I am trying to reconstruct the real-world coordinates of 3D points from two images taken from the same camera. The camera is not calibrated, but the movement (translation and rotation) is known. In short:
Requirement:
No calibration
Extra constraints other than image point correspondences:
Known camera translation and rotation
Same camera used in all views
I understand that, from image point correspondences alone, a scene can be reconstructed only up to a projective transformation. With more constraints, an affine or similarity reconstruction may be done. In my case, I need a similarity reconstruction.
Given the above constraints, is a similarity reconstruction possible? If possible, how should I go about doing it?
I have tried to attack the problem from a few angles. Since I am not mathematically fluent, I try to use opencv as much as possible.
findFundamentalMat() from the two images, hopefully extract the two camera matrices somehow, then triangulatePoints(). As you could have guessed, I got stuck in the middle, unable to obtain camera matrices from fundamental matrix.
The textbook "Multiple View Geometry in Computer Vision" (by Hartley and Zisserman) gives an expression (p.256, Result 9.14) that expresses the camera matrices in terms of fundamental matrix and one of the epipoles. However, without knowing the camera's intrinsic parameters (requirement: no calibration), I don't see how I can get the epipole.
I also try to treat my problem as a stereo system and use opencv's stereo*** functions. But they all seem to require human intervention to calibrate, which violates my requirement.
So, that's why I ask the question here today. The key is still, given those extra constraints, is a similarity reconstruction possible? I am not smart enough to understand the wealth of knowledge out there, and not able to come up with my own solution. Any help is appreciated.
Related
I have a multi-camera system where the field of views are mostly non-overlapping. I have been researching on methods to calibrate the camera extrinsics and the first thing I'm going to try is to take a picture of a chessboard at a known location and use solvePnP from OpenCV to find the extrinsic rotation and translation vectors for each camera separately (following the method described in the answer here).
My problem is, this method uses only one measurement and as every measurement it is prone to errors. I assume that by taking multiple measurements, either by changing the position or the orientation of the chessboard, the accuracy can be improved. But what would be the best way to combine the rotation and translation obtained from the different measurements? A simple average?
In theory I would think that an option could be using solvePnP on all the points at the same time. Since I am calculating extrinsics the camera can't be moved so I would have to change to position and/or orientation of the board for each picture and measure the 3D points positions as accurately as possible each time.
I'm also wondering if using two chessboards in the same picture would be a possible solution, even if OpenCV doesn't seem to support multiple chessboard detection.
Is there a better way to measure extrinsics or anything that I'm missing?
So, I have a stereo camera with left and right cameras that are already calibrated. Since the precision of stereo vision highly depends on the calibration, it would be useful if the system can detect whether itself is slightly out of calibration, e.g, due to temperature change or mechanical shock that changes the baseline/rotation of the two cameras slightly
So my thought is for every new image pair taken by the stereo camera, the software try to find matching points between the two images, and recalculate the fundamental matrix to see if there is a big shift. However, finding matching points is error prone, especially when no constrains applied
My question is: since I know there should be just a slight shift of the calibration, is there a way to leverage the original calibration to enable a relaxed epipolar constrains on finding the matching points between the two images? maybe as well as a disparity constrain. e.g., I use the original calibration to calculate the distance of the feature points, and I roughly know the disparity will still be within a certain range even the calibration shifted. With such assumptions, I believe I can effectively avoid mismatched points between left and right images, therefore ensure my new fundamental matrix calculation.
So I wonder is there a convenient way to relax the epipolar constrain by a few pixels, and also specify a numDisparities for feature point matching? Or maybe there is a better way to do similar things.
I try to match two overlapping images captured with a camera. To do this, I'd like to use OpenCV. I already extracted the features with the SurfFeatureDetector. Now I try to to compute the rotation and translation vector between the two images.
As far as I know, I should use cvFindExtrinsicCameraParams2(). Unfortunately, this method require objectPoints as an argument. These objectPoints are the world coordinates of the extracted features. These are not known in the current context.
