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TECHNICAL PAPERS

# Adaptive Range Sampling Using a Stochastic Model

[+] Author and Article Information
Zvi Devir

Department of Computer Science, Technion-Israel Institute of Technology, Haifa 32000, Israelzdevir@cs.technion.ac.il

Michael Lindenbaum

Department of Computer Science, Technion-Israel Institute of Technology, Haifa 32000, Israelmic@cs.technion.ac.il

This estimator is the maximum likelihood estimator of the variance, and is biased. Since the bias is a constant factor, the priority function may use either this estimator or the unbiased estimator.

The weighting functions are invariant under translations of the coordinate system. A weighting function is invariant under scaling of the coordinate system, if scaling of the coordinate system does not change ratios between the weights. That is, $w(x,y1)∕w(x,y2)=w(αx,αy1)∕w(αx,αy2)$, where $x$, $y1$, and $y2$ are points, and $α>0$ is the scaling factor of the coordinate system.

J. Comput. Inf. Sci. Eng 7(1), 20-25 (Dec 10, 2006) (6 pages) doi:10.1115/1.2432899 History: Received September 14, 2005; Revised December 10, 2006

## Abstract

We consider the task of sequential point sampling for three-dimensional structure reconstruction and focus on terrestrial topographic mapping using a laser range scanner. Both the sampling and the reconstruction rely on a stochastic model of the sampled object. We describe several algorithms for sequential point sampling including a new adaptive algorithm that is specifically designed for mechanical devices and produces grid-like sampling patterns. Experimental results verify that relying on the stochastic model indeed leads to efficient sampling associated with accurate surface reconstruction.

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## Figures

Figure 1

One iteration of the nonadaptive FPS algorithm: (a) the sampled points (sites) and the corresponding Voronoi diagram; (b) the candidates for sampling (Voronoi vertices); (c) the farthest candidate chosen for sampling; and (d) the updated Voronoi diagram

Figure 2

Sampling points produced by the AFPS algorithm. Each distribution is composed of 25 sampling points.

Figure 3

Synthetic DTM (1200×1200). The bold V shape marks the scanner’s point of view.

Figure 4

A range image (left) and its correlation function (right)

Figure 5

Sampling patterns with 561 points: (a) regular FPS; (b) restricted FPS; (c) adaptive FPS; and (d) adaptive grid

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