Local smoothing with robustness against outlying predictors

Reverse engineering of mechanical systems often begins with large datasets produced from laser scanning of physical artifacts. Commonly it is necessary to remove noise and filter them; however, selecting noisy regions and preserving sharp edges on desired features is difficult using standard GUI interfaces. We demonstrate a haptic interface for marking and preserving features in noisy data and for performing local smoothing operations. The force-feedback provides a natural interface for these operations.

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Pinned distance problem, slicing measures, and local smoothing estimates

Transactions of the American Mathematical Society ◽

10.1090/tran/7693 ◽

2018 ◽

Vol 371 (6) ◽

pp. 4459-4474 ◽

Cited By ~ 3

Author(s):

Alex Iosevich ◽

Bochen Liu

Keyword(s):

Local Smoothing ◽

Distance Problem

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Theoretical Analysis on the Measurement Errors of Local 2D DIC: Part II Assessment of Strain Errors of the Local Smoothing Method-Approaching an Answer to the Overlap Question

Strain ◽

10.1111/str.12174 ◽

2016 ◽

Vol 52 (2) ◽

pp. 129-147 ◽

Cited By ~ 13

Author(s):

Y. Wang ◽

P. Lava ◽

P. Reu ◽

D. Debruyne

Keyword(s):

Theoretical Analysis ◽

Measurement Errors ◽

Smoothing Method ◽

Local Smoothing

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Wave Front Sets, Local Smoothing and Bourgain's Circular Maximal Theorem

Annals of Mathematics ◽

10.2307/2946549 ◽

1992 ◽

Vol 136 (1) ◽

pp. 207 ◽

Cited By ~ 35

Author(s):

Gerd Mockenhaupt ◽

Andreas Seeger ◽

Christopher D. Sogge

Keyword(s):

Wave Front ◽

Local Smoothing ◽

Maximal Theorem ◽

Wave Front Sets

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FULLY DISCRETE SCHEMES FOR THE SCHRÖDINGER EQUATION: DISPERSIVE PROPERTIES

Mathematical Models and Methods in Applied Sciences ◽

10.1142/s0218202507002029 ◽

2007 ◽

Vol 17 (04) ◽

pp. 567-591 ◽

Cited By ~ 6

Author(s):

LIVIU I. IGNAT

Keyword(s):

Schrödinger Equation ◽

Schrodinger Equation ◽

Numerical Solutions ◽

Continuous Model ◽

Local Smoothing ◽

Euler Approximation ◽

One Dimensional ◽

Fully Discrete ◽

Backward Euler ◽

The One

We consider fully discrete schemes for the one-dimensional linear Schrödinger equation and analyze whether the classical dispersive properties of the continuous model are presented in these approximations. In particular, Strichartz estimates and the local smoothing of the numerical solutions are analyzed. Using a backward Euler approximation of the linear semigroup we introduce a convergent scheme for the nonlinear Schrödinger equation with nonlinearities which cannot be treated by energy methods.

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