Sorry for e-mailing a large attachment to the whole list. I didn't mean to, I'm in the middle of packing for a trip and doing too much multitasking.
Larry On 11/20/08 5:41 PM, "Larry Meyn" <[EMAIL PROTECTED]> wrote: > I would recommend using numpy, which includes an SVD function that is very > useful for these equations. As the attached paper shows the SVD can be used > for both calibration and determination of the 3D coordinates. At Georgia > Tech, they use four cameras and use SVD to get the least-squares best fit > for the 3D coordinates from up to 4 images. > > Larry Meyn > NASA Ames Research Center > MS 210-15 > Moffett Field CA 94035 > > > > > On 11/20/08 4:38 PM, "Marcos Duarte" <[EMAIL PROTECTED]> wrote: > >> On Thu, Nov 20, 2008 at 2:27 AM, Nitro <[EMAIL PROTECTED]> wrote: >> >>> Can you tell me a bit more about your spatial transformation? Is it >>> something like a mercator projection? Or more involved? If it's a linear >>> one, then fc2 can transform also the image for you. >>> FC2 also offers you to plugin custom transforms instead of the matrix ones >>> as well, but these will most likely only work on the lowest level of the >>> transform chain right now. >>> >> >> I want to find the real coordinates (2D or 3D) of an object (point) >> shown in a single image (2D coordinate) or two or more images from >> different angles of view of the object (3D coordinate). >> This problem is known in computer vision (where they care about the >> image itself, I don't) as camera calibration, which is the process of >> finding the true parameters of the camera that produced a given >> photograph or video >> (http://en.wikipedia.org/wiki/Camera_resectioning). Once we have these >> parameters of the camera we can use them to find the real coordinates >> of an object in an image. >> For the case of a pinhole camera, the relationship between the >> coordinates of a 3D point and its projection onto the image plane can >> be described as a linear transformation. The most employed method to >> find this linear transformation is a method known as direct linear >> transformation (DLT), see >> http://en.wikipedia.org/wiki/Direct_linear_transformation or >> http://www.kwon3d.com/theory/dlt/dlt.html. >> For a 2D case, the DLT produces a set of four linear equations (with 7 >> or 8 independent parameters, I don't remember) that can be used to >> calibrate the camera and find the real coordinates of an object. For >> the 3D case, 11 parameters are produced by the DLT method. >> The DLT method consists of two steps: First, it is used a set of >> control points (at least 4 for 2D and at least 6 for 3D) whose object >> coordinates are already known and the camera parameters are found. >> Second, in a later stage, these parameters are used to find the >> unknown coordinates of other objects. >> >> Doing this math in python is easy (there are many implementations for >> that and I have the dlt in matlab, so it's just a matter of >> translation and a good way for me to learn python). There are also >> open source softwares, like OpenCV which also runs in python, that >> perform camera calibration. >> With respect to FC, for a 2D case this means that the user will have >> to click in at least four points on an image he/she knows the real >> coordinates; these real coordinates have to be informed by the user to >> FC; FC calculates the parameters of this transformation (between the >> object and the image), and this transformation is used to calculate >> the real coordinates of any point when the user clicks on the image. >> Right now FC does not do that, but I am sure I can do that using FC... >> >> Marcos Duarte >> http://lob.iv.fapesp.br/ >> University of Sao Paulo, Brazil >> _______________________________________________ >> FloatCanvas mailing list >> [email protected] >> http://mail.mithis.com/cgi-bin/mailman/listinfo/floatcanvas > > _______________________________________________ > FloatCanvas mailing list > [email protected] > http://mail.mithis.com/cgi-bin/mailman/listinfo/floatcanvas _______________________________________________ FloatCanvas mailing list [email protected] http://mail.mithis.com/cgi-bin/mailman/listinfo/floatcanvas
