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We consolidate an unorganized point cloud with noise, outliers, non-uniformities, and in particular interference between close-by surface sheets as a preprocess to surface generation, focusing on reliable normal estimation. Our algorithm includes two new developments. First, a weighted locally optimal projection operator produces a set of denoised, outlier-free and evenly distributed particles over the original dense point cloud, so as to improve the reliability of local PCA for initial estimate of normals. Next, an iterative framework for robust normal estimation is introduced, where a priority-driven normal propagation scheme based on a new priority measure and an orientation-aware PCA work complementarily and iteratively to consolidate particle normals. The priority setting is reinforced with front stopping at thin surface features and normal flipping to enable robust handling of the close-by surface sheet problem. We demonstrate how a point cloud that is wellconsolidated by our method steers conventional surface generation schemes towards a proper interpretation of the input data.
Points acquired by laser scanners are not intrinsically equipped with normals, which are essential to surface reconstruction and point set rendering using surfels. Normal estimation is notoriously sensitive to noise. Near sharp features, the computation of noise-free normals becomes even more challenging due to the inherent undersampling problem at edge singularities. As a result, common edge-aware consolidation techniques such as bilateral smoothing may still produce erroneous normals near the edges. We propose a resampling approach to process a noisy and possibly outlier-ridden point set in an edge-aware manner. Our key idea is to first resample away from the edges so that reliable normals can be computed at the samples, and then based on reliable data, we progressively resample the point set while approaching the edge singularities. We demonstrate that our Edge-Aware Resampling (EAR) algorithm is capable of producing consolidated point This work is supported in part by grants from NSFC (61103166),
This paper considers optimization techniques for the solution of
nonlinear inverse problems where the forward problems, like
those encountered in electromagnetics, are modelled by
differential equations. Such problems are often solved by
utilizing a Gauss-Newton method in which the forward model
constraints are implicitly incorporated. Variants of Newton's
method which use second-derivative information are rarely
employed because their perceived disadvantage in computational
cost per step offsets their potential benefits of faster
convergence. In this paper we show that, by formulating the
inversion as a constrained or unconstrained optimization
problem, and by employing sparse matrix techniques, we can
carry out variants of sequential quadratic programming and the
full Newton iteration with only a modest additional cost. By
working with the differential equation explicitly we are able to
relate the constrained and the unconstrained formulations and
discuss the advantages of each. To make the comparisons meaningful
we adopt the same global optimization strategy for all
inversions. As an illustration, we focus upon a 1D
electromagnetic (EM) example simulating a magnetotelluric survey.
This problem is sufficiently rich that it illuminates most of
the computational complexities that are prevalent in
multi-source inverse problems and we therefore describe its
solution process in detail. The numerical results illustrate
that variants of Newton's method which utilize second-derivative
information can produce a solution in fewer iterations and, in
some cases where the data contain significant noise, requiring
fewer floating point operations than Gauss-Newton techniques.
Although further research is required, we believe that the
variants proposed here will have a significant impact on
developing practical solutions to large-scale 3D EM
inverse problems.
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