Initial structure and motion

The first step consists of selecting two views that are suited for initializing the sequential structure and motion computation. On the one hand it is important that sufficient features are matched between these views, on the other hand the views should not be too close to each other so that the initial structure is well-conditioned. The first of these criterions is easy to verify, the second one is harder in the uncalibrated case. The image-based distance that we propose is the median distance between points transferred through an average planar-homography and the corresponding points in the target image:

$$\mbox{median}\{ D({\bf H} {\tt m}_i,{\tt m}'_i) \}$$ (E1)

This planar-homography H is determined as follows from the matches between the two views:

$${\bf H}=[{\tt e}]_\times{\bf F}+{\tt e}{\tt a}_{min}^\top \m... ...e}]_\times{\bf F}+{\tt e}{\tt a}^\top) {\tt m}_i,{\tt m}'_i)^2$$ (E2)

In practice the selection of the initial frame can be done by maximizing the product of the number of matches and the image-based distance defined above. When features are matched between sparse views, the evaluation can be restricted to consecutive frames. However, when features are tracked over a video sequence, it is important to consider views that are further apart in the sequence.