Affine reconstruction of curved surfaces from uncalibrated views of apparent contours

In this paper, we show that even if the camera is uncalibrated, and its translational motion is unknown, curved surfaces can be reconstructed from their apparent contours up to a 3D affine ambiguity. Furthermore, we show that even if the reconstruction is nonmetric (non-Euclidean), we can still extract useful information for many computer vision applications just from the apparent contours. We first show that if the camera undergoes pure translation (unknown direction and magnitude), the epipolar geometry can be recovered from the apparent contours without using any search or optimisation process. The extracted epipolar geometry is next used for reconstructing curved surfaces from the deformations of the apparent contours viewed from uncalibrated cameras. The result is applied to distinguishing 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. The proposed method is implemented and tested on real images of curved surfaces.