Stereo matching, reconstruction and refinement of 3D curves using deformable contours

The authors propose to replace a set of connected 3-D points or line segments with a 3-D formable curve, using weighted least-squares approximation. The parameters of the 3-D energy-minimizing curve are updated so that its 2-D projections on two or three stereoscopic images converge toward the corresponding image edges. Thus, a more realistic representation of the real non-polygonal world is obtained. The case where no initial 3-D information is provided is also considered. A novel approach is proposed to match a given 2-D curve in the first image to its corresponding position in the second image. The curve is tracked between the two images by a deformable curve constrained by a 2-D motion model. The position of the 2-D curve in the second image is then refined by relaxing the motion constraint. As a result, the correspondences between the curves of both images are known. An initial estimate of the 3-D curve can be recovered using the calibration parameters of the stereoscopic system. These approaches are illustrated by experimental results