I tried to do 3D reconstruction of multiple views by using multiview essential matrices to construct 3D view of each image view of object. However, I am shocked that the 3D points I found are all on about XY plane. I guess that it maybe regarding to the large value of essential matrix or weird number of projection matrix estimated. What are the suggestions for me to compute precise 3D points coordinate?
If you have the Computer Vision System Toolbox, this example may be helpful.
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I am working on 3d Reconstruction from two views. Till now I have got Fundamental matrix, Essential matrix and Triangulation Points. After this stage, how do I go forward to obtain textured image from the input image? and save those results in VRML model?
Are your cameras calibrated? If so, then you can rectify the images, and get a dense reconstruction. You can then plot the points using the colors from the RGB image. See this example.
I'm trying to make a 3D reconstruction from a set of uncalibrated photographs in MATLAB. I use SIFT to detect feature points and matches between images. I want to make a projective reconstruction first and then update this to a metric one using auto-calibration.
I know how to estimate the 3D points from 2 images by computing the fundamental matrix, camera matrices and triangulation. Now say I have 3 images, a, b and c. I compute the camera matrices and 3D points for image a and b. Now I want to update the structure by adding image c. I estimate the camera matrix by using known 3D points (calculated from a and b) that match with 2D points in image c, since:
However when I reconstruct the 3D points between b and c they don't add up with the existing 3D points from a and b. I'm assuming this is because I don't know the correct depth estimates of the points (depicted by s in above formula).
With the factorization method of Sturm and Triggs I can estimate the depths and find the structure and motion. However in order to do this, all points have to be visible in all views, which is not the case for my images. How can I estimate the depths for points not visible in all views?
This is not a question about Matlab. It is about an algorithm.
It is not mathematically possible to estimate the position of a 3D point in an image when you don't see an observation of the point in said image.
There are extensions for factorization to work with missing data. However, the field seems to have converged to Bundle Adjustment as the Gold Standard.
An excellent tutorial on how to achieve what you want can be found here, which is a culmination of several years of research into a working application. Starting from projective reconstruction up to the metric upgrade.
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, ...).
I copied the matlab code from: http://www.mathworks.fr/fr/help/vision/ug/stereo-image-rectification.html
I can compute the 3D coordinates but I am not sure if it is the correct one.
Starting from the disparity map and calculating the 3D coordinates, how do we take into account of the warping tform1 and tform2?
The problem here is that you are using uncalibrated cameras. In this case you can get up-to-scale reconstruction, but if you want the 3D points in world units, you would need to know actual distances to some points in the world.
I think you would be better off calibrating your stereo system. Please see this example.
I am to create a 3D volume out of grayscale image set using Matlab. A set contains a continuous and quantized slices of 2D grayscale image. I am still considered myself a rookie in Matlab, but this is what I currently have in my mind:
create an empty space for 3D volume.
On each image, we perform all the preprocessing operation so that we only got the part that is of our interest. (In this question, assume that this preprocessing part always work flawlessly)
Go through the image, each pixel's x and y coordinate on 2D will be transfer to the empty space. For z coordinate, we can use the slice number with respect to the distance between each slice. If a pixel is adjacent to another pixel, the 3D points will be connected together.
Repeat the previous 2 steps until all slices are done. We will now have all the points connected just like in the 2D slices.
But here comes the trouble, how can we connect the points between the slices, so that these points can become a volume? Or is there a more robust way to do in Matlab? Any suggestion is highly appreciated.
Part 0 - Assumptions
all 2D images are of the same dimension, hence your 3D volume can hold all of them in a rectangular cube
majority of the pixels in each of the 2D images have 3D spatial relationships (you can't visualize much if the pixels in each of the 2D images are of some random distribution. )
Part 1 - Visualizing 3D Volume from A Stack of 2D Images
To visualize or reconstruct a 3D volume from a stack of 2D images, you can try the following toolkits in matlab.
1 3D CT/MRI images interactive sliding viewer
http://www.mathworks.com/matlabcentral/fileexchange/29134-3d-ctmri-images-interactive-sliding-viewer
[2] Viewer3D
http://www.mathworks.com/matlabcentral/fileexchange/21993-viewer3d
[3] Image3
http://www.mathworks.com/matlabcentral/fileexchange/21881-image3
[4] Surface2Volume
http://www.mathworks.com/matlabcentral/fileexchange/8772-surface2volume
[5] SliceOMatic
http://www.mathworks.com/matlabcentral/fileexchange/764
Note that if you are familiar with VTK, you can try this:
[6] matVTK
http://www.cir.meduniwien.ac.at/matvtk/
I am currently sticking with [5] SliceOMatic for its simplicity and ease of use. However, by default, rendering 3D is quite slow in Matlab. Turning on openGL would give faster rendering. (http://www.mathworks.com/help/techdoc/ref/opengl.html) Or simply put, set(gcf, 'Renderer', 'OpenGL').
Part 2 - Interpolating pixels in between the slices
To interpolate pixels in between the slices, you need to specify an interpolation method (some of the above toolkits have this capability / flexibility. Otherwise, to give you a head start, some examples for interpolation are bicubic, spline, polynomial etc..(you can work this out by looking up on google or google/scholar for interpolation methods much more specific to your problem domain).
Part 3 - 3D Pre-processing
Looking at your procedures, you process the volumetric data by processing each of the 2D images first. In many advanced algorithms, or in true 3D processing, what you can do is to process the volumetric data in 3D domain first (simply put, you take the 26 neighbors or more in to account first.). Once this step is done, you can simply output the volumetric data into a stack of 2D images for cross-sectional viewing or supply to one of the aforementioned toolkits for 3D viewing or output to third party 3D viewing applications.
I have followed the above concepts for my own medical imaging research projects and the above finding is based on my research experience documented here (with latest revisions).
MATLAB generally plots volumetric data using a 3d array. The data points are spatially evenly separated along each axis. If there are sites in the 3d array for which you do not have data for, usually they are assigned the NaN value and the various plotting functions can generally handle this in a reasonable way (i.e. will generally behave as you intended).
If you load the slices into the 3d array such that adjacent points in the z-direction of the data are also adjacent in the 3rd dimension of the array then you should be fine.