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.

Robust Surface Reconstruction from Point Clouds

The problem of generating a surface triangulation from a set of points with normal information arises in several mesh processing tasks like surface reconstruction or surface resampling. In this paper we present a surface triangulation approach which is based on local 2d delaunay triangulations in tangent space. Our contribution is the extension of this method to surfaces with sharp corners and creases. We demonstrate the robustness of the method on difficult meshing problems that include nearby sheets, self intersecting non manifold surfaces and noisy point samples

PetroSurf3D - A Dataset for high-resolution 3D Surface Segmentation

The development of powerful 3D scanning hardware and reconstruction algorithms has strongly promoted the generation of 3D surface reconstructions in different domains. An area of special interest for such 3D reconstructions is the cultural heritage domain, where surface reconstructions are generated to digitally preserve historical artifacts. While reconstruction quality nowadays is sufficient in many cases, the robust analysis (e.g. segmentation, matching, and classification) of reconstructed 3D data is still an open topic. In this paper, we target the automatic and interactive segmentation of high-resolution 3D surface reconstructions from the archaeological domain. To foster research in this field, we introduce a fully annotated and publicly available large-scale 3D surface dataset including high-resolution meshes, depth maps and point clouds as a novel benchmark dataset to the community. We provide baseline results for our existing random forest-based approach and for the first time investigate segmentation with convolutional neural networks (CNNs) on the data. Results show that both approaches have complementary strengths and weaknesses and that the provided dataset represents a challenge for future research.Comment: CBMI Submission; Dataset and more information can be found at http://lrs.icg.tugraz.at/research/petroglyphsegmentation

North Atlantic marine ¹⁴C reservoir effects: implications for late-Holocene chronological studies

We investigated surface ocean–atmosphere 14C offsets for the later Holocene at eight locations in the eastern North Atlantic. This resulted in 11 new ΔR assessments for the west coast of Ireland, the Outer Hebrides, the north coast of the Scottish mainland, the Orkney Isles and the Shetland Isles over the period 1300–500 BP. Assessments were made using a robust Multiple Paired Sample (MPS) approach, which is designed to maximize the accuracy of ΔR determinations. Assessments are placed in context with other available data to enable reconstruction of a realistic picture of surface ocean 14C activity over the Holocene period within the North Atlantic region

Evolutionary approach for finding the atomic structure of steps on stable crystal surfaces

The problem addressed here can be concisely formulated as follows: Given a stable surface orientation with a known reconstruction and given a direction in the plane of this surface, find the atomic structure of the steps oriented along that direction. We report a robust and generally applicable variable-number genetic algorithm for determining the atomic configuration of crystallographic steps, and exemplify it by finding structures for several types of monatomic steps on Si(114)-2×1. We show that the location of the step edge with respect to the terrace reconstructions, the step width (number of atoms), and the positions of the atoms in the step region can all be simultaneously determined

Gauge field for edge state in graphene

By considering the continuous model for graphene, we analytically study a special gauge field for the edge state. The gauge field explains the properties of the edge state such as the existence only on the zigzag edge, the partial appearance in the $k$-space, and the energy position around the Fermi energy. It is demonstrated utilizing the gauge field that the edge state is robust for surface reconstruction, and the next nearest-neighbor interaction which breaks the particle-hole symmetry stabilizes the edge state.Comment: 9 pages, 5 figure