I'm working on an Eye Tracking system with two cameras mounted on some kind of glasses. There are optical lenses so that the screen is perceived at around 420 mm from the eye.
From a few dozen pupil samples, we compute two eye models (one for each camera), located in their respective camera coordinates system. This is based on the works here, but modified so that an estimation of the eye center is found using some kind of brute-force approach to minimize the ellipse projection error on the model given its center position in camera space.
Theorically, an approximation of the cameras parameters would be symetrical to the lenses on the Y axis. So every camera should be at the coordinates (around 17.5mm or -17.5, 0, 3.3) with respect to the lenses coordinates system, a rotation of around 42.5 degrees on the Y axis.
With the However, with these values, there is an offset in the result. See below:
The red point is the gaze center estimated by the left eye tracker, the white one is the right eye tracker, in screen coordinates
The screen limits are represented by the white lines.
The green line is the gaze vector, in camera coordinates (projected in 2D for visualization)
The two camera centers found, projected in 2D, are in the middle of the eye (the blue circle).
The pupil samples and current pupils are represented by the ellipses with matching colors.
The offset on x isn't constant which mean the rotation on Y is not exact. and the position of the camera aren't precise too. In order to fix it, we used: this to calibrate and then this to get the rotation parameters from the rotation matrix.
We added a camera on the middle of the lenses (Close to the theorical 0,0,0 point ?) to get the extrinsics and intrinsic parameters of the cameras, relative to our lens center. However, with about 50 checkerboard captures from different positions, the results given by OpenCV doesn't seems correct.
For example, it gives for a camera a position of about (-14,0,10) in lens coordinates for the translation and something like (-2.38, 49, -2.83) as rotation angles in degrees.
The previous screenshots are taken with theses parameters. The theorical ones are a bit further apart, but are more likely to reach the screen borders, unlike the opencv value.
This is probably because the test camera is in front of the optic, not behind, where our real 0,0,0 would be located (we just add the distance at which the screen is perceived on the Z axis afterwards, which is 420mm).
However, we have no way to put the camera in (0, 0, 0).
As the system is compact (everything is captured within a few cm^2), each degree or millimeter can change the result drastically so without the precise value the cameras, we're a bit stuck.
Our objective here is to find an accurate way to get the extrinsic and intrisic parameters of each cameras, so that we can compute a precise position of the center of the eye of the person wearing the glasses, without other calibration procedure than looking around (so no fixation points)
Right now, the system is precise enough so that we get a global indication on where someone is looking on the screen,but there is a divergence between the right and left camera, it's not precise enough. Any advice or hint that could help us is welcome :)
Related
I have a made a planet and wanted to make an atmosphere around it. So I was referring to this site:
Click to visit site
I don't understand this:
As with the lookup table proposed in Nishita et al. 1993, we can get the optical depth for the ray to the sun from any sample point in the atmosphere. All we need is the height of the sample point (x) and the angle from vertical to the sun (y), and we look up (x, y) in the table. This eliminates the need to calculate one of the out-scattering integrals. In addition, the optical depth for the ray to the camera can be figured out in the same way, right? Well, almost. It works the same way when the camera is in space, but not when the camera is in the atmosphere. That's because the sample rays used in the lookup table go from some point at height x all the way to the top of the atmosphere. They don't stop at some point in the middle of the atmosphere, as they would need to when the camera is inside the atmosphere.
Fortunately, the solution to this is very simple. First we do a lookup from sample point P to the camera to get the optical depth of the ray passing through the camera to the top of the atmosphere. Then we do a second lookup for the same ray, but starting at the camera instead of starting at P. This will give us the optical depth for the part of the ray that we don't want, and we can subtract it from the result of the first lookup. Examine the rays starting from the ground vertex (B 1) in Figure 16-3 for a graphical representation of this.
First Question - isn't optical depth dependent on how you see that is, on the viewing angle? If yes, the table just gives me the optical depth of the rays going from land to the top of the atmosphere in a straight line. So what about the case where the rays pierce the atmosphere to reach the camera? How do I get the optical depth in this case?
Second Question - What is the vertical angle it is talking about...like, is it the same as the angle with the z-axis as we use in polar coordinates?
Third Question - The article talks about scattering of the rays going to the sun..shouldn't it be the other way around? like coming from the sun to a point?
Any explanation on the article or on my questions will help a lot.
Thanks in advance!
