Affine reconstruction of curved surfaces from uncalibrated views of apparent contours

In this paper, we consider uncalibrated reconstruction of curved surfaces f rom apparent contours. Since apparent contours are not fixed features (view point independent), we cannot directly apply the recent results of the unca librated reconstruction from fixed features. We show that, nonetheless, cur ved surfaces can be reconstructed up to an affine ambiguity from their appa rent contours viewed from uncalibrated cameras with unknown linear translat ions. Furthermore, we show that, even if the reconstruction is nonmetric (n on-Euclidean), we can still extract useful information for many computer vi sion applications just from the apparent contours. We first show that if th e camera motion is linear translation (but arbitrary direction and magnitud e), the epipolar geometry can be recovered from the apparent contours witho ut using any optimization process. The extracted epipolar geometry is next used for reconstructing curved surfaces from the deformations of the appare nt contours viewed from uncalibrated cameras. The result is applied to dist inguishing curved surfaces from fixed features in images. It is also shown that the time-to-contact to the curved surfaces can be computed from simple measurements of the apparent contours.