Four cameras are arranged in a ring shape. How to calibrate the relative postures of the four cameras, that is, the attitudes of the other three cameras relative to the camera 0, the difficulties are:
When using a calibration plate, four cameras cannot see the calibration plate at the same time, and only two cameras can see the calibration plate, such as calibrating cam1 relative to cam0, then calibrating cam2 relative to cam0, and cam2 can only be relative to cam0. The indirect calculation, causing errors;
In the case of only calibrating two cameras, such as cam0 and cam1, the calibration plates seen by both cameras are tilted, and the calibration plate changes angle is small, which also causes errors.
Is there any better way to calibrate, thank you
There are many ways and papers introduced to this.
The similiest way is to calibrate two at a time. The pair need to be havig largest common FOV. But there are other methods as well.
You can use structure from motion-based method to move the camera around and jointly optimize for the camera poses. It was first published in CVPR between 2010 to 2016. forgot the exact year, but it about camera calibration with minimal or zero overlap.
You can add an IMU and use kalibra to calibrate them. Anchor all image to this IMU. https://github.com/ethz-asl/kalibr/wiki/camera-imu-calibration.
An alternative that I frequently use is the Robotics HAND EYE calibration System used in VINSMONO https://github.com/HKUST-Aerial-Robotics/VINS-Mono. The VINSMONO one requires no complicated pattern. just moving around.
For my paper, We use sea level vanishing line and vanishing point to calibrate cameras which cant get the same chessboard pattern in the same view.
Han Wang, Wei Mou, Xiaozheng Mou, Shenghai Yuan, Soner Ulun, Shuai Yang, Bok-Suk Shin, “An Automatic Self-Calibration Approach for Wide Baseline Stereo Cameras Using Sea Surface Images”, Unmanned Systems, Vol. 3, No. 4. pp. 277-290. 2015
There are others as well such as using vicon to image tracking system or many other methods. Just find one which you think is suitable for you and try it out.
Related
Assume I have two independent cameras looking at the same scene (there are features that are visible from both) and that I know the calibration parameters of both the cameras individually (I can also perform stereo calibration at a certain baseline but I don't know if that would be useful). One of the cameras is fixed and stable, the other is noisy in terms of its pose (translation and rotation). As the pose keeps changing over time, is it possible to accurately estimate the pose of the moving camera with respect to the stationary one using image data from both cameras (in opencv)?
I've been doing a little bit of reading, and this is what I've gathered so far:
Find features using SIFT and the point correspondences.
Find the fundamental matrix.
Find essential matrix and perform SVD to obtain the R and t values between the cameras.
Does this approach work on a frame-by-frame basis? And how does the setup help in getting the scale factor? Pointers and suggestions would be very helpful.
Thanks!
I am a beginner when it comes to computer vision so I apologize in advance. Basically, the idea I am trying to code is that given two cameras that can simulate a multiple baseline stereo system; I am trying to estimate the pose of one camera given the other.
Looking at the same scene, I would incorporate some noise in the pose of the second camera, and given the clean image from camera 1, and slightly distorted/skewed image from camera 2, I would like to estimate the pose of camera 2 from this data as well as the known baseline between the cameras. I have been reading up about homography matrices and related implementation in opencv, but I am just trying to get some suggestions about possible approaches. Most of the applications of the homography matrix that I have seen talk about stitching or overlaying images, but here I am looking for a six degrees of freedom attitude of the camera from that.
It'd be great if someone can shed some light on these questions too: Can an approach used for this be extended to more than two cameras? And is it also possible for both the cameras to have some 'noise' in their pose, and yet recover the 6dof attitude at every instant?
Let's clear up your question first. I guess You are looking for the pose of the camera relative to another camera location. This is described by Homography only for pure camera rotations. For General motion that includes translation this is described by rotation and translation matrices. If the fields of view of the cameras overlap the task can be solved with structure from motion which still estimates only 5 dof. This means that translation is estimated up to scale. If there is a chessboard with known dimensions in the cameras' field of view you can easily solve for 6dof by running a PnP algorithm. Of course, cameras should be calibrated first. Finally, in 2008 Marc Pollefeys came up with an idea how to estimate 6 dof from two moving cameras with non-overlapping fields of view without using any chess boards. To give you more detail please tell a bit for the intended appljcation you are looking for.
What is the minimum number of chessboard image pairs in order to mathematically calibrate and rectify two cameras ? One pair is considered as a single view of the chessboard by each camera, ending with a left and right image of the same scene. As far as I know we need just one pair for a stereo system, as the stereo calibration seeks the relations between the tow cameras.
Stereo calibration seeks not only the rotation and translation between the two cameras, but also the intrinsic and distortion parameters of each camera. You need at least two images to calibrate each camera separately, just to get the intrinsics. If you have already calibrated each camera separately, then, yes, you can use a single pair of checkerboard images to get R and t. However, you will not get a very good accuracy.
As a rule of thumb, you need 10-20 image pairs. You need enough images to cover the field of view, and to have a good distribution of 3D orientations of the board.
To calibrate a stereo pair of cameras, you first calibrate the two cameras separately, and then you do another joint optimization of the parameters of both cameras plus the rotation and translation between them. So one pair of images will simply not work.
Edit:
The camera calibration algorithm used in OpenCV, Caltech Calibration Toolbox, and the Computer Vision System Toolbox for MATLAB is based on the work by Zhengyou Zhang. His paper explains it better than I ever could.
