I am calibrating an industrial AVT camera. Is it ok, when I focus on the plane where I will do my measurements with the f/4 aperture then close the aperture to f/16, calibrate the internal parameters of the camera and then open the aperture to f/4 ? Will the calibration change with the changing aperture? I know that none of the parameters (focal length, principal point, lens) should physically change, but is there no effect?
I am not changing the focus (focal length). I need to change the aperture due to bigger depth of field during my calibration and faster camera during my measurements.
I think the short answer is: No it doesn't.
The calibration should be the same (within experimental limits) at different apertures. The aperture only affects the depth of field and the amount of light entering the camera. The focal length, principal point, len distortions, etc. don't change - although your ability to measure them accuratley may be affected by the quality of the image you get.
Maybe a larger aperture could in theory capture a better approximation of lens distortion, although reading this article makes me doubt my own words, but if you calibrate at a wide aperture and then capture at a smaller aperture, this should not be a problem. Only if your lens is seriously distorted would it be an issue (IMHO). The article linked says this:
The size of the stop has no effect on the distortion, as the chief ray
does not alter its route when the aperture is made smaller or larger.
It would presumably be a simple procedure to perform camera calibration at different aperture settings and see if the results are similar. Certainly I know of no way to infer the aperture setting from a camera calibration matrix, which implies that this information itself is not captured.
It depends on your lens and exactly what values you are calibrating.
If you are just setting the back focus distance, then there is no problem.
Or if you are only measuring in the center of the field of view.
Without knowing the focal length, widest aperture, and the general
quality of the lens, it's not possible to give a specific answer.
For example, if the widest aperture is f/1.4, then the lens should
perform well at f/4. But if f/4 is the widest aperture, chances
are you will see a lot of aberrations.
Generally speaking, if you start with the widest aperture of a camera
lens and stop down, the resolving power in the center of the field of
view increases for about 2 stops, and the resolving power in the periphery
of the field improves for about 4 stops.
Beyond that, if you continue to stop down, there is no improvement in
image quality (only increased depth-of-field and a dimmer image--as a
previous answer correctly states). Eventually, as the physical diameter
of the f/stop becomes small, resolving power throughout the field will
decrease due to diffraction.
For example, on a "full frame" (35 x 24 mm format) digital camera with
a good lens, f/22 is noticeably less sharp than say, f/8.
Unfortunately, geometrical (Gaussian) analysis cannot predict
the behavior of real lenses, for two reasons: aberrations and
distortion.
Aberrations are imperfections in design, materials and/or
manufacturing that can be corrected by additional elements, better
glass, closer manufacturing tolerances, etc-- but only to a point
and only at a price. Ideal lenses exist only in theory; real lenses
always perform best (i.e. greatest resolving power) for paraxial rays
(traveling near the optical axis).
Not all aberrations are equally affected by stopping down.
Most improvement: higher-order spherical
Much improvement: spherical, oblique spherical and coma
Some improvement: astigmatism, field curvature, axial chromatic
Not affected: lateral chromatic
Geometrical (Petzval) distortion (technically not an aberration)
also is not affected by stopping down.
Diffraction on the other hand, is a fundamental law of optics--you
just have to live with it. Diffraction varies inversely with the
physical diameter of the aperture: the smaller the diameter, the bigger
the angular size of the Airy disk. As we all know, f-number is focal
length divided by diameter--so f/16 is a much smaller hole on f=50 mm
lens than on a f=150 mm lens.
Traditional methods of measuring diffraction and confusion by
diameters at the projected image (film or sensor) -- rather than by
resolving power at the object--tend to understate the performance of
longer lenses and depth-of-field of larger formats. But MTF charts
tell the real story about the former: the best performing lens in
any manufacture's catalog is a long lens or telephoto.
understate the performance of longer focal length lenses.
Diffraction is why pinholes -- which have no aberrations (and no
distortions if properly designed) -- are not sharp.
