ON THE INTERPOLATION PROBLEM OF AUTOMATED 
SURFACE RECONSTRUCTION 
Raid Al-Tahir 
Toni Schenk 
Department of Geodetic Science and Surveying 
The Ohio State University, Columbus, Ohio 43210-1247 
USA 
Commission III 
ABSTRACT 
Automatic surface reconstruction entails two major problems: determining conjugate points or features (matching) and den- 
sifying the matched points in object space (interpolation). The two tasks are usually performed sequentially in a hierarchical 
approach, without interacting with one another. In order to improve the success rate and the reliability of automated surface 
reconstruction, particularly in large-scale urban areas, the matching on subsequent levels must take into account the results 
from densifying and analyzing the surface. In this paper we focus on a surface interpolator that produces as realistic surface 
representation as possible. The interpolation and surface analysis may give clues about surface discontinuities and occlusions 
- a vital feedback for the matching process on the next level in the hierarchical approach. 
KEY WORDS: Machine Vision, Image Analysis, Surface Reconstruction. 
1. INTRODUCTION 
The main objective of digital photogrammetry is to collect 
enough information to model the portion of the real world 
that has been photographed. Two kinds of information are of 
major interest to accomplish that goal; surface topography, 
represented by Digital Elevation Model (DEM), and objects 
on the surface (natural or man-made) which are character- 
ized as discontinuities in the surface. Besides being an essen- 
tial intermediate step for object recognition, reconstruction 
of a portion of the earth's surface is the end product for 
digital photogrammetry. 
Automatic surface reconstruction entails two major prob- 
lems: determining conjugate points or features in the im- 
ages (matching), and densifying the matched points in object 
space (interpolation). The two tasks are usually performed 
sequentially in a hierarchical approach, without interacting 
with one another. In order to improve the success rate and 
the reliability of automated surface reconstruction, particu- 
larly in large-scale urban areas, the matching on subsequent 
levels must take into account the results from densifying and 
analyzing the surface. 
This paper is a part of ongoing research focusing on the 
process of surface interpolation and analysis. The purpose of 
this paper is to define the tasks for such a process. The paper 
reviews previous works that have been done in the related 
fields. The emphasis is on the applicability of suitable for an 
automated surface interpolation. 
2. OSU SURFACE RECONSTRUCTION SYSTEM 
Due to the large amount and variety of information in the 
aerial images, the success of any image processing operation 
can not be guaranteed. This is especially the case of large- 
scale urban scenes because occlusion is more frequent, and 
the visible surface is less smooth. The only alternative to 
constrain the processes is to adopt a scale-space approach 
that proceeds hierarchically from the lowest resolution for a 
227 
  
| 
Image Pyramid, level i 
Warped Images 
Edge Detection 
    
  
  
     
Surface Interpolation 
— DEM! 
Surface Analysis 
Edge Matching i=i+1, Final Level? 
Figure 1: Outline of OSU surface reconstruction system. 
    
  
  
    
  
    
     
  
   
stereo pair to the finest. OSU surface reconstruction (Schenk 
& Toth, 1992) is such hierarchical approach. It consists 
of several modules that are executed in an iterative fash- 
ion(Figure 1). Each level of the process aims at refining the 
geometry of the images and improving the surface represen- 
tation. 
In the OSU surface reconstruction system, the process starts 
by having two conjugate images sampled at the lowest level 
of resolution. The orientation of these images is obtained 
through edge detection and matching. The results of this 
step are the orientation parameters, as well as a set of highly 
reliable matched points. The raw surface is then constructed 
by computing the 3-D object space coordinate for the set of 
points. These points are sparsely and irregularly distributed. 
Thus, a dense surface representation (DEM) must be inter- 
polated for. A DEM, tesselated at the next higher level of 
resolution, is essential for surface analysis, and for the subse- 
quent cycles. The final step is surface analysis for hypothesis 
generation and verification concerning potential break lines 
and surface segmentation. 
A new cycle starts with sampling the original stereo pair at