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International Archives of Photogrammetry and Remote Sensing, Vol. 32, Part 3W14, La Jolla, CA, 9-11 Nov. 1999
SEGMENTATION OF LASER SURFACES
Bea Csathó!, Kim Boyer?, and Sagi Filin!
! Geomatics Laboratory for Ice Dynamics
Byrd Polar Research Center, OSU,
csatho.1@osu.edu, filin.1@osu.edu
? Signal Analysis and Machine Perception Laboratory
Department of Electrical Engineering, OSU
kim@ee.eng.ohio-state.edu
KEY WORDS: Segmentation, surface parameterization, waveform analysis, sequential estimators
ABSTRACT
Laser scanning systems provide raw surface points, that is x, y, z coordinates for each laser footprint. To obtain an explicit
description of the surface to be mapped, such as breaklines or surface patches that can be analytically described, the raw
laser surface should be segmented. The segmented surface is more suitable for further analysis, such as object recognition and
surface matching. However, the segmentation of laser surfaces is not an easy task. The error distribution is non-Gaussian,
more likely a thick-tailed distribution contaminated by outliers. Outliers result from laser reflections on object boundaries or
steep surfaces. The true underlying surface model is rarely known before hand and it might be different from the visible surface
since the laser energy can penetrate vegetation or water. We propose to use an autonomous, statistically robust, sequential
function approximation approach to segment the surface into surface patches that can be described analytically. Its core is
the Robust Sequential Estimator, a robust extension to the method of sequential least squares. Unlike most existing surface
characterization techniques, this method generates complete surface hypotheses in parameter space. Given a noisy set of raw
laser points, the algorithm first selects appropriate seed points representing possible surfaces. For each nonredundant seed it
chooses the best approximating model from a given set of competing models. With this best model, each surface is expanded
from its seed over the entire area to find all points of that particular surface. In the final step, the ambiguities are resolved and
the isolated points are removed. The end result is a set of parameterized surfaces and their boundaries. We work with two
models, planar and biquadratic, because they approximate most natural and man-made surfaces well. The segmentation may
be followed by the joint inversion of the laser waveforms over the given surface patch to refine and verify the surface model.
Synthetic and real laser surfaces are used to demonstrate the segmentation concept.
1 Introduction
Range information provides a basic, fundamental contribution
toward the understanding and reconstruction of 3-D shape,
which is required for general purpose object recognition and
image understanding. The goal of segmentation is to make
surface properties explicit. Surface properties include explicit
description of discontinuities, description of piecewise contin-
uous surface patches, and other surface properties, such as
surface roughness, and reflectivity. Segmentation also pro-
vides input for data fusion, object recognition and change
detection.
Surface segmentation algorithms have extensively being used
in computer vision (e.g., [Besl, 1988]). Segmentation orga-
nizes the surface points into spatially coherent surface prim-
itives by using low-level processes as well as generic informa-
tion. In this fashion a precise, general and compact symbolic
representation of the original point set is created without us-
ing high-level, object information. The various surface seg-
mentation approaches in computer vision have not yet fully
exploited in the processing Airborne Laser Ranging (ALR)
data. Here, usually data or application specific, often pro-
prietary data thinning and blunder detection procedures are
followed immediately by model based object recognition.
First we provide some background on surface segmentation
followed by specifics of the surfaces and laser point sets con-
sidered in ALR. Then a robust, sequential surface segmenta-
tion approach [Boyer et al., 1994] is presented in detail. We
recommend this procedure as a part of a multisensor (e.g.,
laser, stereo, multispectral) object recognition process, that
includes the following steps:
e Preprocessing of sensory data, geometric and radio-
metric corrections.
e Transformation of surface points measured by laser and
stereo into a common reference system.
e Segmentation and feature extraction of surfaces and
imagery. Each data set can be processed individu-
ally. On the other hand it may be advantageous to
combine the data for providing an explicit descrip-
tion of surface properties for example by classification
[Csathó et al., 1999]
e Grouping and model based object recognition.
N
Background on object recognition from digital
surfaces
2.1 Range image understanding in computer vision
The literature on automated surface model construc-
tion from 3D point sets contains two main paradigms
[Hoover et al., 1998]. In the mesh paradigm, a triangular-
patch or regular grid surface model is constructed from laser
points, followed by the selection of a subset of the vertices.
The selected vertices determine a polygonal surface which ap-
proximate the original data within predetermined error bars.
A variety of methods have been explored for the purpose of