Smaller aperture diameters always have more diffraction (i.e., a
larger Airy disk), but diffraction is only significant when the
Airy disk is larger than the lens's circle-of-confusion. The better
correct the lens, the close it is to being "limited by diffraction"
--the technical term for an ideal optical system.
More information:
https://www.diyphotography.net/what-actually-happens-when-you-stop-down-a-lens/
Related
I'm working with an stereo camera setup that has auto-focus (which I cannot turn off) and a really low baseline of less than 1cm.
Auto-focus process can actually change any intrinsic parameter of both cameras (as focal length and principal point, for example) and without a fix relation (left camera may add focus while right one decrease it). Luckily cameras always report the current state of intrinsics with great precision.
On every frame an object of interest is being detected and disparities between camera images are calculated. As baseline is quite low and resolution is not the greatest, performing stereo triangulation leads to quite poor results and for this matter several succeeding computer vision algorithms relay only on image keypoints and disparities.
Now, disparities being calculated between stereo frames cannot be directly related. If principal point changes disparities will be in very different magnitudes after the auto-focus process.
Is there any way to relate keypoint corners and/or disparities between frames after auto-focus process? For example, calculate where would the object lie in the image with the previous intrinsics?
Maybe using a bearing vector towards object and then seek for intersection with image plane defined by previous intrinsics?
Quite challenging your project, perhaps these patents could help you in some way:
Stereo yaw correction using autofocus feedback
Autofocus for stereo images
Depth information for auto focus using two pictures and two-dimensional Gaussian scale space theory
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 am doing a project on stereo vision, basically the system should estimate the distance in real time to avoid collision. The thing is i am not able to decide the proper baseline value . in formula what is the value of disparity.
Look at the formula that relates a baseline to disparity
D=focal*Baseline/z
where focal length is in pixels, Baseline is in mm and z, a distance along the optical axis, is also in mm. Pick your Baseline so that you have a few pixels of disparity at the longest working distance. Also keep in mind that though a long Baseline will accomplish this, at a closer distance you would have a lager dead zone where the cameras' field of views do not overlap enough to have a meaningful disparity calculation.
Also, when selecting the resolution for your images don't go too high since a stereo processing is very intensive and a higher resolution may have stronger noise. Typically people don't use color in stereo matching for the same reason. For your task, the algorithm that uses gray VGA images and works at least at 20 fps with a Baseline = 40-60 cm may be a reasonable choice given vehicle speed <40mph.
I have a photocamera mounted vertically under water in a tank, looking downwards.
There is a flat grid on the bottom of the tank (approx 2m away from the camera).
I want to be able to place markers on the bottom, and use computer vision to know their real life exact position.
So, I need to map from pixels to mm.
If I am not mistaken, cv::calibrateCamera(...) does just this, but is dependent on moving a pattern in front of the camera.
I have just static pictures of the scene, and the camera never moves in relation to the grid. Thus, I have only a "single" image to find the parameters.
How can I do this using the grid?
Thank you.
Interesting problem! The "cute" part is the effect on the intrinsic parameters of the refraction at the water-glass interface, namely to increase the focal length (or, conversely, to reduce the field of view) compared to the same lens in air. In theory, you could calibrate in air and then correct for the difference in refraction index, but calibrating directly in water is likely to give you more accurate results.
Do know your accuracy requirements? And have you verified that your lens/sensor combination is adequate to meet them (with an adequate margin)? To answer the question you need to estimate (either by calculation from the lens and sensor specifications, or experimentally using a resolution chart) whether you can resolve in an image the minimal distances required by your application.
From the wording of your question I think that you are interested only in measurements on a single plane. So you only need to (a) remove the nonlinear (barrel or pincushion) lens distortion and (b) estimate the homography between the plane of interest and the image. Once you have the latter, you can directly convert from undistorted image coordinates to world ones by matrix multiplication. Additionally if (as I imagine) the plane of interest is roughly parallel to the image plane, you should not have any problem keeping the entire field-of-view in focus.
