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Hey there I try to do a realtime visual odometry system for a monocular camera.
Now I'm looking for an equation to describe 3d points movement in 2d vectors. While researching I came across a very interesting looking equation. I'm refering to page 22. It basically makes a simplification under the assumption of a relatively small time step. But now I'm struggeling about the image coordinates x and y. It's said that x would be sth like x=(px-px0) and y=(py-py0). When I understand it right p0 is the center of rotation. But if this is the case the whole formular would make no sense for my case cause I would need a prior knowledge of the center of rotation. Which is based on the translation again.
So maybe can help understanding it or maybe point me to a better way to do it.
To use this equation, you must have calibrated your camera (with a pinhole model), so you have a set of distortion coefficients, a focal distance and the principal point, which is the intersection of the optical axis with the image plane, as illustrated here: http://docs.opencv.org/2.4/modules/calib3d/doc/camera_calibration_and_3d_reconstruction.html.
In the equation you mention, x and y coordinates are in pixels after distortion correction and relative to the center of projection, not the center of rotation. So, the px0 and py0 you are looking for, are the coordinates of the principal point, that is, cx0 and cy0 using the naming convention of the link above.
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So my problem, as I said in the title is that I have an image that is in an perspective view and I to transform it into the orthographic view.
But as far as I can understand this example :
the distance from the camera to the NearClip plane and to the FarClip plane is required.
I was wondering if I'm going completly wrong and if there is a way to accomplish that without knowing those distances?
If yes, I Suppose it's something easy such as a matrix multiplication, but after few hours of research, I turn to you searchin any help that can come...
Thanks a lot!
Best regards!
EDIT : I will explain the context, maybe it can helps.
I have a Fish-eye camera that took a panoramic picture (like below, for example)
And my final goal is to create 6 cubics (6 image that corresponde to the up, the down, right, left, front and back of a cube if you're in the cube). So I tried to use the equirectangular projection to create a picture that contains the 6 cubics.
But the problem is that the fisheye take perspective view. So my 6 pictures are perspectives. And I want them to be ortho... :'(
No this is not possible without making several assumptions. Distances or object sizes..
Of course you don't have any informaton of what is behind your objects from your perspective. This information is not available even if you had the distances.
If that was possible there would be no need for 3d-imaging or telecentric lenses.
Of course you can also assume that your objects are spheres. Then you know what to add in your reconstruction but in general this is not viable.
This may be an old question, but the existing answer of "not possible" is not correct for pictures that are less extreme than the example. Photoshop has a Lens Correction tool, as does the free program Gimp. A tutorial for the Photoshop tool is at https://helpx.adobe.com/photoshop/using/correcting-image-distortion-noise.html#correct_lens_distortion_and_adjust_perspective showing it can be done through Choose Filter > Lens Correction. And though you would need to know specific measurements from the camera or scene to perfectly correct the image, you can get pretty close and use assumptions that some objects will have straight edges or certain lines will be parallel.
Gimp's tool is under Filters -> Distorts -> Lens Distortions, and some examples can be found at http://www.texturemate.com/content/how-easily-remove-lens-distortion-photos-using-gimp and there's a StackExchange answer for it at https://gamedev.stackexchange.com/questions/129415/converting-real-life-perspective-photos-into-orthographic-view-for-texture-creat
Neither of these may be extensive enough to un-distort an image from fisheye lenses, but these options are available to anyone who found this page and hopes to adjust an image with more common distortions.
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I'm getting 3D points from the Kinect via OpenNI. Let's say I have :
X = [93.7819,76.8463,208.386,322.069,437.946,669.999]
Y = [-260.147,-250.011,-230.717,-211.104,-195.538,-189.851]
Z = [958,942,950,945,940,955]
That's the points I was able to catch from my moving ball. Now I would like to be able to compute something like an interpolation or least square with those points to know the trajectory of the ball. I can then know where the ball is going and where it will hit the wall.
