Reconstruction of curved surfaces

We first describe the procedure for reconstructing curved surfaces from their apparent contours viewed from an uncalibrated camera with unknown translations.

1. We first fit B-spline curves to images [ 2 ] and extract parameterised contour curves.
2. The frontier points and the epipoles are extracted from the bi-tangency on the consecutive contour curves.
3. The curved surface is computed from the changes in apparent contour, the frontier points and the epipoles.

We next show the results of some experiments. Fig.  3 (a) shows artificial image data of a sphere viewed from a camera with unknown translating motion. Fig.  3 (b) shows the result of reconstruction. Since the reconstruction has ambiguity up to a 3D affine, this figure represents the reconstructed surface with the exact camera parameters.

   
Figure 3: Results of the reconstruction of a curved surface. (a) shows the sequential images of artificial contour curves of a sphere viewed from a translating camera. (b) shows the reconstructed surface of a sphere as a coordinate grid. The longitudinal and latitudinal lines of the mesh correspond to contour generators and epipolar curves. The reference sphere is also shown in (b).