I'd like to find a transformation that projects the image from the Left camera onto the image from the Right camera so that the two become aligned. I already managed to do that with two similar cameras (IGB and RGB), by using the disparity map and shifting each pixel by the corresponding disparity value. My problem is that this doesn't work for other cameras that I'm using (for example multispectral and infrared sensors), because the calculated disparity maps have very little detail. I am currently using the Matlab Computer Vision Tool Box, and I suspect that the problem is the poor correlation of information in the images (little correspondences found by the disparity algorithm).
I would like to know if there is another way of doing this transformation, for example just by using the Extrinsic and Intrinsic Parameters of the cameras (the are already calibrated).
The disparity IS the transformation you are looking for. Any sensible left-right mapping depends on 3D information, which the disparity provides. Anything else is just hallucinating some values based on assumptions that may or may not make sense.
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I am trying to obtain a disparity map from a homemade stereo camera setup. The baseline is 125mm and both cameras are fixed to a 3D-printed support. I've previously calibrated the cameras with 15 images of a checkboard pattern of 80mm square size using MatLab's calibration tool.
Using the intrinsics an extrinsics given by MatLab calibration tool, I rectified the images and build the disparity map on a MatLab script. However, the disparity is not good enough for my application. Do you think the calibration is not good or could be due to other problems?
Here are the results:
As you see through the lines I draw, the rectification of the images is not well done, since the epipolar constraint doesn't apply.
As you can see I used one of the calibration images to check. However, it happens the same on other images. I'm particularly concerned about the ground, as it contains a lot of noise and invalid points, which is not good enough for my algorithms, so I need to improve it.
I have two closed curve stereo rectified edge images. Is it possible to find the disparity(along x-axis in image coordinates) between the edge images and do a 3D reconstruction since I know the camera matrix. I am using matlab for the process. And I will not be able to do a window based technique as it's a binary image since a window based technique requires texture. The question how will I compute the disparity between the edge images? The images are available in the following links. Left Edge image https://www.dropbox.com/s/g5g22f6b0vge9ct/edge_left.jpg?dl=0 Right Edge Image https://www.dropbox.com/s/wjmu3pugldzo2gw/edge_right.jpg?dl=0
For this type of images, you can easily map each edge pixel from the left image to its counterpart in the right image, and therefore calculate the disparity for those pixels as usual.
The mapping can be done in various ways, depending on how typical these images are. For example, using DTW like approach to match curvatures.
For all other pixels in the image, you just don't have any information.
#Photon: Thanks for the suggestion. I did what you suggested. I matched each edge pixel in the left and right image in a DTW like fashion. But there are some pixels whose y-pixel coordinate value differ by 1 or 2 pixels, albeit they are properly rectified. So I calculated the depth by averaging those differing(up to 2-pixel difference in y-axis) edge pixels using least squares method. But I ended getting this space curve (https://www.dropbox.com/s/xbg2q009fjji0qd/false_edge.jpg?dl=0) when they actually should have been like this (https://www.dropbox.com/s/0ib06yvzf3k9dny/true_edge.jpg?dl=0) which is obtained using RGB images.I couldn't think of any other reason why it would be the case since I compared by traversing along the 408 edge pixels.
Using Stereo vision and based on Multiple View Geometry book (http://www.robots.ox.ac.uk/~vgg/hzbook/), I have created a 3D point cloud in MATLAB. To do that, I first calibrated the cameras and rectified the stereo images. Then feature extraction and matching. Then eliminated the noisy matched based on camera locations. Finally created the 3D point cloud using triangulation.
Now my question is how to convert this 3D point cloud from pixel domain to actual millimeter/centimeter domain knowing my focal length and camera calibration matrices?
the goal is to find DEPTH IN MILLIMETERS.
I know how to do it in disparity/depth map case using formula: Z=(t*f)/d.
But here in the sparse case, can I do something like this? http://matlab.wikia.com/wiki/FAQ#How_do_I_measure_a_distance_or_area_in_real_world_units_instead_of_in_pixels.3F
or there is a more sophisticated method with more in depth explanation?
Thanks.
The formula you wrote is valid only in the special case when the image planes of the two cameras are on the same geometrical plane, and the motion from one to the other is a translation parallel to one of the image axes.
In the general case you'll need to triangulate actual rays in 3D space, using one of the techniques described in that book (it has a whole chapter on reconstruction). The reconstruction will be metrical if your calibration is. In particular, if the coordinate transform between the cameras has a translation vector whose units are meters (or millimeters, or inches, ...).
This paper describes nicely the geometry of a stereo image system. I am trying to figure out, if the cameras tilted towards each other with a certain angle, how the calculation would change? I looked around but couldn't find any reference to tilted camera systems.
Unfortunately, the calculation changes significantly. The rectified case (where both cameras are well-aligned to each other) has the advantage that you can calculate the disparity and the depth is proportional to the disparity. This is not the case in the general case.
When you introduce tilts, you end up with something called epipolar geometry. Here is a paper about this I just googled. In order to calculate the depth from a pixel-pair you need the fundamental matrix or the essential matrix. Both are not easy to obtain from the image pair. If, however, you have the geometric relation of both cameras (translation and rotation), calculating these matrices is a lot easier.
There are several ways to calculate the depth of a pixel-pair. One way is to use the fundamental matrix to rectify both images (although rectifying is not easy either, or even unique) and run a simple disparity check.
I am doing a project in Matlab on Image processing
Is there any possibility of getting 3d image from 2d image?
If you have multiple images of the same object and the position of the camera when the picure was taken, then it is possible, but still not easy. You can find two such datasets and links to relevant articles here: http://vision.middlebury.edu/mview/
a 3d image would be a projection from 4d (and to show one of those you've got to project down to 2d) and most images that can be displayed on computer or in a picture frame are 2d projections of 3d objects due to this projection which in fact selects a slice of the higher dimensional space it doesn't contain the information needed to invert that projection and get back to 3d from a 2d image
but if you have sufficient sampling of the space it is possible to reconstruct a 3d object from 2d images of it but i don't know of any simple ways to do this
You can't do this without supporting data such as multiple 2D images describing the same 3D object. You then need to figure out the perspectives from which each image was taken, reconcile those into real space, and generate your points using a method such as intersection of stereo lines through each image plane onto the same physical coordinate.
You can also attempt a superpixel approach by exploiting lighting data within a single image, though these methods aren't as accurate.
This is a big field.
The Radon transform is used in tomography applications to reconstruct 3D representations (i.e.images) from many 2D projections of the 3D "scene". This transform and its inverse are present in the image processing toolbox of Matlab. You might want to have a look at it.
Hope this helps.
A.