I'm not sure of which mathematical tool to use and how to translate it in C++. I've seen lots of resources for 2D interpolation (cubic,...) or least squares, but it seems that it's harder for 3D or I missed something maybe.
Best regards
EDIT : the question is marked as too broad by moderators, so I will reduce the scope with the responses I got : if I use 2D polynomial regression with the 3 plans separately (thx yephick), what can I use in C++ to implement it ?
For what you are interested in there's hardly any difference between 3D and 2D.
All you do is work with planes independently (XY plane, XZ plane, and YZ plane). This will reduce the complexity significantly and allow you to "draw" much simpler diagrams on a piece of paper when you work on this problem.
Once you figured the coordinates in each of the planes it is quite trivial to not only reconcile the coordinates into a 3D space but also provides an added benefit of error checking. For example an X coordinate found in XY plane should match (or be "close enough") to the same X coordinate found in XZ plane.
If the accuracy is not too critical you don't even need to go higher than the first power of polynomial approximation, using just a simple plain-old arithmetical average of the two consequential points.
You can use spline interpolation to create a smooth trajectory.
If not in the "mood" to implement it yourself, a quick google search will give you open source libraries like SINTEF's SISL that have such functionallity.
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I am trying to present a point cloud and its projection with OpenGL on the plane normal to the line connecting the two most distant points. I have succeed in presenting the point cloud on the scene with an orthonormal system. I have found the two farthest point in the cloud. And I found the plan on which I projected.
I tried to make this projection but envin.
I tried with the transformation matrices as GL_PROJECTION but envin.
Can someone give me hand?
You can calculate the coordinates of the projected points by mathematical formulas, then draw them with OpenGL.
Take a look at this link
You can drop a perpendicular from each point to your found plane, and compute its foot point on the plane. Then draw another point there.
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I'm trying to detect the location of a fingertip from an image. I've been able to crop out a region in the image where it must have a fingertip, and extract the edges using Canny Edge Detector. However I'm stuck. Since my project description says I can't use the skin color for detection, I cannot find the exact contour of the finger, and will have to try to separate the fingertip with edges alone. Right now I'm thinking since the finger has a curved arch shape/letter U shape, maybe that could be used for detection. But since it has to be rotation/scale invariant, most algorithms I found so far are not up to it. Does anyone have an idea of how to do this? Thanks for anyone that responds!
This is the result I have now. I want to put a bounding box around the index fingertip, or the highest fingertip, whichever is the easiest.
You may view the tip of U as a corner, and try corner detection method such as the Foerstner Algorithm that will position of a corner with sub-pixel accuracy, and Haris corner detector which has implementation included in the feature2D class in opencv.
There is a very clear and straighforward lecture on Haris corner detector that I would like to share with you.
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I'm working on a graphics project trying to create an impossible cube in 3D. An impossible cube looks like that:
The trick behind this is two of the edges which are 'cut' and a picture taken from a specific angle to give the illusion of the impossibility.
Well I'm trying to make this but instead of a static image, I want to be able to animate it (rotate around) maintaining the impossible properties.
I have managed to make a cube in blender as you can see in the screenshot below:
I would like to hear your suggestions as to how I can achieve the desired effect. An idea would be to make transparent the portion of the edge that has an edge(or more) behind it, so that every time the camera angle changes, the transparent patch moves along.
It doesn't have to be done in Blender exclusively so any solutions in OpenGL etc are welcome.
To give you an idea of what the end result should be, this is a link to such an illustration:
3D Impossible Cube Illusion Animation
It's impossible (heh). Try to imagine rotating the cube so that the impossibly-in-front bit moves to the left. As soon as it would "cross" the current leftmost edge, the two properties of "it's in front" and "it's in the back" will not be possible to fulfill simultaneously.
If you have edge culling enabled, but clipping (depth-testing) disabled, and draw primitives in the right order, you should get the Escher cube without any need for cuts. This should be relatively easy to animate.