Non-manifold curve reconstruction based on l₁ minimization

Curve reconstruction from unorganized points is widely used in various fields such as computer vision, reverse engineering and medical image processing, among which non-manifold curve reconstruction is a difficult problem. In this paper, an l₁ norm minimization method is proposed for non-manifold curve reconstruction based on compressive sensing theory. First, we give the sparse representation of the points' normals and locations, and restore them via l₁ norm optimization. Then, the restored normals and positions are used to calculate the bilateral weights and build a minimum spanning tree on them. Finally, post-processing is performed to manage the open and close states of the curves. Experiments show that the algorithm is robust to noise and can handle complex family of curves which contains open/closed curves, manifold/non-manifold curves and curves with sharp features.