Can anybody give me a hint how to solve this problem?
The problem of simultaneously computing relative pose between two images and the unknown 3d world coordinates has been treated here:
Berthold K. P. Horn. Relative orientation revisited. Berthold K. P. Horn. Artificial Intelligence Laboratory, Massachusetts Institute of Technology, 545 Technology ...
EDIT: here is a link to the paper:
http://citeseer.ist.psu.edu/viewdoc/summary?doi=10.1.1.64.4700
Please see my answer to a related question where I propose a solution to this problem:
OpenCV extrinsic camera from feature points
EDIT: You may want to take a look at bundle adjustments too,
http://en.wikipedia.org/wiki/Bundle_adjustment
That assumes an initial estimate is available.
EDIT: I found some code resources you might want to take a look at:
Resource I:
http://www.maths.lth.se/vision/downloads/
Two View Geometry Estimation with Outliers
C++ code for finding the relative orientation of two calibrated
cameras in presence of outliers. The obtained solution is optimal in
the sense that the number of inliers is maximized.
Resource II:
http://lear.inrialpes.fr/people/triggs/src/ Relative orientation from
5 points: a somewhat more polished C routine implementing the minimal
solution for relative orientation of two calibrated cameras from
unknown 3D points. 5 points are required and there can be as many as
10 feasible solutions (but 2-5 is more common). Also requires a few
CLAPACK routines for linear algebra. There's also a short technical
report on this (included with the source).
Resource III:
http://www9.in.tum.de/praktika/ppbv.WS02/doc/html/reference/cpp/toc_tools_stereo.html
vector_to_rel_pose Compute the relative orientation between two
cameras given image point correspondences and known camera parameters
and reconstruct 3D space points.
There is a theoretical solution, however, the OpenCV implementation of camera pose estimation lacks the needed tools.
The theoretical approach:
Step 1: extract the homography (the matrix describing the geometrical transform between images). use findHomography()
Step 2. Decompose the result matrix into rotations and translations. Use cv::solvePnP();
Problem: findHomography() returns a 3x3 matrix, corresponding to a projection from a plane to another. solvePnP() needs a 3x4 matrix, representing the 3D rotation/translation of the objects. I think that with some approximations, you can modify the solvePnP to give you some results, but it requires a lot of math and a very good understanding of 3D geometry.
Read more about at http://en.wikipedia.org/wiki/Transformation_matrix
Is it necessary to calibrate the camera if I were to implement a natural marker tracker?
Actually I don't quite get the idea of camera calibration although I have read that it is required for augmenting 3d/2d objects onto the image feed.
Camera-calibration means finding intrinsic parameters of the camera. It is necessary, of course, if you want to detect natural features sucessfully, and here I explain why.
Then you only have to look for extrinsic parameters. You only have to do calibration once, as the camera is always the same (considering you cannot zoom in/out, change focal length, etc). Without camera calibration you will have many problems for the natural features tracking task, as it is more challenging than fiducials tracking.
In the link I passed you, you will also find how to calculate the pose from a planar marker. It is theoretical, but you can find a lot of code in the web. If you need more help tell me, I can explain in more detail if necessary.
Strictly speaking, you could detect features, do pattern matching to recognize the marker and then track those features without camera calibration. Calibration allows us to determine both intrinsic (e.g. distortion coefficients) and extrinsic (e.g. rotation) camera parameters, which are required when someone is to determine marker boundaries or perform 3D pose estimation.
Is it necessary? No.
Is it useful? You bet. The rule of thumb is ALWAYS, if you can perform camera calibration for your stationary camera, do it.
You can do many things with such information: remove distortion, get distance in some type of metric space, ... Most trackers have an underlying assumption/models, these models are best fit when the data is in a space where the model makes sense. Camera calibration is one easy way to achieve this.
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.