Tenth MSU Conference on Differential Equations and Computational Simulations.
Electron. J. Diff. Eqns., Conference 23 (2016), pp. 4757.
Digital elevation modeling via curvature interpolation for LiDAR data
Hwamog Kim, Jeffrey L. Willers, Seongjai Kim
Abstract:
Digital elevation model (DEM) is a threedimensional (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 illposed 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.
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Hwamog Kim
Department of Mathematics and Statistics
Mississippi State University
Mississippi State, MS 39762, USA
email: hk404@msstate.edu


Jeffrey L. Willers
USDAARS, Genetics and Precision Agriculture Research
Mississippi State, MS 39762, USA
email: jeffrey.willers@ars.usda.gov


Seongjai Kim
Department of Mathematics and Statistics
Mississippi State University
Mississippi State, MS 39762, USA
email: skim@math.msstate.edu

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