I've spent some time trying to calibrate two similar cameras (ExCam IPQ1715 and ExCam IPQ1765) to varying degrees of success, with the eventual goal of using them for short-range photogrammetry. I've been using a charuco board, along with the OpenCV Charuco calibration library, and have noticed that the quality of my calibration is closely tied to how much of the images is taken up by the board. (I measure calibration quality by RMS reprojection error given by OpenCV, and also by just seeing if the undistorted images appear to have straighter lines on the board than the originals).
I'm still pretty inexperienced, and there have been other factors messing with my calibration (leaving autofocus on, OpenCV charuco identification sometimes getting strange false positives on some images without me noticing), so my question is less about my results and more about best practice for camera calibration in general:
How crucial is it that the board (charuco, chessboard) take up most of the image space? Is there generally a minimum amount that it should cover? Is this even an issue at all, or am I likely mistaking it for another cause of bad calibration?
I've seen lots of calibration tutorials online where the board seems to take up a small portion of the image, but then have also found other people experiencing similar issues. In short, I'm horribly lost.
Any guidance would be awesome - thanks!
Consider the point that camera calibration calculation is a model fitting.
i.e. optimize the model parameters with the measurements.
So... You should pay attention to:
If the board image is too small to see the distortion in the board image,
is it possible to optimize the distortion parameters with such image?
If the pattern image is only distributed near the center of the image,
is it possible to estimate valid parameter values for regions far from the center?
(this will be an extrapolation).
If the pattern distribution is not uniform, the density of the data can affect the results.
e.g. With least square optimization, errors in regions with little data can be neglected.
Therefore, my suggestion is:
Pattern images that are extremely small are useless.
The data should cover the entire field of view of the camera image, and the distribution should be as uniform as possible.
Use enough data. With few data may cause overfitting.
Check the pattern recognition results of all images(sample code often omit this).
Related
i used the opencv sample code for stereo camera calibration to get the intrinsics and extrinsics of my stereo camera. I used 149 image pairs and the program detected 114 image pairs
Result of my Calibration:
..... 114 pairs have been successfully detected.
Running stereo calibration ...
done with RMS error = 1.60208
average epipolar error = 1.15512
i know the error should be below 1 but i only get below 1 of error in small number of image pairs. so im not sure if my result is good or bad.
You should be able to get an error below 1, but it's not so bad. I also do the calibration with around 100 of images. I often got a few images to discard in which the detection was not reliable.
If you decreased the number of images down to 10 images, then the calibration might overfit for these cases. The error would then not be reliable.
In the calibration process, the problems I faced came from the calibration setup. My recommendations are the following:
Check that your calibration pattern is perfectly flat. In my case I printed on adhesive paper and glued it on a piece of glass.
Check that your calibration pattern is not symmetrical in rotation, otherwise the pose estimation could be wrong.
Check the intermediate pattern points detection. There are some examples in opencv to show the corners or circles centers detected points.
The error can be also displayed for each frame. This can help you to understand for which images you have a problem. If you see that these images actually have a detection problem, you can discard them.
If you acquire videos and not images, both cameras should be synchronized with a hardware connection. In my case I cannot have such a link, therefore I built some kind of holder for the calibration target to keep it still, and I acquired only images, not videos.
This won't reduce your calibration error, but use very different pattern positions to cover the maximum of the field of view.
If your depth of field is small and you have blurry images before/after the focus because of that, change from the chessboard pattern to a circles pattern (functions also available in opencv).
If you don't have a strong distortion in your images (e.g. a photo with an iphone doesn't really show a strong fisheye-like distortion), consider forcing K3=0.
In my case, I fixed the "principal point" in the middle of the image, because the algorithm always found crazy values for these parameters, like for K3.
Hope this helps a bit. Good luck!
I am trying to calibrate a camera using a checkerboard by the well known Zhang's method followed by bundle adjustment, which is available in both Matlab and OpenCV. There are a lot of empirical guidelines but from my personal experience the accuracy is pretty random. It could sometimes be really good but also sometimes really bad. The result actually can vary quite a bit just by simply placing the checkerboard at different locations. Suppose the target camera is rectilinear with 110 degree horizontal FOV.
Does the number of squares in the checkerboard affect the accuracy? Zhang uses 8x8 in his original paper without really explaining why.
