9-11 Nov. 1999 
     
International Archives of Photogrammetry and Remote Sensing, Vol. 32, Part 3W14, La Jolla, CA, 9-11 Nov. 1999 
A NEW APPROACH FOR MATCHING SURFACES FROM LASER SCANNERS AND OPTICAL SCANNERS 
Ayman Habib and Toni Schenk 
Department of Civil and Environmental Engineering and Geodetic Science, OSU 
habib.1@osu.edu, schenk.2@osu.edu 
KEY WORDS: Surface Matching, Correspondence Problem, Hough Transform, Change Detection, DTM analysis, Cali- 
bration, Fusion 
ABSTRACT 
Surfaces play an important role in diverse applications, such as orthophoto production, city modeling, ice sheet 
monitoring, and object recognition. Surfaces are usually obtained by a sampling process. The raw sampled data 
must be processed further. A frequently occurring task is the comparison of two surfaces. In the most general 
case, the two surfaces are described by discrete sets of points, whereby the point density may be different as well as 
the reference systems. We propose to compare two surfaces by computing the shortest distance between points in 
one surface and locally interpolated surface patches of the second surface. This entails a correspondence between 
points and surface patches. We describe a solution to this matching problem that is based on a parameter space 
representation. After a brief problem statement we explain the proposed matching scheme by way of an example. 
We then apply the method to determine the transformation parameters between the two surfaces. To arrive at an 
operational solution, we reduce the n-parameter space to one dimension by an iterative solution. The feasibility 
of our matching scheme is demonstrated with simulated data sets as well as real data. We show how a surface 
determined by laser scanning can be compared with the same physical surface but established by photogrammetry. 
As a natural extension, one can use the method for change detection. 
1 Introduction 
There is an increasing demand for the rapid generation 
of digital surface models (DSM). The production of digi- 
tal orthophotos as backdrops for GIS requires DSMs, for 
example. More recently, city modeling is an application 
that poses a challenge for generating DSMs. Surfaces 
play also an important role in such diverse applications 
as ice sheet monitoring and recognizing objects in aerial 
and satellite scenes. 
Surfaces are typically determined by a sampling process. 
This is certainly true for airborne laser scanning and 
stereo photogrammetry. The net result of data acquisi- 
tion is a set of points that constitutes a discrete surface 
description. In case of laser scanning, the point distri- 
bution is irregular and the surface characteristics, for 
example breaklines, are not explicitly encoded. 
The set of points obtained during data acquisition is 
hardly a useful end product. There are a number of ba- 
sic operations that must be performed on surfaces. One 
of the first steps usually involves what we may consider 
a resampling process. The classical example is interpo- 
lating the original set into a regular grid (gridding) be- 
cause most every subsequent process assumes regularly 
spaced data. 
In one way or another, many processes involve the com- 
parison between surfaces. Examples are abundant; cal- 
ibrating data acquisition systems involves the compar- 
ison between the observed surface and the known sur- 
face (e.g. test field); change detection compares two sur- 
faces sampled at different times; merging two or more 
data sets for a combined surface (fusion) requires quality 
control; a data set acquired in a local reference system 
must be transformed into a differently registered set. 
Surface comparison is usually performed by interpolat- 
ing both data sets into a regular grid. Then, the compar- 
ison is reduced to analyzing the elevations at the grid 
posts. Not all applications allow this simple procedure, 
however. Take the example of two irregularly spaced 
data sets that are acquired in different reference systems 
with unknown transformation parameters. We describe 
in this paper a new approach for solving this general 
problem. 
Ebner and Strunz (1988) and Ebner and Ohlhof (1994) 
describe a solution that is based on interpolating the 
data to a grid, subject to a transformation with unknown 
parameters, which are determined in an adjustment pro- 
cedure whereby the elevation differences at the grid 
posts are minimized. We propose to minimize the dis- 
tance between the points of one set along surface nor- 
mals to locally interpolated surface patches of the other 
surface. As shown in Schenk (1999a) this makes a weak- 
posed problem well-posed. 
The next section provides a more detailed problem state- 
ment and discusses solutions. We then concentrate on 
the solution of the matching problem and illustrate the 
proposed approach of using a voting scheme to analyze 
the parameter space by an example. Finally, we present 
experimental results obtained from synthetic and real 
data sets. 
2 Problem Statements and Solutions 
2.1 Simple Case 
Given are two sets of points that describe the same 
surface. Let $1 — Ípi,p»,..., pa) be the first set and 
S» = {q1,92,.-- ,qQm} the second set, n += m. Suppose 
the points are randomly distributed (no point to point 
correspondence). The problem is to determine how well 
the two data sets agree describing the same surface.