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Introduction to Stereo Imaging -- Theory

Let us consider a simplified approach to the mathematics of the problem in order to aid understanding of the tasks involved.

We will consider a set up using two cameras in stereo. -- other methods that involve stereo are similar.

Let's consider a simplified optical set up:

 

Fig. 5 A simplified stereo imaging system

Fig. 5 shows:

Consider a point (x,y,z), in three-dimensional world coordinates, on an object.

Let this point have image coordinates tex2html_wrap_inline3026 and tex2html_wrap_inline3028 in the left and right image planes of the respective cameras.

Let f be the focal length of both cameras, the perpendicular distance between the lens centre and the image plane. Then by similar triangles:
eqnarray84

Solving for (x,y,z) gives:
eqnarray100

The quantity tex2html_wrap_inline3034 which appears in each of the above equations is called the disparity.

There are several practical problems with this set up:

However as the camera separation becomes large difficulties arise in correlating the two camera images.

In order to measure the depth of a point it must be visible to both cameras and we must also be able to identify this point in both images.

As the camera separation increases so do the differences in the scene as recorded by each camera.

Thus it becomes increasingly difficult to match corresponding points in the images.

This problem is known as the stereo correspondence problem.


next up previous
Next: Methods of Acquisition Up: 3D imaging Previous: Why use 3D data?

tex2html_wrap_inline2984 David Marshall 1994-1997