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From: Rise on 10 May 2010 16:25
Hi,

I am a beginner at Matlab and a beginner in image processing.

I am working with 2D images with a still object in a static scene.
I've calibrated the camera so I have information on the parameters of
the scene.

I want to compute a set of corresponding 3D vectors that lie on a
plane containing each 2D vector in the image and the camera optical
center. The corresponding vectors could be 30 degrees apart from each
other on the plane.

I've drawn it out on paper, but am not sure if I am approaching this
correctly when I begin to think about it using Matlab. I've been
looking through the threads in this forum and elsewhere online
(spatial transformations, backprojecting, forward projecting), but I
am getting more and more confused on what steps I need to take, and in
trying to visualize things using matrices and vectors in matlab.

P1 = <x_1,y_1> % camera optical center
P2 = <x_2,y_2> % a 2D vector in image plane
p = <x,y> % line containing camera optical center
and 2D vector
p_1 = <x_0, y_0> % a point on the line

% equation of a line
p = p_1 + t* P1P2; % <x,y> =
<x_0,y_0> + t* <x_2 - x_1, y_2 - y_1>
x = x_0 + t(x_2-x_1); y = y_0 + t(y_2 - y_1); % parametric
equations of the line


% equation of a plane
0 = n*P1P2; % find the vector orthogonal to the plane

Please assist. Thanks.

From: Rise on 13 May 2010 11:04
Ok, from the silence...I thought that i post what I've been reading
more about just in case any new-to-matlab-new-to-image-processing-
folks-not-enrolled-in-any-courses would like to know...

Read more about the inverse perspective transformation to understand
how to find a 3D vector in world space from a 2D vector of an image
plane.

Online sources:
http://blogs.mathworks.com/steve/category/spatial-transforms/

It's still rather confusing, but I'm trying...

onward.
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