Does the length of the square affect the accuracy? Zhang uses 17cm x 17cm without really explaining why.
What is the optimal number of snap shots of different checkerboard position/orientation? Zhang uses 5 images only. I saw people suggesting 20~30 images with checkerboards at various angles, fills the entire field of view, tilted to the left, right, top and bottom, and suggested there should be no checkerboard placed at similar position/orientation otherwise the result will be biased towards that position/orientation. Is this correct?
The goal is to figure out a workflow to get consistent calibration result.
If the accuracy you get is "pretty random" then you are likely not doing it right: with stable optics and a well conducted procedure you should consistently be getting RMS projection errors within a few tenths of a pixel. Whether this corresponds to variances of millimeters or meters in 3D space depends, of course, on your optics and sensor resolution (calibration is not a way around physics).
I wrote time ago a few suggestions in this answer, and I recommend you follow them. In particular, pay attention to locking the focus distance (I have seen & heard countless people trying to calibrate a camera on autofocus, and be sorely disappointed). As for the size of the target, again it depends on your optics and camera resolution, but generally speaking the goals are (1) to fill with measurements both the field of view and the volume of space you'll be working with, and (2) to observe significant perspective foreshortening, because that is what constrains the solution for the FOV. Good luck!
[Ed.to address a comment]
Concerning variations on the parameter values across successive calibrations, the first thing I'd do is calculate the cross RMS errors, i.e. the RMS error on dataset 1 with the camera calibrated on dataset 2, and vice versa. If either is significantly higher than the calibration errors, it's an indication that the camera has changed between the two calibrations and so all odds are off. Do you have auto-{focus,iris,zoom,stabilization} on? Turn them all off: auto-anything is the bane of calibration, with the only exception of exposure time. Otherwise, you need to see if the variations you observe on the parameters are actually meaningful (hint, they often are not). A variation of the focal length in pixels of several parts per thousand is probably irrelevant with today's sensor resolutions - you can verify that by expressing it in mm, and comparing it to the dot pitch of the sensor. Also, variations of the position of the principal point in the order of tens of pixels are common, since it is poorly observed unless your calibration procedure is very carefully designed to estimate it.
Ideally you want to place your checkerboard at roughly the same distance from the the camera, as the distance at which you want to do your measurements. So your checkerboard squares must be large enough to be resolvable from that distance. You also do want to cover the entire field of view with points, especially close to the edges and corners of the frame. Also, the smaller the board is, the more images you should take to cover the entire field of view. So 20-30 images is usually a good rule of thumb.
Another thing is that the checkerboard should be asymmetric. Ideally, you want to have an even number of squares along one side, and an odd number of squares along the other. This way the board's in-plane orientation is unambiguous.
Also, I would suggest that you try the Camera Calibrator app in MATLAB. At the very least, look at the documentation, which has a lot of useful suggestions for calibrating cameras.
I took the example of code for calibrating a camera and undistorting images from this book: shop.oreilly.com/product/9780596516130.do
As far as I understood the usual camera calibration methods of OpenCV work perfectly for "normal" cameras.
When it comes to Fisheye-Lenses though we have to use a vector of 8 calibration parameters instead of 5 and also the flag CV_CALIB_RATIONAL_MODEL in the method cvCalibrateCamera2.
At least, that's what it says in the OpenCV documentary
So, when I use this on an array of images like this (Sample images from OCamCalib) I get the following results using cvInitUndistortMap: abload.de/img/rastere4u2w.jpg
Since the resulting images are cut out of the whole undistorted image, I went ahead and used cvInitUndistortRectifyMap (like it's described here stackoverflow.com/questions/8837478/opencv-cvremap-cropping-image). So I got the following results: abload.de/img/rasterxisps.jpg
And now my question is: Why is not the whole image undistorted? In some pics of my later results you can recognize that the laptop for example is still totally distorted. How can I acomplish even better results using the standard OpenCV methods?
I'm new to stackoverflow and I'm new to OpenCV as well, so please excuse any of my shortcomings when it comes to expressing my problems.
All chessboard corners should be visible to be found. The algorithm expect a certain size of chessboard such as 4x3 or 7x6 (for example). The white border around a chess board should be visible too or dark squares may not be defined precisely.
