I have a simple problem, but still it confuses me somehow.
I have two cameras. One is closer to an object than the other one. I have both intrinsic matrices from each camera, as well as the distortion vectors(which are 0). I already calculated the extrinsic matrix between both cameras.
Now I want to transform the image from the camera, which is further away, into the same coordinates as the closer image. Such that the images are aligned, and have the same size.
Does anyone know how I can do this? By using the intrinsic an extrinsic matrices?
Thanks in advance!
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For one stereo camera, stereo calibration is performed to obtain intrinsic and extrinsic parameters during manufacturing. During the process of usage, intrinsic and extrinsic parameters may be changed, and left image and right image are not aligned any more if rectification is applied.
I have some point correspondences between left image and right image.The y coordinates of the correpondences is not same. If I rectify the left and right images, I can find the disparity may be negative which means that the points are behind the camera.I can also triangulate the point correpondences using intrinsic and extrinsic parameters to obtain 3d point coordinates, and the z coordinates of 3d points may be negative.
Is there any way to know whether the disparity is negative without stereo rectification?
Is there any way to know the case the calcuated points is behind the camera without trigulation?
I know the corresponding point doesn't lie on the epipolar line for such case, however such information can't tell me whether the 3d point of point correspondence is behind the camera. I try to calculate the sign of the distance from the point to the epipolar line but it seems the sign can't tell me such information.
I am using opencv to calibrate my webcam. So, what I have done is fixed my webcam to a rig, so that it stays static and I have used a chessboard calibration pattern and moved it in front of the camera and used the detected points to compute the calibration. So, this is as we can find in many opencv examples (https://docs.opencv.org/3.1.0/dc/dbb/tutorial_py_calibration.html)
Now, this gives me the camera intrinsic matrix and a rotation and translation component for mapping each of these chessboard views from the chessboard space to world space.
However, what I am interested in is the global extrinsic matrix i.e. once I have removed the checkerboard, I want to be able to specify a point in the image scene i.e. x, y and its height and it gives me the position in the world space. As far as I understand, I need both the intrinsic and extrinsic matrix for this. How should one proceed to compute the extrinsic matrix from here? Can I use the measurements that I have already gathered from the chessboard calibration step to compute the extrinsic matrix as well?
Let me place some context. Consider the following picture, (from https://docs.opencv.org/2.4/modules/calib3d/doc/camera_calibration_and_3d_reconstruction.html):
The camera has "attached" a rigid reference frame (Xc,Yc,Zc). The intrinsic calibration that you successfully performed allows you to convert a point (Xc,Yc,Zc) into its projection on the image (u,v), and a point (u,v) in the image to a ray in (Xc,Yc,Zc) (you can only get it up to a scaling factor).
In practice, you want to place the camera in an external "world" reference frame, let's call it (X,Y,Z). Then there is a rigid transformation, represented by a rotation matrix, R, and a translation vector T, such that:
|Xc| |X|
|Yc|= R |Y| + T
|Zc| |Z|
That's the extrinsic calibration (which can be written also as a 4x4 matrix, that's what you call the extrinsic matrix).
Now, the answer. To obtain R and T, you can do the following:
Fix your world reference frame, for example the ground can be the (x,y) plane, and choose an origin for it.
Set some points with known coordinates in this reference frame, for example, points in a square grid in the floor.
Take a picture and get the corresponding 2D image coordinates.
Use solvePnP to obtain the rotation and translation, with the following parameters:
objectPoints: the 3D points in the world reference frame.
imagePoints: the corresponding 2D points in the image in the same order as objectPoints.
cameraMatris: the intrinsic matrix you already have.
distCoeffs: the distortion coefficients you already have.
rvec, tvec: these will be the outputs.
useExtrinsicGuess: false
flags: you can use CV_ITERATIVE
Finally, get R from rvec with the Rodrigues function.
You will need at least 3 non-collinear points with corresponding 3D-2D coordinates for solvePnP to work (link), but more is better. To have good quality points, you could print a big chessboard pattern, put it flat in the floor, and use it as a grid. What's important is that the pattern is not too small in the image (the larger, the more stable your calibration will be).
And, very important: for the intrinsic calibration, you used a chess pattern with squares of a certain size, but you told the algorithm (which does kind of solvePnPs for each pattern), that the size of each square is 1. This is not explicit, but is done in line 10 of the sample code, where the grid is built with coordinates 0,1,2,...:
objp[:,:2] = np.mgrid[0:7,0:6].T.reshape(-1,2)
And the scale of the world for the extrinsic calibration must match this, so you have several possibilities:
Use the same scale, for example by using the same grid or by measuring the coordinates of your "world" plane in the same scale. In this case, you "world" won't be at the right scale.
