2,156 research outputs found
Fast and Robust Normal Estimation for Point Clouds with Sharp Features
Proceedings of the 10th Symposium of on Geometry Processing (SGP 2012), Tallinn, Estonia, July 2012.International audienceThis paper presents a new method for estimating normals on unorganized point clouds that preserves sharp fea- tures. It is based on a robust version of the Randomized Hough Transform (RHT). We consider the filled Hough transform accumulator as an image of the discrete probability distribution of possible normals. The normals we estimate corresponds to the maximum of this distribution. We use a fixed-size accumulator for speed, statistical exploration bounds for robustness, and randomized accumulators to prevent discretization effects. We also propose various sampling strategies to deal with anisotropy, as produced by laser scans due to differences of incidence. Our experiments show that our approach offers an ideal compromise between precision, speed, and robustness: it is at least as precise and noise-resistant as state-of-the-art methods that preserve sharp features, while being almost an order of magnitude faster. Besides, it can handle anisotropy with minor speed and precision losses
Robust Estimation of Surface Curvature Information from Point Cloud Data
This paper surveys and evaluates some popular state of the art methods for
algorithmic curvature and normal estimation. In addition to surveying existing
methods we also propose a new method for robust curvature estimation and
evaluate it against existing methods thus demonstrating its superiority to
existing methods in the case of significant data noise. Throughout this paper
we are concerned with computation in low dimensional spaces (N < 10) and
primarily focus on the computation of the Weingarten map and quantities that
may be derived from this; however, the algorithms discussed are theoretically
applicable in any dimension. One thing that is common to all these methods is
their basis in an estimated graph structure. For any of these methods to work
the local geometry of the manifold must be exploited; however, in the case of
point cloud data it is often difficult to discover a robust manifold structure
underlying the data, even in simple cases, which can greatly influence the
results of these algorithms. We hope that in pushing these algorithms to their
limits we are able to discover, and perhaps resolve, many major pitfalls that
may affect potential users and future researchers hoping to improve these
methodsComment: 16 pages, 13 figure
Static/Dynamic Filtering for Mesh Geometry
The joint bilateral filter, which enables feature-preserving signal smoothing
according to the structural information from a guidance, has been applied for
various tasks in geometry processing. Existing methods either rely on a static
guidance that may be inconsistent with the input and lead to unsatisfactory
results, or a dynamic guidance that is automatically updated but sensitive to
noises and outliers. Inspired by recent advances in image filtering, we propose
a new geometry filtering technique called static/dynamic filter, which utilizes
both static and dynamic guidances to achieve state-of-the-art results. The
proposed filter is based on a nonlinear optimization that enforces smoothness
of the signal while preserving variations that correspond to features of
certain scales. We develop an efficient iterative solver for the problem, which
unifies existing filters that are based on static or dynamic guidances. The
filter can be applied to mesh face normals followed by vertex position update,
to achieve scale-aware and feature-preserving filtering of mesh geometry. It
also works well for other types of signals defined on mesh surfaces, such as
texture colors. Extensive experimental results demonstrate the effectiveness of
the proposed filter for various geometry processing applications such as mesh
denoising, geometry feature enhancement, and texture color filtering
A narrow-band unfitted finite element method for elliptic PDEs posed on surfaces
The paper studies a method for solving elliptic partial differential
equations posed on hypersurfaces in , . The method allows
a surface to be given implicitly as a zero level of a level set function. A
surface equation is extended to a narrow-band neighborhood of the surface. The
resulting extended equation is a non-degenerate PDE and it is solved on a bulk
mesh that is unaligned to the surface. An unfitted finite element method is
used to discretize extended equations. Error estimates are proved for finite
element solutions in the bulk domain and restricted to the surface. The
analysis admits finite elements of a higher order and gives sufficient
conditions for archiving the optimal convergence order in the energy norm.
Several numerical examples illustrate the properties of the method.Comment: arXiv admin note: text overlap with arXiv:1301.470
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