You still have high distortions at the image periphery after undistort() since distortions are radial (that is they increase with the radius) and your found coefficients are wrong. The latter are wrong since a calibration process minimizes the sum of squared errors in pixel coordinates and you did not represent the periphery with enough samples.
TODO: You have to have 20-40 chess board pattern images if you use 8 distCoeff. Slant your boards at different angles, put them at different distances and spread them around, especially at the periphery. Remember, the success of calibration depends on sampling and also on seeing vanishing points clearly from your chess board (hence slanting and tilting).
I am totally new to camera calibration techniques... I am using OpenCV chessboard technique... I am using a webcam from Quantum...
Here are my observations and steps..
I have kept each chess square side = 3.5 cm. It is a 7 x 5 chessboard with 6 x 4 internal corners. I am taking total of 10 images in different views/poses at a distance of 1 to 1.5 m from the webcam.
I am following the C code in Learning OpenCV by Bradski for the calibration.
my code for calibration is
cvCalibrateCamera2(object_points,image_points,point_counts,cvSize(640,480),intrinsic_matrix,distortion_coeffs,NULL,NULL,CV_CALIB_FIX_ASPECT_RATIO);
Before calling this function I am making the first and 2nd element along the diagonal of the intrinsic matrix as one to keep the ratio of focal lengths constant and using CV_CALIB_FIX_ASPECT_RATIO
With the change in distance of the chess board the fx and fy are changing with fx:fy almost equal to 1. there are cx and cy values in order of 200 to 400. the fx and fy are in the order of 300 - 700 when I change the distance.
Presently I have put all the distortion coefficients to zero because I did not get good result including distortion coefficients. My original image looked handsome than the undistorted one!!
Am I doing the calibration correctly?. Should I use any other option than CV_CALIB_FIX_ASPECT_RATIO?. If yes, which one?
Hmm, are you looking for "handsome" or "accurate"?
Camera calibration is one of the very few subjects in computer vision where accuracy can be directly quantified in physical terms, and verified by a physical experiment. And the usual lesson is that (a) your numbers are just as good as the effort (and money) you put into them, and (b) real accuracy (as opposed to imagined) is expensive, so you should figure out in advance what your application really requires in the way of precision.
If you look up the geometrical specs of even very cheap lens/sensor combinations (in the megapixel range and above), it becomes readily apparent that sub-sub-mm calibration accuracy is theoretically achievable within a table-top volume of space. Just work out (from the spec sheet of your camera's sensor) the solid angle spanned by one pixel - you'll be dazzled by the spatial resolution you have within reach of your wallet. However, actually achieving REPEATABLY something near that theoretical accuracy takes work.
Here are some recommendations (from personal experience) for getting a good calibration experience with home-grown equipment.
If your method uses a flat target ("checkerboard" or similar), manufacture a good one. Choose a very flat backing (for the size you mention window glass 5 mm thick or more is excellent, though obviously fragile). Verify its flatness against another edge (or, better, a laser beam). Print the pattern on thick-stock paper that won't stretch too easily. Lay it after printing on the backing before gluing and verify that the square sides are indeed very nearly orthogonal. Cheap ink-jet or laser printers are not designed for rigorous geometrical accuracy, do not trust them blindly. Best practice is to use a professional print shop (even a Kinko's will do a much better job than most home printers). Then attach the pattern very carefully to the backing, using spray-on glue and slowly wiping with soft cloth to avoid bubbles and stretching. Wait for a day or longer for the glue to cure and the glue-paper stress to reach its long-term steady state. Finally measure the corner positions with a good caliper and a magnifier. You may get away with one single number for the "average" square size, but it must be an average of actual measurements, not of hopes-n-prayers. Best practice is to actually use a table of measured positions.
Watch your temperature and humidity changes: paper adsorbs water from the air, the backing dilates and contracts. It is amazing how many articles you can find that report sub-millimeter calibration accuracies without quoting the environment conditions (or the target response to them). Needless to say, they are mostly crap. The lower temperature dilation coefficient of glass compared to common sheet metal is another reason for preferring the former as a backing.
Needless to say, you must disable the auto-focus feature of your camera, if it has one: focusing physically moves one or more pieces of glass inside your lens, thus changing (slightly) the field of view and (usually by a lot) the lens distortion and the principal point.
