Shape reconstruction from unorganized points with a data-driven level set method

We propose a new method for shape reconstruction from noisy and unorganized point data. We represent a shape through its signed distance function and formulate shape reconstruction as a constrained energy minimization problem directly based on the observed point set. The associated energy function includes both the likelihood of the observed data points and a smoothness prior on the reconstructed shape. To solve this optimization problem, an efficient data-driven level set method is developed. Our method is robust to local minima, clutter, and noise. It is also applicable to situations where the data are sparse. The topological nature of the underlying shape is handled automatically through the level set formalism.