Journal article
Nonasymptotic Densities for Shape Reconstruction
Abstract and applied analysis, Vol.2014, pp.1-14
2014
Handle:
https://hdl.handle.net/2376/117135
Abstract
In this work, we study the problem of reconstructing shapes from simple nonasymptotic densities measured only along shape boundaries. The particular density we study is also known as the integral area invariant and corresponds to the area of a disk centered on the boundary that is also inside the shape. It is easy to show uniqueness when these densities are known for all radii in a neighborhood ofr=0, but much less straightforward when we assume that we only know the area invariant and its derivatives for only oner>0. We present variations of uniqueness results for reconstruction (modulo translation and rotation) of polygons and (a dense set of) smooth curves under certain regularity conditions.
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Details
- Title
- Nonasymptotic Densities for Shape Reconstruction
- Creators
- Sharif Ibrahim - Department of Mathematics, Washington State University, Pullman, WA 99164-3113, USAKevin Sonnanburg - Department of Mathematics, University of Tennessee Knoxville, Knoxville, TN 37996-1320, USAThomas J Asaki - Department of Mathematics, Washington State University, Pullman, WA 99164-3113, USAKevin R Vixie - Department of Mathematics, Washington State University, Pullman, WA 99164-3113, USA
- Publication Details
- Abstract and applied analysis, Vol.2014, pp.1-14
- Academic Unit
- Mathematics and Statistics, Department of
- Identifiers
- 99900548002501842
- Language
- English
- Resource Type
- Journal article