Place the camera on a stable mount that won't vibrate easily. Focus (and f-stop the lens, if it has an iris) as is needed for the application (not the calibration - the calibration procedure and target must be designed for the app's needs, not the other way around). Do not even think of touching camera or lens afterwards. If at all possible, avoid "complex" lenses - e.g. zoom lenses or very wide angle ones. For example, anamorphic lenses require models much more complex than stock OpenCV makes available.
Take lots of measurements and pictures. You want hundreds of measurements (corners) per image, and tens of images. Where data is concerned, the more the merrier. A 10x10 checkerboard is the absolute minimum I would consider. I normally worked at 20x20.
Span the calibration volume when taking pictures. Ideally you want your measurements to be uniformly distributed in the volume of space you will be working with. Most importantly, make sure to angle the target significantly with respect to the focal axis in some of the pictures - to calibrate the focal length you need to "see" some real perspective foreshortening. For best results use a repeatable mechanical jig to move the target. A good one is a one-axis turntable, which will give you an excellent prior model for the motion of the target.
Minimize vibrations and associated motion blur when taking photos.
Use good lighting. Really. It's amazing how often I see people realize late in the game that you need a generous supply of photons to calibrate a camera :-) Use diffuse ambient lighting, and bounce it off white cards on both sides of the field of view.
Watch what your corner extraction code is doing. Draw the detected corner positions on top of the images (in Matlab or Octave, for example), and judge their quality. Removing outliers early using tight thresholds is better than trusting the robustifier in your bundle adjustment code.
Constrain your model if you can. For example, don't try to estimate the principal point if you don't have a good reason to believe that your lens is significantly off-center w.r.t the image, just fix it at the image center on your first attempt. The principal point location is usually poorly observed, because it is inherently confused with the center of the nonlinear distortion and by the component parallel to the image plane of the target-to-camera's translation. Getting it right requires a carefully designed procedure that yields three or more independent vanishing points of the scene and a very good bracketing of the nonlinear distortion. Similarly, unless you have reason to suspect that the lens focal axis is really tilted w.r.t. the sensor plane, fix at zero the (1,2) component of the camera matrix. Generally speaking, use the simplest model that satisfies your measurements and your application needs (that's Ockam's razor for you).
When you have a calibration solution from your optimizer with low enough RMS error (a few tenths of a pixel, typically, see also Josh's answer below), plot the XY pattern of the residual errors (predicted_xy - measured_xy for each corner in all images) and see if it's a round-ish cloud centered at (0, 0). "Clumps" of outliers or non-roundness of the cloud of residuals are screaming alarm bells that something is very wrong - likely outliers due to bad corner detection or matching, or an inappropriate lens distortion model.
Take extra images to verify the accuracy of the solution - use them to verify that the lens distortion is actually removed, and that the planar homography predicted by the calibrated model actually matches the one recovered from the measured corners.
This is a rather late answer, but for people coming to this from Google:
The correct way to check calibration accuracy is to use the reprojection error provided by OpenCV. I'm not sure why this wasn't mentioned anywhere in the answer or comments, you don't need to calculate this by hand - it's the return value of calibrateCamera. In Python it's the first return value (followed by the camera matrix, etc).
The reprojection error is the RMS error between where the points would be projected using the intrinsic coefficients and where they are in the real image. Typically you should expect an RMS error of less than 0.5px - I can routinely get around 0.1px with machine vision cameras. The reprojection error is used in many computer vision papers, there isn't a significantly easier or more accurate way to determine how good your calibration is.
Unless you have a stereo system, you can only work out where something is in 3D space up to a ray, rather than a point. However, as one can work out the pose of each planar calibration image, it's possible to work out where each chessboard corner should fall on the image sensor. The calibration process (more or less) attempts to work out where these rays fall and minimises the error over all the different calibration images. In Zhang's original paper, and subsequent evaluations, around 10-15 images seems to be sufficient; at this point the error doesn't decrease significantly with the addition of more images.
Other software packages like Matlab will give you error estimates for each individual intrinsic, e.g. focal length, centre of projection. I've been unable to make OpenCV spit out that information, but maybe it's in there somewhere. Camera calibration is now native in Matlab 2014a, but you can still get hold of the camera calibration toolbox which is extremely popular with computer vision users.
http://www.vision.caltech.edu/bouguetj/calib_doc/
Visual inspection is necessary, but not sufficient when dealing with your results. The simplest thing to look for is that straight lines in the world become straight in your undistorted images. Beyond that, it's impossible to really be sure if your cameras are calibrated well just by looking at the output images.
