projective pose estimation

For every additional view the pose towards the pre-existing reconstruction is determined, then the reconstruction is updated. This is illustrated in Figure 5.1.

Figure 5.1: Image matches ( ${\tt m}_{k-1},{\tt m}_k$) are found as described before. Since the image points, ${\tt m}_{k-1}$, relate to object points, ${\tt M}_k$, the pose for view $k$ can be computed from the inferred matches ( ${\tt M}, {\tt m}_k$).

The first step consists of finding the epipolar geometry as described in Section 4.3. Then the matches which correspond to already reconstructed points are used to compute the projection matrix ${\bf P}_k$. This is done using a robust procedure similar to the one laid out in Table 4.3. In this case a minimal sample of 6 matches is needed to compute ${\bf P}_k$. Once ${\bf P}_k$ has been determined the projection of already reconstructed points can be predicted. This allows to find some additional matches to refine the estimation of ${\bf P}_k$. This means that the search space is gradually reduced from the full image to the epipolar line to the predicted projection of the point. This is illustrated in Figure 5.2.

Figure 5.2: (a) a priori search range, (b) search range along the epipolar line and (c) search range around the predicted position of the point.