I am no expert in the matter but have played with Atmospheric scattering and various physical and optical simulations. I strongly recommend to look at this:
my VEEERRRYYY Simplified version of atmospheric scattering in GLSL
It odes not do the full volume intergration but just linear path integration along the ray and does only the Rayleight scatering with isotropic coefficients. As you can see its still good enough.
In real scattering the viewing angle is impacting the real scattering equation as the scattering coefficients are different in different angles (against main light source and viewer) So answer to your first question is Yes it does.
Not sure what you are refer to in your second question. The scattering itself is dependent on angle between light source, particle and camera. That lies on arbitrary plane. However if the Earth surface is accounted to the equation too then its dependent on the horizontal and vertical angles (against terrain) so azimuth,elevation as usually more light is reflected when camera is facing sun (azimuth) and the reflected rays are closer to your elevation. So my guess is that's what the horizontal angle is about accounting for reflected light from the surface.
To answer your 3th question is called back ray tracing. You can cast rays both ways (from camera or from sun) however if you start from light source you do not know which way to go to hit a pixel on camera screen so you need to cast a lot of rays to increase the probability of hit enough to fill the screen which is too slow and inaccurate (produce holes). If you start from screen pixel then you cast just single or per wavelength ray instead which is much much faster. The resulting color is the same.
[Edit1] vertical angle
OK I read the linked topic a bit and this is How I understand it:
So its just angle between surface normal and the casted ray. Its scaled so vert.angle=0 means that ray and normal are the same and vert.angle=1 means the are opposite directions.
I am working on building 3D point cloud from features matching using OpenCV3.1 and OpenGL.
I have implemented 1) Camera Calibration (Hence I am having Intrinsic Matrix of the camera) 2) Feature extraction( Hence I have 2D points in Pixel Coordinates).
I was going through few websites but generally all have suggested the flow for converting 3D object points to pixel points but I am doing completely backword projection. Here is the ppt that explains it well.
I have implemented film coordinates(u,v) from pixel coordinates(x,y)(With the help of intrisic matrix). Can anyone shed the light on how I can render "Z" of camera coordinate(X,Y,Z) from the film coordinate(x,y).
Please guide me on how I can utilize functions for the desired goal in OpenCV like solvePnP, recoverPose, findFundamentalMat, findEssentialMat.
With single camera and rotating object on fixed rotation platform I would implement something like this:
Each camera has resolution xs,ys and field of view FOV defined by two angles FOVx,FOVy so either check your camera data sheet or measure it. From that and perpendicular distance (z) you can convert any pixel position (x,y) to 3D coordinate relative to camera (x',y',z'). So first convert pixel position to angles:
ax = (x - (xs/2)) * FOVx / xs
ay = (y - (ys/2)) * FOVy / ys
and then compute cartesian position in 3D:
x' = distance * tan(ax)
y' = distance * tan(ay)
z' = distance
That is nice but on common image we do not know the distance. Luckily on such setup if we turn our object than any convex edge will make an maximum ax angle on the sides if crossing the perpendicular plane to camera. So check few frames and if maximal ax detected you can assume its an edge (or convex bump) of object positioned at distance.
If you also know the rotation angle ang of your platform (relative to your camera) Then you can compute the un-rotated position by using rotation formula around y axis (Ay matrix in the link) and known platform center position relative to camera (just subbstraction befor the un-rotation)... As I mention all this is just simple geometry.
In an nutshell:
obtain calibration data
FOVx,FOVy,xs,ys,distance. Some camera datasheets have only FOVx but if the pixels are rectangular you can compute the FOVy from resolution as
FOVx/FOVy = xs/ys
Beware with Multi resolution camera modes the FOV can be different for each resolution !!!
extract the silhouette of your object in the video for each frame
you can subbstract the background image to ease up the detection
obtain platform angle for each frame
so either use IRC data or place known markers on the rotation disc and detect/interpolate...
detect ax maximum
just inspect the x coordinate of the silhouette (for each y line of image separately) and if peak detected add its 3D position to your model. Let assume rotating rectangular box. Some of its frames could look like this:
So inspect one horizontal line on all frames and found the maximal ax. To improve accuracy you can do a close loop regulation loop by turning the platform until peak is found "exactly". Do this for all horizontal lines separately.
btw. if you detect no ax change over few frames that means circular shape with the same radius ... so you can handle each of such frame as ax maximum.