The routine provided by Francesco is good, follow that. I use a shelf board as my plane, with the pattern printed on poster paper. Make sure the images are well exposed - avoid specular reflection! I use a standard 8x6 pattern, I've tried denser patterns but I haven't seen such an improvement in accuracy that it makes a difference.
I think this answer should be sufficient for most people wanting to calibrate a camera - realistically unless you're trying to calibrate something exotic like a Fisheye or you're doing it for educational reasons, OpenCV/Matlab is all you need. Zhang's method is considered good enough that virtually everyone in computer vision research uses it, and most of them either use Bouguet's toolbox or OpenCV.
If I take a picture with a camera, so I know the distance from the camera to the object, such as a scale model of a house, I would like to turn this into a 3D model that I can maneuver around so I can comment on different parts of the house.
If I sit down and think about taking more than one picture, labeling direction, and distance, I should be able to figure out how to do this, but, I thought I would ask if someone has some paper that may help explain more.
What language you explain in doesn't matter, as I am looking for the best approach.
Right now I am considering showing the house, then the user can put in some assistance for height, such as distance from the camera to the top of that part of the model, and given enough of this it would be possible to start calculating heights for the rest, especially if there is a top-down image, then pictures from angles on the four sides, to calculate relative heights.
Then I expect that parts will also need to differ in color to help separate out the various parts of the model.
As mentioned, the problem is very hard and is often also referred to as multi-view object reconstruction. It is usually approached by solving the stereo-view reconstruction problem for each pair of consecutive images.
Performing stereo reconstruction requires that pairs of images are taken that have a good amount of visible overlap of physical points. You need to find corresponding points such that you can then use triangulation to find the 3D co-ordinates of the points.
Epipolar geometry
Stereo reconstruction is usually done by first calibrating your camera setup so you can rectify your images using the theory of epipolar geometry. This simplifies finding corresponding points as well as the final triangulation calculations.
If you have:
the intrinsic camera parameters (requiring camera calibration),
the camera's position and rotation (it's extrinsic parameters), and
8 or more physical points with matching known positions in two photos (when using the eight-point algorithm)
you can calculate the fundamental and essential matrices using only matrix theory and use these to rectify your images. This requires some theory about co-ordinate projections with homogeneous co-ordinates and also knowledge of the pinhole camera model and camera matrix.
If you want a method that doesn't need the camera parameters and works for unknown camera set-ups you should probably look into methods for uncalibrated stereo reconstruction.
Correspondence problem
Finding corresponding points is the tricky part that requires you to look for points of the same brightness or colour, or to use texture patterns or some other features to identify the same points in pairs of images. Techniques for this either work locally by looking for a best match in a small region around each point, or globally by considering the image as a whole.
If you already have the fundamental matrix, it will allow you to rectify the images such that corresponding points in two images will be constrained to a line (in theory). This helps you to use faster local techniques.
There is currently still no ideal technique to solve the correspondence problem, but possible approaches could fall in these categories:
Manual selection: have a person hand-select matching points.
Custom markers: place markers or use specific patterns/colours that you can easily identify.
Sum of squared differences: take a region around a point and find the closest whole matching region in the other image.
Graph cuts: a global optimisation technique based on optimisation using graph theory.
For specific implementations you can use Google Scholar to search through the current literature. Here is one highly cited paper comparing various techniques:
A Taxonomy and Evaluation of Dense Two-Frame Stereo Correspondence Algorithms.
Multi-view reconstruction
Once you have the corresponding points, you can then use epipolar geometry theory for the triangulation calculations to find the 3D co-ordinates of the points.
This whole stereo reconstruction would then be repeated for each pair of consecutive images (implying that you need an order to the images or at least knowledge of which images have many overlapping points). For each pair you would calculate a different fundamental matrix.
Of course, due to noise or inaccuracies at each of these steps you might want to consider how to solve the problem in a more global manner. For instance, if you have a series of images that are taken around an object and form a loop, this provides extra constraints that can be used to improve the accuracy of earlier steps using something like bundle adjustment.
