I'm struggling to understand how I can use the results given by the solvePnP function into my 3D world.
So far what I did is: using the solvePnP function to get the rotation and translation vectors. And then use this rotation vector to move my stick in the 3d World
transform.rotation = Quaternion.Euler(new Vector3(x, z, y));
It seems to work okay when my stick is positioned at a certain angle and if I move slowly...but most of the time it moves everywhere.
By looking for answers online, most of people are doing several more steps after solvePnP - from what I understand:
Using Rodrigues to convert the rotation vector to a rotation matrix
Copy the rotation matrix and translation vector into a extrinsic matrix
Inverse the extrinsic matrix
I understand that these steps are necessary if I was working with matrix like in OpenGL - but what about Unity3D? Are these extra steps necessary? Or can I directly use the vectors given by the solvePnP function (which I doubt as the results I'm having so far aren't good).
This is old, but the answer to the question "what about Unity3D? Are these extra steps necessary? Or can I directly use the vectors given by the solvePnP function"
is:
-No, you can't directly use them. I tried to convert rvec using Quaternion.Euler and as you've posted, the results were bad.
-Yes, you have to use Rodrigues, which converts rvec correctly into a rotation matrix.
-About inversing the extrinsic matrix: it depends.
If your object is at (0,0,0) in world space and you want to place the camera, you have to invert the transform resulting from tvec and rvec, in order to get the desired result.
If on the other hand your camera has a fixed position and you want to position the object relatively to it, you have to apply the camera's localToWorld matrix to your transform resulting from rvec and tvec, in order to get the desired result
OpenCV docs for solvePnp
In an augmented reality app, I detect the image in the scene so I know imagePoints, but the object I'm looking for (objectPoints) is a virtual marker just stored in memory to search for in the scene, so I don't know where it is in space. The book I'm reading(Mastering OpenCV with Practical Computer Vision Projects ) passes it as if the marker is a 1x1 matrix and it works fine, how? Doesn't solvePnP needs to know the size of the object and its projection so we know who much scale is applied ?
Assuming you're looking for a physical object, you should pass the 3D coordinates of the points on the model which are mapped (by projection) to the 2D points in the image. You can use any reference frame, and the results of the solvePnp will give you the position and orientation of the camera in that reference frame.
If you want to get the object position/orientation in camera space, you can then transform both by the inverse of the transform you got from solvePnp, so that the camera is moved to the origin.
For example, for a cube object of size 2x2x2, the visible corners may be something like: {-1,-1,-1},{1,-1,-1},{1,1,-1}.....
You have to pass the 3D coordinates of the real-world object that you want to map with the image. The scaling and rotation values will depend on the coordinate system that you use.
This is not as difficult as it sounds. See this blog post on head pose estimation. for more details with code.
I want to project a point in 3D space into 2D image coordinates. I have the calibrated intrinsics and extrinsics of the camera I'm using. I have the camera matrix K and distortion coefficients D. However, I want the projected image coordinates to be of the undistorted image.
From my research, I found two ways to do this.
Use opencv's getOptimalNewCameraMatrix function to compute a new undistorted image's camera matrix K'. Then use this K' in opencv's projectPoints function, with the distortion parameters set to 0, to get the projected point.
Use projectPoints function using the raw camera matrix K, along with the distortion coefficients D in this function and get the projected point.
Should the output of both methods match?
I think that there is something missing in your thought.
Camera matrix K and dist. coefficent D are the parameters for make the undistortion (if your lens is distorting the image like in a fisheye). They are what is called intrinsic camera parameters.
If we change terms from computer vision to computer graphics, those parameters are the one you use for defining the frustum of the view, and, for example, they are used for getting the focal length of the camera.
But they are not enough to do the projection stuff.
For the projection, if you think in a computer graphics term (like opengl, for instance) you need to have the model-view-projection matrix. The model matrix is the matrix that specifies the position of the object in the world. The view matrix specifies the position of the camera, and the projection matrix specify the frustum (focal angle, perspective distortion, etc).
If you want to know how to transform the points of the model from 3d to 2d (or viceversa) you need the projection and the view matrixes (you have the model matrix because you have the 3d points from which you want to start). And in computer vision the view matrix is called estrinsic parameters.
So, you need the estrinsic parameters too, that are the position of the camera in the world. That is, for instance, those parameters are the rvec and tvec that cv:: projectPoints needs.
If you want to compute them, they are exactly the output of cv::solvePnP that do the opposite of what you want to do: from some known 3d points coupled with the known 2d projection on them on the camera screen, this function gives you the estrinsic parameters (from which you can get the view matrix for some opengl-opencv-augmented-reality-whatever application via cv::Rodrigues).
Last note: while the instrinsic parameters are fixed in all the pictures you shoot with a camera (while you don't change the focal length of course), the estrinisc parameters changes every time you move the camera for take a new picture from a different view point (that is: this changes the perspective point of view, so the 3D-2D projection you want to find)
Hope could help!
I'm now trying to analyze the perspective transform/homography matrix between two images capturing the same object (e.g., a rectangle) but at different perspectives/shooting angles. The perspective transform can be derived by using the function getPerspectiveTransform in OpenCV 2.3.1. I want to find the corresponding rotation and translation matrices.
The output of getPerspectiveTransform is a 3x3 matrix which I can directly use it to warp the source image into the target image. But my question is that how I can find the rotation and translation matrices based on the obtained 3x3 matrix?
I was looking into the funciton decomposeProjectionMatrix for the corresponding rotation and translation matrices. But the input is required to be a 3x4 projection matrix. How can I relate the perspective transformation (i.e., a 3x3 matrix) to the 3x4 projection matrix? Am I on the right track?
Thank you very much.
The information contained in the homography matrix (returned from getPerspectiveTransform) is not enough to extract rotation/translation. The missing column is key to correctly find the angles.
The good news is that in some scenarios, you can use the solvePnP() function to extract the desired parameters from two sets of points.
Also, this question is about the same thing you are asking for. It should help
Analyze camera movement with OpenCV
I have a small cube with n (you can assume that n = 4) distinguished points on its surface. These points are numbered (1-n) and form a coordinate space, where point #1 is the origin.
Now I'm using a tracking camera to get the coordinates of those points, relative to the camera's coordinate space. That means that I now have n vectors p_i pointing from the origin of the camera to the cube's surface.
With that information, I'm trying to compute the affine transformation matrix (rotation + translation) that represents the transformation between those two coordinate spaces. The translation part is fairly trivial, but I'm struggling with the computation of the rotation matrix.
Is there any build-in functionality in OpenCV that might help me solve this problem?
Sounds like cvGetPerspectiveTransform is what you're looking for; cvFindHomograpy might also be helpful.
solvePnP should give you the rotation matrix and the translation vector. Try it with CV_EPNP or CV_ITERATIVE.
Edit: Or perhaps you're looking for RQ decomposition.
Look at the Stereo Camera tutorial for OpenCV. OpenCV uses a planar chessboard for all the computation and sets its Z-dimension to 0 to build its list of 3D points. You already have 3D points so change the code in the tutorial to reflect your list of 3D points. Then you can compute the transformation.