Robust and Efficient Surface Reconstruction From Range Data

Abstract

We describe a robust but simple algorithm to reconstruct a surface from a set of merged range scans. Our key contribution is the formulation of the surface reconstruction problem as an energy minimisation problem that explicitly models the scanning process. The adaptivity of the Delaunay triangulation is exploited by restricting the energy to inside/outside labelings of Delaunay tetrahedra. Our energy measures both the output surface quality and how well the surface agrees with soft visibility constraints. Such energy is shown to perfectly fit into the minimum s-t cuts optimisation framework, allowing fast computation of a globally optimal tetrahedra labeling, while avoiding the "shrinking bias" that usually plagues graph cuts methods. The behaviour of our method confronted to noise, undersampling and outliers is evaluated on several data sets and compared with other methods through different experiments: its strong robustness would make our method practical not only for reconstruction from range data but also from typically more difficult dense point clouds, resulting for instance from stereo image matching. Our effective modeling of the surface acquisition inverse problem, along with the unique combination of Delaunay triangulation and minimum s-t cuts, makes the computational requirements of the algorithm scale well with respect to the size of the input point cloud.

Robust Poisson Surface Reconstruction

“…Parametric techniques represent the surface as a topological embedding of a 2D parameter domain into 3D space. Among them, approaches based on computational geometry partition the space into Voronoi cells from the input samples and exploit the intuitive idea that eliminating facets of Delaunay tetrahedra provides a triangulated parametrization of the surface [21,22,23,24,25,26,27]. The reconstructed surface thus interpolates most of the input samples and requires post-processing to smooth the surface and correct the topology.…”

Minimizing edge length to connect sparsely sampled unstructured point sets

“…In [27] the problem is formulated as a graph cut by weighting approximate visibility and minimizing the longestto-shortest ratio of edges in triangles, but they require carefully optimized parameters to be specified for every point set. In [28] a global algorithm which minimizes a criterion for the surface and analyzes different heuristics is proposed.…”

Hallucination-Free Multi-View Stereo

“…Recent work of Vu [1], which produces the initial mesh as in [10] and later refines it by using a variational method, demonstrates that this approach can be used to produce excellent results for closed objects and scenes sufficiently represented by images from all directions. surface wireframe before removing hallucinations, (c) 3D surface after removing hallucinations using approach proposed in [7], (d) 3D surface after removing hallucinations using our method.…”

“…In this work, we focus on removing hallucinated surfaces which are often generated by the approach [10] when reconstructing complicated scenes with multiple objects and free open space. This happens, for instance, when reconstructing outdoor scenes where a hallucinated surface is generated in place of the sky to obtain a closed surface, Figures 1(a,b) and 2(a,b).…”

“…We build on the global approach to 3D reconstruction based on the minimal s-t cut of the graph derived from the Delaunay tetrahedralization of a dense 3D point cloud [4,10]. It solves the visibility task by accumulating energy in free space between the surface and cameras, which is later used to solve the s-t cut.…”