Hwamog Kim, Jeffrey L. Willers, Seongjai Kim
Abstract:
Digital elevation model (DEM) is a three-dimensional (3D) representation
of a terrain's surface - for a planet (including Earth), moon, or asteroid
- created from point cloud data which measure terrain elevation.
Its modeling requires surface reconstruction for the scattered data,
which is an ill-posed problem and most computational algorithms become
overly expensive as the number of sample points increases.
This article studies an effective partial differential equation
(PDE)-based algorithm, called the curvature interpolation method (CIM).
The new method iteratively utilizes curvature information,
estimated from an intermediate surface, to construct a reliable
image surface that contains all of the data points.
The CIM is applied for DEM for point cloud data acquired by
light detection and ranging (LiDAR) technology.
It converges to a piecewise smooth image,
requiring O(N) operations independently of the number
of sample points, where $N$ is the number of grid points.
Published March 21, 2016.
Math Subject Classifications: 65M06, 62H35, 65D05.
Key Words: Digital elevation model; curvature interpolation method (CIM);
surface reconstruction; point cloud data.
Show me the PDF file (1067 K), TEX and other files for this article.
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Hwamog Kim Department of Mathematics and Statistics Mississippi State University Mississippi State, MS 39762, USA email: hk404@msstate.edu |
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Jeffrey L. Willers USDA-ARS, Genetics and Precision Agriculture Research Mississippi State, MS 39762, USA email: jeffrey.willers@ars.usda.gov |
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Seongjai Kim Department of Mathematics and Statistics Mississippi State University Mississippi State, MS 39762, USA email: skim@math.msstate.edu |
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