Section: New Results
Reconstruction
NoiseAdaptive Shape Reconstruction from Raw Point Sets
Participants : Simon Giraudot, Pierre Alliez.
In collaboration with David CohenSteiner (GEOMETRICA projectteam)
We devised a noiseadaptive shape reconstruction method specialized to smooth, closed shapes [7] . Our algorithm takes as input a defectladen point set with variable noise and outliers, and comprises three main steps. First, we compute a novel noiseadaptive distance function to the inferred shape, which relies on the assumption that the inferred shape is a smooth submanifold of known dimension. Second, we estimate the sign and confidence of the function at a set of seed points, through minimizing a quadratic energy expressed on the edges of a uniform random graph. Third, we compute a signed implicit function through a random walker approach with soft constraints chosen as the most confident seed points computed in the previous step.
Surface Reconstruction through Point Set Structuring
Participants : Florent Lafarge, Pierre Alliez.
We present a method for reconstructing surfaces from point sets [8] . The main novelty lies in a structurepreserving approach where the input point set is first consolidated by structuring and resampling the planar components, before reconstructing the surface from both the consolidated components and the unstructured points. Structuring facilitates the surface reconstruction as the point set is substantially reduced and the points are enriched with structural meaning related to adjacency between primitives. Our approach departs from the common dichotomy between smooth/piecewisesmooth and primitivebased representations by gracefully combining canonical parts from detected primitives and freeform parts of the inferred shape (Figure 6 ).
Hybrid Multiview Stereo for Modeling Urban Scenes
Participant : Florent Lafarge.
In collaboration with Renaud Keriven (Acute3D), Mathieu Bredif (IGN), and Hiep Vu (Ecole des Ponts ParisTech).
We present an original multiview stereo reconstruction algorithm which allows the 3Dmodeling of urban scenes as a combination of meshes and geometric primitives [9] . The method provides a compact model while preserving details: irregular elements are described by meshes whereas regular structures are described by canonical geometric primitives. We adopt a twostep strategy consisting first in segmenting the initial meshbased surface using a multilabel Markov Random Field based model and second, in sampling primitive and mesh components simultaneously on the obtained partition by a JumpDiffusion process. The quality of a reconstruction is measured by a multiobject energy model which takes into account both photoconsistency and semantic considerations (i.e. geometry and shape layout). The segmentation and sampling steps are embedded into an iterative refinement procedure which provides an increasingly accurate hybrid representation (Figure 7 ).

Indoor Scene Reconstruction using Primitivedriven Space Partitioning and Graphcut
Participants : Sven Oesau, Florent Lafarge, Pierre Alliez.
In collaboration with EADS ASTRIUM
We present a method for automatic reconstruction of permanent structures of indoor scenes, such as walls, floors and ceilings, from raw point clouds acquired by laser scanners [15] . Our approach employs graphcut to solve an inside/outside labeling of a space decomposition. To allow for an accurate reconstruction the space decomposition is aligned with permanent structures. A Hough Transform is applied for extracting the wall directions while allowing a flexible reconstruction of scenes. The graphcut formulation takes into account data consistency through an inside/outside prediction for the cells of the space decomposition by stochastic ray casting, while favoring low geometric complexity of the model. Our experiments produces watertight reconstructed models of multilevel buildings and complex scenes (Figure 8 ).
Watertight Scenes from Urban LiDAR and Planar Surfaces
Participant : Thijs Van Lankveld.
In collaboration with Marc Van Kreveld and Remco Veltkamp
The demand for large geometric models is increasing, especially of urban environments. This has resulted in production of massive point cloud data from images or LiDAR. Visualization and further processing generally require a detailed, yet concise representation of the scene's surfaces. Related work generally either approximates the data with the risk of oversmoothing, or interpolates the data with excessive detail. Many surfaces in urban scenes can be modeled more concisely by planar approximations. We present a method that combines these polygons into a watertight model [10] . The polygonbased shape is closed with freeform meshes based on visibility information. To achieve this, we divide 3space into inside and outside volumes by combining a constrained Delaunay tetrahedralization with a graphcut. We compare our method with related work on several large urban LiDAR data sets. We construct similar shapes with a third fewer triangles to model the scenes. Additionally, our results are more visually pleasing and closer to a human modeler's description of urban scenes using simple boxes (Figure 10 ).
FeaturePreserving Surface Reconstruction and Simplification from DefectLaden Point Sets
Participant : Pierre Alliez.
In collaboration with David CohenSteiner, Julie Digne, Mathieu Desbrun and Fernando de Goes
We introduce a robust and featurecapturing surface reconstruction and simplification method that turns an input point set into a low trianglecount simplicial complex [5] . Our approach starts with a (possibly nonmanifold) simplicial complex filtered from a 3D Delaunay triangulation of the input points. This initial approximation is iteratively simplified based on an error metric that measures, through optimal transport, the distance between the input points and the current simplicial complex, both seen as mass distributions. Our approach exhibits both robustness to noise and outliers, as well as preservation of sharp features and boundaries (Figure 10 ). Our new featuresensitive metric between point sets and triangle meshes can also be used as a postprocessing tool that, from the smooth output of a reconstruction method, recovers sharp features and boundaries present in the initial point set.
Splatbased Surface Reconstruction from DefectLaden Point Sets.
Participant : Pierre Alliez.
In collaboration with Mariette Yvinec (EPI GEOMETRICA), Ricard Campos (University of Girona), Raphael Garcia (University of Girona)
We introduce a method for surface reconstruction from point sets that is able to cope with noise and outliers. First, a splatbased representation is computed from the point set. A robust local 3D RANSACbased procedure is used to filter the point set for outliers, then a local jet surface – a lowdegree surface approximation – is fitted to the inliers. Second, we extract the reconstructed surface in the form of a surface triangle mesh through Delaunay refinement (Figure 11 ). The Delaunay refinement meshing approach requires computing intersections between line segment queries and the surface to be meshed. In the present case, intersection queries are solved from the set of splats through a 1D RANSAC procedure. [3] .