The crux of the issue here is that the points on the chessboard are co-planar, which is a degenerate configuration. You simply cannot solve for the intrinsics using just one view of a planar board. You need more than one view, with the board in different 3-D orientations. Views where the boards are in parallel planes do not add any information.
"One image with 3 corners give us 6 pieces of information can be used to solve both intrinsic and distortion. "
I think that this is your main error. These corners are not independent. A pattern with a 100x100 chessboard pattern does not provide more information than a 10x10 pattern in your perfect world as the points are on the same plane.
If you have a single view of a chessboard, a closer distance to the board can be compensated by the focus so that you are not (even in your perfect world) able to calibrate your camera's intrinsic AND extrinsic parameters.
i have a stereopair,
photo 1: http://savepic.org/1671682.jpg
photo 2: http://savepic.org/1667586.jpg
there is coordinate system in each image. How can I find coordinates of point A in this system using OpenCV library. It would be nice to see sample code.
I've looked for it at opencv.willowgarage.com/documentation/cpp/camera_calibration_and_3d_reconstruction.html but haven't found (or haven't understood :) )
Your 'stereo' images are fine. What you have already done is solve the correspondence problem: in both images you have indicated points 'A'. This means that you know which pixel corresponds to eachother labeling point 'A'.
What you want to do, is triangulate where your camera is. You can only do this by first calibrating your camera. This is inside of OpenCV already.
http://docs.opencv.org/doc/tutorials/calib3d/camera_calibration/camera_calibration.html
http://docs.opencv.org/modules/calib3d/doc/camera_calibration_and_3d_reconstruction.html
This gives you the exact vector/ray of light for each vector, and the optical center of your cameras through which the ray passes. Moreover, you need stereo calibration. This establishes the orientation and position of each camera with respect through each other.
From that point on, your triangulation is simple, knowing the pixel location in both images of point 'A'. You have
Location and orientation of camera 1 and camera 2
Otical Ray Vector (pixel location) from the cameras to label 'A'.
So you have 2 locations in space, and 2 rays from these location. The intersection of these rays is your 3D answer.
Note that in practice there rays will never exactly intersect (2 lines in 3D rarely do), so you need to approximate. Use opencv function triangulatePoints(), using the input of the stereo calibration and the pixel index relating to label A.
Firstly of all this is not truly a stereo pair. A nice stereo pair needs to have 60%-80% overlap usually small rotation differences between images. Even if this pair had the necessary BASE to be a good stereo pair due to the extremely kappa rotation the resulting epipolar image would be useless.
Secondly among others you should take a look at the camera calibration and collinearity equations both supported by OpenCV
http://en.wikipedia.org/wiki/Camera_resectioning
http://en.wikipedia.org/wiki/Collinearity_equation
You need to understand the maths.
If the page isn't enough then you should look at the opencv book - it devotes a couple of chapters to this. Then there are a lot of textbooks that cover it in more detail
I am aware of the chessboard camera calibration technique, and have implemented it.
If I have 2 cameras viewing the same scene, and I calibrate both simultaneously with the chessboard technique, can I compute the rotation matrix and translation vector between them? How?
If you have the 3D camera coordinates of the corresponding points, you can compute the optimal rotation matrix and translation vector by Rigid Body Transformation
If You are using OpenCV already then why don't you use cv::stereoCalibrate.
It returns the rotation and translation matrices. The only thing you have to do is to make sure that the calibration chessboard is seen by both of the cameras.
The exact way is shown in .cpp samples provided with OpenCV library( I have 2.2 version and samples were installed by default in /usr/local/share/opencv/samples).
The code example is called stereo_calib.cpp. Although it's not explained clearly what they are doing there (for that You might want to look to "Learning OpenCV"), it's something You can base on.
If I understood you correctly, you have two calibrated cameras observing a common scene, and you wish to recover their spatial arrangement. This is possible (provided you find enough image correspondences) but only up to an unknown factor on translation scale. That is, we can recover rotation (3 degrees of freedom, DOF) and only the direction of the translation (2 DOF). This is because we have no way to tell whether the projected scene is big and the cameras are far, or the scene is small and cameras are near. In the literature, the 5 DOF arrangement is termed relative pose or relative orientation (Google is your friend).
If your measurements are accurate and in general position, 6 point correspondences may be enough for recovering a unique solution. A relatively recent algorithm does exactly that.
Nister, D., "An efficient solution to the five-point relative pose problem," Pattern Analysis and Machine Intelligence, IEEE Transactions on , vol.26, no.6, pp.756,770, June 2004
doi: 10.1109/TPAMI.2004.17
Update:
Use a structure from motion/bundle adjustment package like Bundler to solve simultaneously for the 3D location of the scene and relative camera parameters.
Any such package requires several inputs:
camera calibrations that you have.
2D pixel locations of points of interest in cameras (use a interest point detection like Harris, DoG (first part of SIFT)).
Correspondences between points of interest from each camera (use a descriptor like SIFT, SURF, SSD, etc. to do the matching).
Note that the solution is up to a certain scale ambiguity. You'll thus need to supply a distance measurement either between the cameras or between a pair of objects in the scene.
Original answer (applies primarily to uncalibrated cameras as the comments kindly point out):
This camera calibration toolbox from Caltech contains the ability to solve and visualize both the intrinsics (lens parameters, etc.) and extrinsics (how the camera positions when each photo is taken). The latter is what you're interested in.
The Hartley and Zisserman blue book is also a great reference. In particular, you may want to look at the chapter on epipolar lines and fundamental matrix which is free online at the link.