As you can see, both stereo and multi-view reconstruction are far from solved problems and are still actively researched. The less you want to do in an automated manner the more well-defined the problem becomes, but even in these cases quite a bit of theory is required to get started.
Alternatives
If it's within the constraints of what you want to do, I would recommend considering dedicated hardware sensors (such as the XBox's Kinect) instead of only using normal cameras. These sensors use structured light, time-of-flight or some other range imaging technique to generate a depth image which they can also combine with colour data from their own cameras. They practically solve the single-view reconstruction problem for you and often include libraries and tools for stitching/combining multiple views.
Epipolar geometry references
My knowledge is actually quite thin on most of the theory, so the best I can do is to further provide you with some references that are hopefully useful (in order of relevance):
I found a PDF chapter on Multiple View Geometry that contains most of the critical theory. In fact the textbook Multiple View Geometry in Computer Vision should also be quite useful (sample chapters available here).
Here's a page describing a project on uncalibrated stereo reconstruction that seems to include some source code that could be useful. They find matching points in an automated manner using one of many feature detection techniques. If you want this part of the process to be automated as well, then SIFT feature detection is commonly considered to be an excellent non-real-time technique (since it's quite slow).
A paper about Scene Reconstruction from Multiple Uncalibrated Views.
A slideshow on Methods for 3D Reconstruction from Multiple Images (it has some more references below it's slides towards the end).
A paper comparing different multi-view stereo reconstruction algorithms can be found here. It limits itself to algorithms that "reconstruct dense object models from calibrated views".
Here's a paper that goes into lots of detail for the case that you have stereo cameras that take multiple images: Towards robust metric reconstruction
via a dynamic uncalibrated stereo head. They then find methods to self-calibrate the cameras.
I'm not sure how helpful all of this is, but hopefully it includes enough useful terminology and references to find further resources.
Research has made significant progress and these days it is possible to obtain pretty good-looking 3D shapes from 2D images. For instance, in our recent research work titled "Synthesizing 3D Shapes via Modeling Multi-View Depth Maps and Silhouettes With Deep Generative Networks" took a big step in solving the problem of obtaining 3D shapes from 2D images. In our work, we show that you can not only go from 2D to 3D directly and get a good, approximate 3D reconstruction but you can also learn a distribution of 3D shapes in an efficient manner and generate/synthesize 3D shapes. Below is an image of our work showing that we are able to do 3D reconstruction even from a single silhouette or depth map (on the left). The ground-truth 3D shapes are shown on the right.
The approach we took has some contributions related to cognitive science or the way the brain works: the model we built shares parameters for all shape categories instead of being specific to only one category. Also, it obtains consistent representations and takes the uncertainty of the input view into account when producing a 3D shape as output. Therefore, it is able to naturally give meaningful results even for very ambiguous inputs. If you look at the citation to our paper you can see even more progress just in terms of going from 2D images to 3D shapes.
This problem is known as Photogrammetry.
Google will supply you with endless references, just be aware that if you want to roll your own, it's a very hard problem.
Check out The Deadalus Project, althought that website does not contain a gallery with illustrative information about the solution, it post several papers and info about the working method.
I watched a lecture from one of the main researchers of the project (Roger Hubbold), and the image results are quite amazing! Althought is a complex and long problem. It has a lot of tricky details to take into account to get an approximation of the 3d data, take for example the 3d information from wall surfaces, for which the heuristic to work is as follows: Take a photo with normal illumination of the scene, and then retake the picture in same position with full flash active, then substract both images and divide the result by a pre-taken flash calibration image, apply a box filter to this new result and then post-process to estimate depth values, the whole process is explained in detail in this paper (which is also posted/referenced in the project website)
Google Sketchup (free) has a photo matching tool that allows you to take a photograph and match its perspective for easy modeling.
EDIT: It appears that you're interested in developing your own solution. I thought you were trying to obtain a 3D model of an image in a single instance. If this answer isn't helpful, I apologize.
Hope this helps if you are trying to construct 3d volume from 2d stack of images !! You can use open source tool such as ImageJ Fiji which comes with 3d viewer plugin..
https://quppler.com/creating-a-classifier-using-image-j-fiji-for-3d-volume-data-preparation-from-stack-of-images/