Dense Correspondence and Its Applications - Computer Vision for Visual Effects - page 172

(a) (b)

(c) (d)

Figure 5.12. An example of estimating the epipolar geometry using the normalized eight-point
algorithm. (a) and (b) Images of the same scene fromdifferent perspectives, with feature matches
overlaid. (c) and (d) The green lines are epipolar lines computed from the estimated fundamental
matrix. We can see that corresponding points lie on conjugate epipolar lines (for example, the
corners of the roof and the brown line down the right side of the building). Note that the epipoles
(where the epipolar lines in each image intersect) are not visible in this example.

Hartley and Zisserman [ 188 ] describe further extensions of the eight-point algo-
rithmand discuss how the estimate of the fundamental matrix can be improved (e.g.,
to a maximum likelihood estimate under the assumptions that the measurement
errors in each feature location are Gaussian). Nonlinear minimization is required to
solve the problem and RANSAC can be used to detect and remove outliers in the data
to obtain a robust estimate.
So far, we have avoided detailed discussion of the 3D configuration of the cameras,
focusing on purely 2D considerations of the relationship between correspondences.
When we discuss matchmoving in Chapter 6 , these 3D relationships will be made
more explicit. In particular, when each camera's location, orientation, and internal
configuration are known, the fundamental matrix can be computed directly (see
Section 6.4.1 ). Conversely, estimating the fundamental matrix is often involved in the
early process of matchmoving.

5.4.3 Image Rectification

As we can see from Figure 5.12 , epipolar lines are typically slanted, which can
make estimating correspondences along conjugate epipolar lines complicated due to
repeated image resampling operations. It's conventional to rectify the images before
estimating stereo correspondence — that is, to apply a projective transformation to
each image so that in the resulting image pair, conjugate epipolar lines coincide with
aligned image rows (or scanlines ). This means that the images are resampled only