Easy as pie resulting in 3D point cloud. Which you can sort by platform angle to ease up conversion to mesh ... That angle can be also used as texture coordinate ...
But do not forget that you will lose some concave details that are hidden in the silhouette !!!
If this approach is not enough you can use this same setup for stereoscopic 3D reconstruction. Because each rotation behaves as new (known) camera position.
You can't, if all you have is 2D images from that single camera location.
In theory you could use heuristics to infer a Z stacking. But mathematically your problem is under defined and there's literally infinitely many different Z coordinates that would evaluate your constraints. You have to supply some extra information. For example you could move your camera around over several frames (Google "structure from motion") or you could use multiple cameras or use a camera that has a depth sensor and gives you complete XYZ tuples (Kinect or similar).
Update due to comment:
For every pixel in a 2D image there is an infinite number of points that is projected to it. The technical term for that is called a ray. If you have two 2D images of about the same volume of space each image's set of ray (one for each pixel) intersects with the set of rays corresponding to the other image. Which is to say, that if you determine the ray for a pixel in image #1 this maps to a line of pixels covered by that ray in image #2. Selecting a particular pixel along that line in image #2 will give you the XYZ tuple for that point.
Since you're rotating the object by a certain angle θ along a certain axis a between images, you actually have a lot of images to work with. All you have to do is deriving the camera location by an additional transformation (inverse(translate(-a)·rotate(θ)·translate(a)).
Then do the following: Select a image to start with. For the particular pixel you're interested in determine the ray it corresponds to. For that simply assume two Z values for the pixel. 0 and 1 work just fine. Transform them back into the space of your object, then project them into the view space of the next camera you chose to use; the result will be two points in the image plane (possibly outside the limits of the actual image, but that's not a problem). These two points define a line within that second image. Find the pixel along that line that matches the pixel on the first image you selected and project that back into the space as done with the first image. Due to numerical round-off errors you're not going to get a perfect intersection of the rays in 3D space, so find the point where the ray are the closest with each other (this involves solving a quadratic polynomial, which is trivial).
To select which pixel you want to match between images you can use some feature motion tracking algorithm, as used in video compression or similar. The basic idea is, that for every pixel a correlation of its surroundings is performed with the same region in the previous image. Where the correlation peaks is, where it likely was moved from into.
With this pixel tracking in place you can then derive the structure of the object. This is essentially what structure from motion does.
I'm building an interactive floor. The main idea is to match the detections made with a Xtion camera with objects I draw in a floor projection and have them following the person.
I also detect the projection area on the floor which translates to a polygon. the camera can detect outside the "screen" area.
The problem is that the algorithm detects the the top most part of the person under it using depth data and because of the angle between that point and the camera that point isn't directly above the person's feet.
I know the distance to the floor and the height of the person detected. And I know that the camera is not perpendicular to the floor but I don't know the camera's tilt angle.
My question is how can I project that 3D point onto the polygon on the floor?
I'm hoping someone can point me in the right direction. I've been reading about camera projections but I'm not seeing how to use it in this particular problem.
Thanks in advance
UPDATE:
With the awnser from Diego O.d.L I was able to get an almost perfect detection. I'll write the steps I used for those who might be looking for the same solution (I won't get into much detail on how detection is made):
Step 1 : Calibration
Here I get some color and depth frames from the camera, using openNI, with the projection area cleared.
The projection area is detected on the color frames.
I then convert the detection points to real world coordinates (using OpenNI's CoordinateConverter). With the new real world detection points I look for the plane that better fits them.
Step 2: Detection
I use the detection algorithm to get new person detections and to track them using the depth frames.
These detection points are converted to real world coordinates and projected to the plane previously computed. This corrects the offset between the person's height and the floor.
The points are mapped to screen coordinates using a perspective transform.
Hope this helps. Thank you again for the awnsers.
Work with the camera coordinate system initially. I'm assuming you don't have problems converting from (row,column,distance) to a real world system aligned with the camera axis (x,y,z):
calculate the plane with three or more points (for robustness) with
the camera projection (x,y,z). (choose your favorite algorithm,
i.e
Then Find the projection of your head point to the floor plane
(example)
Finally, you can convert it to the floor coordinate system or just
keep it in the camera system
From the description of your intended application, it is probably more useful for you to recover the image coordinates, I guess.
