Curve evolution and 3D reconstruction

In this paper, we apply the geometric curve evolution approach to 3D reconstruction for a number of images (greater than or equal to 2) in the stereo vision. The curve evolution approach is based on the Euclidean curve shortening evolution theory, and the level set method is introduced into it for numerical computation. The Euler-Lagrange equations that are deduced from the variational principle provide a set of curve evolving equations. These PDE's describe the process of the geometric curve evolution on the relevant epipolar plane. In 3D space, the each epipolar plane is monogamously projected as a unique pair of the intra-scanlines on stereo pairs. These PDE's are used to deform an initial set of curves that then move towards the object outlines to be detected. The level set implementation of these PDE's provides an efficient and robust computational way for the kind of the geometric-driven evolving equations. The velocity term in the level set equations can be obtained from the above geometric curve evolving equations. It is intrinsic and only depends upon the stereo problem. We present the close form of the velocity. Finally, the results of implementation of our theory are presented on synthetic images.