Of course, for all of this to work as expected, you should make sure that the tank bottom is really flat, within the measurement tolerances of your application. Otherwise you are really dealing with a 3D problem, and need to modify your procedures accordingly.
The actual procedure depends a lot on the size of the tank, which you don't indicate clearly. If it's small enough that it is practical to manufacture a chessboard-like movable calibration target, by all means go for it. You may want to take a look at this other answer for suggestions. In the following I'll discuss the more interesting case in which your tank is large, e.g. the size of a swimming pool.
I'd proceed by sticking calibration markers in a regular grid at the pool bottom. I'd probably choose checker-like markers like these, maybe printing them myself with a good laser printer on plastic with an adhesive backing (assuming you can leave them in place forever). You should plan on having quite a few of them, say, an 8x8 or 10x10 grid, covering as much as possible of the field of view of the camera in its operating position and pose. To help with lining up the grid nicely you might use a laser line projector of suitable fan angle, or a laser pointer attached to a rotating support. Note carefully that it is not necessary that they be affixed in a precise X-Y grid (which may be complicated, depending on the size of your pool), only that their positions with respect any arbitrarily chosen (but fixed) three of them be known. In other words, you can attach them to the bottom approximately in a grid, then measure the distances of three extreme corners from each other as accurately as you can, thus building a base triangle, then measure the distances of all the other corners from the vertices of the triangle, and finally reconstruct their true positions with a bit of trigonometry. It's basically a surveying problem and, depending on your accuracy requirements and budget, you may want to enroll a local friendly professional surveyor (and their tools) to get it done as precisely as necessary.
Once you have your grid, you can fill the pool, get your camera, focus and f-stop the lens as needed for the application. From now on you may not touch the focus and f-stop ever again, under penalty of miscalibrating - exposure can only be controlled by the exposure time, so make sure to have enough light. Disable any and all auto-focus and auto-iris functions, if any. If the camera has a non-rigid lens mount (e.g. a DLSR), you'll need some kind of mechanical rig to ensure that the lens-body pair stay rigid. F-stop as close as you can, given the available lighting and sensor, so to have a fair bit of depth of field available. Then take several photos (~ 10) of the grid, moving and rotating the camera, and going a bit closer and farther away than your expected operating distance from the plane. You'll want to "see" in some images some significant perspective foreshortening of the grid - this is needed to accurately calibrate the focal length. Avoid JPG and any other lossy compression format when storing the images - use lossless PNG or TIFF.
Once you have the images, you can manually mark and identify the checker markers in the images. For a once-off project like this I would not bother with automatic identification, just do it manually (e.g. in Matlab, or even in Photoshop or Gimp). To help identify the markers, you could, e.g. print a number next to them. Once you have the manual marks, you can refine them automatically to subpixel accuracy, e.g. using cv::findCornerSubpix.
You're almost done. Feed the "reference" measured position of the real corners, and the observed ones in all images, to your favorite camera calibration routine, e.g. cv::calibrateCamera. You use the nominal focal length of the camera (converted to pixels) for an initial estimate, along with null distortion. If all goes well, you will obtain the camera intrinsic parameters, which you will keep, and the camera poses at all images, which you'll throw away.
Now you can mount the camera in your final setup, as needed by your application, and take one further image of the grid. Mark and refine the corner positions as before. Undistort their image positions using the distortion parameters returned by the calibration. Finally compute the homography between the reference positions of the real markers (in meters) and their undistorted positions, and you're done.
HTH
To calibrate the camera you do need multiple images of the checkerboard (or one of the other patterns found here). What you can do, is calibrate the camera outside of the water or do a calibration sequence once.
Once you have that information (focal length, center of lens, distortion, etc). You can use the solvePNP function to estimate the orientation of a single board. This estimation provides you with a distance from the camera to the board.
A completely different alternative could be to find what kind of lens the camera uses and manually fill in the data. I've not tried this, so I'm uncertain how well this would work.
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.