GetPerspectiveTransform mathematical explanation

asked 2012-12-09 03:07:20 -0600

lindstorm
24 ●3

Hi guys! I'm doing a course project devoted to perspective transformations. I have a ready opencv function GetPerspectiveTransform that takes my source array CvPoint2D32f srcQuad[4] and gets destination array CvPoint2D32f dstQuad[4] using a matrix of perspective transformation CvMat* warp_matrix = cvCreateMat(3,3,CV_32FC1); But is there a mathematical analogue of this function? I mean can I using some mathematical formulas replace ready function GetPerspectiveTransform? Thank you very much for any assistance.

answered 2012-12-09 05:24:52 -0600

AlexanderShishkov

3577 ●14 ●32 ●57

updated 2012-12-11 10:36:46 -0600

SR
1560 ●1 ●14 ●29

The function GetPerspectiveTransform calculates the matrix of perspective transformation between srcQuad points and dstQuad points. In other words it calculates coefficients of perspective transformation which maps (xi,yi) to (ui,vi), (i=1,2,3,4):

      c00*xi + c01*yi + c02
 ui = ---------------------
      c20*xi + c21*yi + c22

       c10*xi + c11*yi + c12
  vi = ---------------------
       c20*xi + c21*yi + c22

Coefficients are calculated by solving linear system:

  / x0 y0  1  0  0  0 -x0*u0 -y0*u0 \ /c00\    /u0\
  | x1 y1  1  0  0  0 -x1*u1 -y1*u1 | |c01|    |u1|
  | x2 y2  1  0  0  0 -x2*u2 -y2*u2 | |c02|    |u2|
  | x3 y3  1  0  0  0 -x3*u3 -y3*u3 |.|c10| =  |u3|
  |  0  0  0 x0 y0  1 -x0*v0 -y0*v0 | |c11|    |v0|
  |  0  0  0 x1 y1  1 -x1*v1 -y1*v1 | |c12|    |v1|
  |  0  0  0 x2 y2  1 -x2*v2 -y2*v2 | |c20|    |v2|
  \  0  0  0 x3 y3  1 -x3*v3 -y3*v3 / \c21/    \v3/

where: cij - matrix coefficients, c22 = 1

edit flag offensive delete link

Comments

Hey, do you know any paper where it is explained more specific?

Bomber19 ( 2012-12-12 06:31:57 -0600 )edit

Sorry, but I don't know such paper.

AlexanderShishkov ( 2012-12-12 09:15:54 -0600 )edit

add a comment

GetPerspectiveTransform mathematical explanation

1 answer

Comments

Links

Question Tools

Stats

Related questions

GetPerspectiveTransform mathematical explanation edit

1 answer

Comments

Links

Question Tools

Stats

Related questions

GetPerspectiveTransform mathematical explanation