Recommended: redo the intrinsic calibration with the right scale, something like:
objp[:,:2] = (size_of_a_square*np.mgrid[0:7,0:6]).T.reshape(-1,2)
Where size_of_a_square is the real size of a square.
(Haven't done this, but is theoretically possible, do it if you can't do 2) Reuse the intrinsic calibration by scaling fx and fy. This is possible because the camera sees everything up to a scale factor, and the declared size of a square only changes fx and fy (and the T in the pose for each square, but that's another story). If the actual size of a square is L, then replace fx and fy Lfx and Lfy before calling solvePnP.
Two cameras , Calibration is done between them and both intrinsic and extrinsic matrices are obtained , I am able to get (U,V) of the first camera , How could i get (U,V) of the second camera ? What is the kind of transformation could be made ?
Positions of cameras is fixed
Homography is the way a two 2D planes could be related
Since these cameras are paralel to each other(i.e. stereo), y axis of a point(x,y) in the first image will remain the same in the second image, i.e . y' = y. Only x will change. ( y is vertical axis, x is horizontal).
There are some techniques to find x'. The easiest one is normalized cross correlation. Choose a window around the points, do normalized cross correlation. The result will be an array of width of the image.
Unless you are searching for a point in a smooth region, maximum value in your array (peak) is expected to be your matching point.
Alternatively, you can try SIFT/SURF feature but I am not expert on those. I only know there are functions you can use in Matlab (such as detectSURFfeatures).
Note that if you are using two different cameras, you have to calibrate both of them.
In my case, i use four sets of points to do the Bird's Eye Projection.But i forgot to do the camera calibration first!
So i want to know is the result is same doing Camera calibration before Bird's Eye Projection and after Bird's Eye Projection in OpenCV?
Can you give me some advice?Thank you very much.
Can you specify what calibration do you refer to? There are generally 2 kinds of camera parameters you can estimate during calibration - intrinsic and extrinsic.
Intrinsic parameters can be for simplicity assumed 'fixed' for particular camera, which includes lens and sensor. Those parameters typically include focal length, sensor's dimensions, and distortion coefficients.
Extrinsic parameters are 'dynamic', and typically refer to camera position and orientation.
Now, if you represent those as some abstract transformations - they don't commute, which means you can't change their order. So, if you want to apply homography to an image - you have to undistort it first, because generally homography maps plane to another plane, and after distortion your planes will be messed up.
But on the other hand, once you apply one transform, you can estimate how much of other transform you have 'left to do'. This is OK for linear stuff, but turns ugly if you warp distorted image using homography and THEN try to undistort it.
Tl,Dr - perform intrinsic calibration and undistortion first, since it is easier and they are fixed for camera, then apply your transformations.
My problem statement is very simple. But I am unable to get the opencv calibration work for me. I am using the code from here : source code.
I have to take images parallel to the camera at a fixed distance. I tried taking test images (about 20 of them) only parallel to the camera as well as at different planes. Also I changed the size and the no of squares.
What would be the best way to calibrate in this scenario?
The undistorted image is cropped later, that's why it looks smaller.
After going through the images closely, the pincushion distortion seems to have been corrected. But the "trapezoidal" distortion still remains. Since the camera is mounted in a closed box, the planes at which I can take images is limited.
To simplify what Vlad already said: It is theoretically impossible to calibrate your camera with test images only parallel to the camera. You have to change your calibration board's orientation. In fact, you should have different orientation in each test image.
Check out the first two images in the link below to see how the calibration board should be slanted (or tilted):
http://www.vision.caltech.edu/bouguetj/calib_doc/
think about calibration problem as finding a projection matrix P:
image_points = P * 3d_points, where P = intrinsic * extrinsic
Now just bear with me:
You basically are interested in intrinsic part but the calibration algorithm has to find both intrinsic and extrinsic. Now, each column of projection matrix can be obtained if you select a 3D point at infinity, for example xInf = [1, 0, 0, 0]. This point is at infinity because when you transform it from homogeneous coordinates to Cartesian you get
[1/0, 0, 0]. If you multiply a projection matrix with a point at infinity you will get its corresponding column (1st for Xinf, 2nd for yInf, 3rd for zInf and 4th for camera center).
Thus the conclusion is simple - to get a projection matrix (that is a successful calibration) you have to clearly see points at infinity or vanishing points from the converging extensions of lines in your chessboard rig (aka end of the railroad tracks at the horizon). Your images don’t make it easy to detect vanishing points since you don’t slant your chessboard, nor rotate nor scale it by stepping back. Thus your calibration will always fail.