I'm using SceneKit. I have created and assigned my own camera to the scene and I have adjusted its xFov and yFov. When I set a value higher than 50, there starts to be some distortion. Everything near the edges of the screen is stretched – almost like the camera suddenly becomes a "Fish Eye."
I need the xFov and yFov to be above 50 (I actually need it to be 100), but I can't have that distortion. What do I do?
What you're asking isn't theoretically impossible per se, but theoretically interesting at least.
What happens to a physical camera when you increase the field of view? The wider it gets, the more "fisheye" it looks. The projection matrix and perspective divide of a 3D graphics pipeline like SceneKit works in a similar way. It looks a little different because it's a rectilinear transformation rather than the effect of a spherical lens, but it's the same general idea — it maps a volume (called a frustum) of 3D space "seen" by the camera onto the viewing plane. This is a general aspect of 3D graphics, not something specific to SceneKit, so you can find plenty of good tutorials that cover the underlying math pretty well.
That frustum projection fixes a certain relationship between the amount of viewing angle something takes up and its width on the viewing plane. You can't really change that relationship and still have a linear (well, rational, but mostly linear) transformation that 3D hardware can apply with a single matrix multiplication (and perspective divide).
You could, in theory, define a different relationship — say, one where a large angular size corresponds to a much larger part of the viewing plane near the center of the view, but to a much smaller part farther away from the center. But you can't do that in the camera transform... You'd have to do such calculations pixel by pixel in some kind of post-processing shader. (In fact, this is generally how rendering for the lenses of a VR headset works.)
Related
I am trying to build a solution where I could differentiate between a 3D textured surface with the height of around 200 micron and a regular text print.
The following image is a textured surface. The black color here is the base surface.
Regular text print will be the 2D print of the same 3D textured surface.
[EDIT]
Initial thought about solving this problem, could look like this:
General idea here would be, images shot at different angles of a 3D object would be less related to each other than the images shot for a 2D object in the similar condition.
One of the possible way to verify could be: 1. Take 2 images, with enough light around (flash of the camera). These images should be shot at as far angle from the object plane as possible. Say, one taken at camera making 45 degree at left side and other with the same angle on the right side.
Extract the ROI, perspective correct them.
Find GLCM of the composite of these 2 images. If the contrast of the GLCM is low, then it would be a 3D image, else a 2D.
Please pardon the language, open for edit suggestion.
General idea here would be, images shot at different angles of a 3D object would be less related to each other than the images shot for a 2D object in the similar condition.
One of the possible way to verify could be:
1. Take 2 images, with enough light around (flash of the camera). These images should be shot at as far angle from the object plane as possible. Say, one taken at camera making 45 degree at left side and other with the same angle on the right side.
Extract the ROI, perspective correct them.
Find GLCM of composite of these 2 images. If contrast of the GLCM is low, then it would be a 3D image, else a 2D.
Please pardon the language, open for edit suggestion.
If you can get another image which
different angle or
sharper angle or
different lighting condition
you may get result. However, using two image with different angle with calibrate camera can get stereo vision image which solve your problem easily.
This is a pretty complex problem and there is no plug-in-and-go solution for this. Using light (structured or laser) or shadow to detect a height of 0.2 mm will almost surely not work with an acceptable degree of confidence, no matter of how much "photos" you take. (This is just my personal intuition, in computer vision we verify if something works by actually testing).
GLCM is a nice feature to describe texture, but it is, as far as I know, used to verify if there is a pattern in the texture, so, I believe it would output a positive value for 2D print text if there is some kind of repeating pattern.
I would let the computer learn what is text, what is texture. Just extract a large amount of 3D and 2D data, and use a machine learning engine to learn which is what. If the feature space is rich enough, it may be able to find a way to differentiate one from another, in a way our human mind wouldn't be able to. The feature space should consist of edge and colour features.
If the system environment is stable and controlled, this approach will work specially well, since the training data will be so similar to the testing data.
For this problem, I'd start by computing colour and edge features (local image pixel sums over different edge and colour channels) and try a boosted classifier. Boosted classifiers aren't the state of the art when it comes to machine learning, but they are good at not overfitting (meaning you can just insert as much data as you want), and will most likely work in a stable environment.
Hope this helps,
Good luck.
