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- William K. Allard
- SIAM J. Imaging Sciences
- 2008

Let F(R2) = {f âˆˆ Lâˆž(R) âˆ© L1(R) : f â‰¥ 0}. Suppose s âˆˆ F(R2) and Î³ : R â†’ [0,âˆž). Suppose Î³ is zero at zero, positive away from zero and convex. For f âˆˆ F(Î©) let

Data sets are often modeled as point clouds in R, for D large. It is often assumed that the data has some interesting low-dimensional structure, for example that of a d-dimensional manifold M, with dâ€¦ (More)

- William K. Allard, Guangliang Chen, Mauro Maggioni
- ArXiv
- 2011

Let Î© be an open subset of R where 2 â‰¤ n â‰¤ 7; the reason for restriction on n is that our work will make use of the regularity theory for area minimizing hypersurfaces. Let s âˆˆ Lâˆž(Î©), let Î³ : [0,âˆž) â†’â€¦ (More)

- William K. Allard
- SIAM J. Imaging Sciences
- 2009

- William K. Allard
- SIAM J. Math. Analysis
- 2007

Let Î© be an open subset of R where 2 â‰¤ n â‰¤ 7; we assume n â‰¥ 2 because the case n = 1 has been treated elsewhere (see [Alli]) and is quite different from the case n > 1; we assume n â‰¤ 7 because weâ€¦ (More)

We develop a novel geometric multiresolution analysis for analyzing intrinsically low-dimensional point clouds in h ig dimensional spaces, modeled as samples from a d-dimensional setM (in particular,â€¦ (More)

1 Introduction

Suppose T is a triangulation T of R with edges E and vertices V, and suppose Î© is a bounded open subset of R. Let Vin = {v âˆˆ V : v âˆˆ Î©}. In this paper we will give an algorithm which uses Vin andâ€¦ (More)

- William K. Allard
- PPSC
- 1999

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