This type of problems usually benefits from clearly defining the variables.
In this case, you have a head at physical position {x,y,z} and you want the ground projection {x,y,0}. That's trivial, but your camera gives you {u,v,d} (d being depth) and you need to transform that to {x,y,z}.
The easiest solution to find the transform for a given camera positioning may be to simply put known markers on the floor at {0,0,0}, {1,0,0}, {0,1,0} and see where they pop up in your camera.
I am wondering if I have got my thinking write about this, I have calibration done for my camera and now I want to get the angle of detected objects relative to the camera only on the x-axis, the horizontal.
I am thinking I can put some grid lines across the image at known pixel values and match those with know real world distances and calculate the angle per pixel that way, knowing the distances of the triangles. Starting at the centre of the image 0 degrees, and as we move towards the right +X degrees and towards the left -X pixels.
Assuming this is a correct way to go about it, for some reason the video I'm working with was recorded at 704x576 pixels, but when I plug the camera into my computer to work with it's 640x480 pixels and it's the same camera that made the recordings. I assume this will affect my results somewhat, with the calibration and definitely with the angle per pixel measurement that I want. I am working with OpenCV in C++, I am wondering if there's a way/function to adjust the screen size for when I call up the camera to 704x576 and if I then do my measurements at this size can I get a somewhat accurate angle per pixel measurement? Or do I need to do something else?
I'm still figuring my way around camera geometry and openCV, and any help would be much appreciated, thanks.
It is probably easier than you think. Say your camera has 60.0 deg horizontal field of view (FOV). Than each pixel along X axis is just 60.0/640 deg. You can easily calculate FOV by considering a right triangle with sides formed by a focal length vector and half of the screen width:
FOV = 2*atan(640/2, focal) where focal length is in pixels
for example, for focal=500 pixels
FOV = 2*atan(640/2, 500) = 1.14rad = 65.2deg
One thing to keep in mind is that focal length changes proportionally with screen resolution. For example, if you calculated focal=500 based on 640x320 image, then for 320x160 image focal=250.
I'd like to know how I can go about calculating the angle of some pixel in a photo relative to the webcam that I'm using. I'm new to this sort of thing and I'm using a webcam. Essentially, I take a photo, process it, and I end up with a pixel value in the image that is what I'm looking for. I then need to somehow turn that pixel value into some meaningful quantity---I need to find a line/vector that passes through the pixel and the camera. I don't need magnitude, just phase.
How does one go about doing this? Is camera calibration necessary? I've been reading a bit about it but am unsure.
Thanks
You don't need to know the distance to the object, only the resolution and angle of view of the camera.
Computing the angle requires only simple linear interpolation. For example, let's assume a camera with a resolution of 1920x1080 that covers a 45 degree angle of view across the diagonal.
In this case, sqrt(19202 + 10802) gives 2292.19 pixels along the diagonal. That means each pixel represents 45/2292.19 = .0153994 degrees.
So, compute the distance from the center (in pixels), multiply by .0153994, and you have its angle from the center (for that camera -- for yours, you'll obviously have to use its resolution and angle of view).
Of course, this is somewhat approximate -- its accuracy will depend on how much distortion the lens has. With a zoom lens (especially wider angle) you can generally count on that being fairly high. With a fixed focal length lens (especially if it doesn't cover an angle wider than 90 degrees or so) it'll usually be pretty low.
If you want to improve accuracy, you can start by taking a picture of a flat rectangle with straight lines just inside the angle of view of the camera, then compute the distortion based on the deviation from perfectly straight in the resulting picture. If you're working with an extremely wide angle lens, this may be nearly essential. With a lens covering a narrower angle of view (especially, as already mentioned, if it's fixed focal length) it's rarely likely to be worthwhile (such lenses often have only a fraction of a percent of distortion).
Recipe:
1 - Calibrate the camera, obtaining the camera matrix K and distortion parameters D. In OpenCV this is done as described in this tutorial.
2 - Remove the nonlinear distortion from the pixel positions of interest. In OpenCV is done using the undistortPoints routine, without passing arguments R and P.
3 - Back-project the pixels of interest into rays (unit vectors with the tail at the camera center) in camera 3D coordinates, by multiplying their pixel positions in homogeneous coordinates times the inverse of the camera matrix.
4 - The angle you want is the angle between the above vectors and (0, 0, 1), the vector associated to the camera's focal axis.