I'm currently working on an augmented reality application using a medical imaging program called 3DSlicer. My application runs as a module within the Slicer environment and is meant to provide the tools necessary to use an external tracking system to augment a camera feed displayed within Slicer.
Currently, everything is configured properly so that all that I have left to do is automate the calculation of the camera's extrinsic matrix, which I decided to do using OpenCV's solvePnP() function. Unfortunately this has been giving me some difficulty as I am not acquiring the correct results.
My tracking system is configured as follows:
The optical tracker is mounted in such a way that the entire scene can be viewed.
Tracked markers are rigidly attached to a pointer tool, the camera, and a model that we have acquired a virtual representation for.
The pointer tool's tip was registered using a pivot calibration. This means that any values recorded using the pointer indicate the position of the pointer's tip.
Both the model and the pointer have 3D virtual representations that augment a live video feed as seen below.
The pointer and camera (Referred to as C from hereon) markers each return a homogeneous transform that describes their position relative to the marker attached to the model (Referred to as M from hereon). The model's marker, being the origin, does not return any transformation.
I obtained two sets of points, one 2D and one 3D. The 2D points are the coordinates of a chessboard's corners in pixel coordinates while the 3D points are the corresponding world coordinates of those same corners relative to M. These were recorded using openCV's detectChessboardCorners() function for the 2 dimensional points and the pointer for the 3 dimensional. I then transformed the 3D points from M space to C space by multiplying them by C inverse. This was done as the solvePnP() function requires that 3D points be described relative to the world coordinate system of the camera, which in this case is C, not M.
Once all of this was done, I passed in the point sets into solvePnp(). The transformation I got was completely incorrect, though. I am honestly at a loss for what I did wrong. Adding to my confusion is the fact that OpenCV uses a different coordinate format from OpenGL, which is what 3DSlicer is based on. If anyone can provide some assistance in this matter I would be exceptionally grateful.
Also if anything is unclear, please don't hesitate to ask. This is a pretty big project so it was hard for me to distill everything to just the issue at hand. I'm wholly expecting that things might get a little confusing for anyone reading this.
Thank you!
UPDATE #1: It turns out I'm a giant idiot. I recorded colinear points only because I was too impatient to record the entire checkerboard. Of course this meant that there were nearly infinite solutions to the least squares regression as I only locked the solution to 2 dimensions! My values are much closer to my ground truth now, and in fact the rotational columns seem correct except that they're all completely out of order. I'm not sure what could cause that, but it seems that my rotation matrix was mirrored across the center column. In addition to that, my translation components are negative when they should be positive, although their magnitudes seem to be correct. So now I've basically got all the right values in all the wrong order.
Mirror/rotational ambiguity.
You basically need to reorient your coordinate frames by imposing the constraints that (1) the scene is in front of the camera and (2) the checkerboard axes are oriented as you expect them to be. This boils down to multiplying your calibrated transform for an appropriate ("hand-built") rotation and/or mirroring.
The basic problems is that the calibration target you are using - even when all the corners are seen, has at least a 180^ deg rotational ambiguity unless color information is used. If some corners are missed things can get even weirder.
You can often use prior info about the camera orientation w.r.t. the scene to resolve this kind of ambiguities, as I was suggesting above. However, in more dynamical situation, of if a further degree of automation is needed in situations in which the target may be only partially visible, you'd be much better off using a target in which each small chunk of corners can be individually identified. My favorite is Matsunaga and Kanatani's "2D barcode" one, which uses sequences of square lengths with unique crossratios. See the paper here.
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.
Is it possible to set up GL_PROJECTION in OpenGL to compensate screen rotations?
I think there is a lot of applications to that, in augmented reality or stereoscopic views, for instance.
Particularly, I would like to make a "fake" change of perspective when the mobile device is tilted.
This effect is shown in the image
Actually your particular case requires adjustment of both the projection and the modelview. The modelview is responsible for setting the point of origin. By having an angled view the vantage point shifts. However also the lens get shifted (literaly, it's just like a shift lens on a real camera), that requires a shift term.
Now your sketch is a bit unclear on what actually is desired. What I can clearly say is, that it's not rotated, but shifted. Suggestion: Download Blender, set up a simple scene and tinker with the "Shift" parameters of the camera object; as you'll see you will have to apply a combination of lens shift and camera shift.
But generally speaking: Yes, adjustment of the projection matrix is required in some situations.
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.