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What is the value of the points from the findFundamentalMat() function?

asked 2014-04-14 03:47:24 -0600

hassan-bdw gravatar image

hello i'm using stereo vision in my final year project and one of the steps is to determine the real world coordinates in a certain volume so does this function at least give the x,y coordinates or really what does it output and in what is the reference

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answered 2014-04-14 03:57:57 -0600

The functions in this section use a so-called pinhole camera model. In this model, a scene view is formed by projecting 3D points into the image plane using a perspective transformation.

s \; m' = A [R|t] M'

or

s \vecthree{u}{v}{1} = \vecthreethree{fx}{0}{cx}{0}{fy}{cy}{0}{0}{1} \begin{bmatrix} r{11} & r{12} & r{13} & t1 \ r{21} & r{22} & r{23} & t2 \ r{31} & r{32} & r{33} & t3 \end{bmatrix} \begin{bmatrix} X \ Y \ Z \ 1 \end{bmatrix}

where:

    (X, Y, Z) are the coordinates of a 3D point in the world coordinate space
    (u, v) are the coordinates of the projection point in pixels
    A is a camera matrix, or a matrix of intrinsic parameters
    (cx, cy) is a principal point that is usually at the image center
    fx, fy are the focal lengths expressed in pixel units.

Thus, if an image from the camera is scaled by a factor, all of these parameters should be scaled (multiplied/divided, respectively) by the same factor. The matrix of intrinsic parameters does not depend on the scene viewed. So, once estimated, it can be re-used as long as the focal length is fixed (in case of zoom lens). The joint rotation-translation matrix [R|t] is called a matrix of extrinsic parameters. It is used to describe the camera motion around a static scene, or vice versa, rigid motion of an object in front of a still camera. That is, [R|t] translates coordinates of a point (X, Y, Z) to a coordinate system, fixed with respect to the camera. The transformation above is equivalent to the following (when z \ne 0 ):

\begin{array}{l} \vecthree{x}{y}{z} = R \vecthree{X}{Y}{Z} + t \ x' = x/z \ y' = y/z \ u = fx*x' + cx \ v = fy*y' + cy \end{array}

Real lenses usually have some distortion, mostly radial distortion and slight tangential distortion. So, the above model is extended as:

\begin{array}{l} \vecthree{x}{y}{z} = R \vecthree{X}{Y}{Z} + t \ x' = x/z \ y' = y/z \ x'' = x' \frac{1 + k1 r^2 + k2 r^4 + k3 r^6}{1 + k4 r^2 + k5 r^4 + k6 r^6} + 2 p1 x' y' + p2(r^2 + 2 x'^2) \ y'' = y' \frac{1 + k1 r^2 + k2 r^4 + k3 r^6}{1 + k4 r^2 + k5 r^4 + k6 r^6} + p1 (r^2 + 2 y'^2) + 2 p2 x' y' \ \text{where} \quad r^2 = x'^2 + y'^2 \ u = fx*x'' + cx \ v = fy*y'' + cy \end{array}

k1, k2, k3, k4, k5, and k6 are radial distortion coefficients. p1 and p2 are tangential distortion coefficients. Higher-order coefficients are not considered in OpenCV. Dog Insulin ELISA Kitlink ... (more)

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Thank you a lot it was a very clear explanation..

hassan-bdw gravatar imagehassan-bdw ( 2014-04-15 00:56:36 -0600 )edit

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Asked: 2014-04-14 03:47:24 -0600

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Last updated: Apr 14 '14