Robust Poisson Surface Reconstruction

Abstract. We propose a method to reconstruct surfaces from oriented point clouds with non-uniform sampling and noise by formulating the problem as a convex minimization that reconstructs the indicator func-tion of the surface’s interior. Compared to previous models, our recon-struction is robust to noise and outliers because it substitutes the least-squares fidelity term by a robust Huber penalty; this allows to recover sharp corners and avoids the shrinking bias of least squares. We choose an implicit parametrization to reconstruct surfaces of unknown topology and close large gaps in the point cloud. For an efficient representation, we approximate the implicit function by a hierarchy of locally supported basis elements adapted to the geometry of the surface. Unlike ad-hoc bases over an octree, our hierarchical B-splines from isogeometric analysis locally adapt the mesh and degree of the splines during reconstruction. The hi-erarchical structure of the basis speeds-up the minimization and efficiently represents clustered data. We also advocate for convex optimization, in-stead isogeometric finite-element techniques, to efficiently solve the min-imization and allow for non-differentiable functionals. Experiments show state-of-the-art performance within a more flexible framework.

Fast Algorithms for Surface Reconstruction from Point Cloud

We consider constructing a surface from a given set of point cloud data. We explore two fast algorithms to minimize the weighted minimum surface energy in [Zhao, Osher, Merriman and Kang, Comp.Vision and Image Under., 80(3):295-319, 2000]. An approach using Semi-Implicit Method (SIM) improves the computational efficiency through relaxation on the time-step constraint. An approach based on Augmented Lagrangian Method (ALM) reduces the run-time via an Alternating Direction Method of Multipliers-type algorithm, where each sub-problem is solved efficiently. We analyze the effects of the parameters on the level-set evolution and explore the connection between these two approaches. We present numerical examples to validate our algorithms in terms of their accuracy and efficiency

Application des surfaces de Bézier pour la reconstruction 3-D

Dans ce travail, nous présentons une méthode de reconstruction 3-D basée sur l’utilisation des surfaces de Bézier, combinée au lissage tridimensionnel. L’idée principale est de générer, à partir d’un nuage de points issus de la numérisation d’un objet 3-D, une représentation de surfaces à partir de la quelle nous procédons à la reconstruction 3-D de l’objet en question. Ensuite nous présentons les résultats de notre méthode appliquées à quelques objets

Bilaplacian reconstruction of point clouds

A key process of the geometry processing pipeline is the reconstruction of surfaces from point clouds. The traditional problem addressed by surface reconstruction is to recover the digital representation of the shape that has been inputted, where the data could potentially contain a wide variety of drawbacks. The goal of this thesis would be to test the Bilaplacian Smoothness in order to enforce the smooth prior to the surface reconstruction. By considering our thesis goal we will build an application that not only will solve different sparse linear systems of equations using different possible methods for position, normal, and smoothness equation's constraints but also will make use of more complex and effective surface reconstruction solving techniques such as the multigrid or quadree reconstruction