computer vision - Create OpenGL matrices from affine camera matrix -

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i have set of 2d 3d point correspondences, , estimate affine camera matrix these correspondences (basically, assuming orthographic projection)[1]. output of camera estimation 3x4 matrix third row [0, 0, 0, 1] (the "affine constraint").

now camera matrix, i'd render model using opengl. in essence, create modelview , (orthographic) projection matrix camera matrix have.

i've read hours of material on camera matrix dissection/decomposition, of perspective cameras, , "z" information missing in matrix, not apply these techniques.

i've tried numerous attempts, of failed @ stage. 1 thing tried taking dot product of first , second row of matrix (without last column of course) create new row transforms z, it's [0, 0, 1], of course makes sense. thing tried converting 2d points clip coordinate space (i.e. "reversing" window transform) before estimating camera matrix, can take window transform , flipping y (in screen space, origin on upper-left) out of picture.

i'm frankly @ loss on how fundamentally approach problem.

[1]: gold standard algorithm estimating affine camera matrix world image correspondences, algorithm 7.2 in multiple view geometry, hartley & zisserman, 2nd edition, 2003.

the affine camera (see e.g. here) performs ortho projection followed affine warp.

given 1 can use opengl orthographic camera rasterization device arbitrary image transformation, affine camera can emulated follows:

  1. create orthographic camera scene. render scene using it, read generated image.
  2. apply affine transform induced camera model on image, pushing said affine transform texture transformation matrix.
  3. render rectangle in front of ortho camera (a "card") covering field of view, , texture said rectangle image produced in step 1. warped using affine transform requested.

this sequence can optimized if performance issue. read on "render texture" how.


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