Linear feature extraction with LSB-Snakes from multiple images 
Armin Gruen, Haihong Li 
Institute of Geodesy and Photogrammetry 
Swiss Federal Institute of Technology (ETH Zurich) 
ETH-Hoenggerberg 
CH-8093, Zurich, Switzerland 
ISPRS Commission III, Working Group III/2 
KEY WORDS: Feature extraction, B-splines, Snakes, Least squares matching, Multiple images 
ABSTRACT 
In general, the snakes or active contour models feature extraction algorithm integrates both photometric and geometric constraints, 
with an initial estimate of the location of the feature of interest, by an integral measure referred to as the total energy of snakes. The 
local minimum of this energy defines the feature of interest. To improve the stability and convergence of the solution of snakes, we 
propose a new implementation based on parametric B-spline approximation. Furthermore, the energies and solutions are formulated in 
a least squares approach and extended to integrate multiple images in a fully 3-D mode. This novel concept of LSB-Snakes (Least 
Squares B-spline Snakes) improves considerably active contour models by using three new elements: (i) the exploitation of any a 
priori known geometric (e. g. splines for a smooth curve) and photometric information to constrain the solution, (ii) the simultaneous 
use of any number of images through the integration of camera models and (iii) the solid background of least squares estimation. The 
mathematical model of LSB-Snakes is formulated in terms of a combined least squares adjustment. The observation equations consist 
of the equations formulating the matching of a generic object model with image data, and those that express the geometric constraints 
and the location of operator-given seed points. By connecting image and object space through the camera models, any number of 
images can be simultaneously accommodated. Compared to the classical two-image approach this multi-image mode allows to control 
blunders, like occlusions, which may appear in some of the images. very well. The issues related to the mathematical modelling of the 
proposed method are discussed and experimental results are shown in this paper. 
1. Introduction 
This paper deals with semi-automatic linear feature extraction 
from digital images for GIS data capture, where the identification 
task is performed manually on a single image, while a special 
automatic digital module performs the high precision line 
extraction. A human operator is used to identify the object from 
an on-screen display of a digital image, selects the particular 
class this object belongs to and provides some very few seed 
points coarsely distributed. This is done through activation of a 
mouse in a convenient interactive graphics-image user interface. 
Subsequently, with these seed points as approximation of the 
position and shape, the linear feature will be extracted 
automatically. There are several techniques available to solve this 
problem. These techniques can be either used in a monoplotting 
mode (combining one image with the underlying DTM) or in a 
multi-image mode. This semi-automatic feature extraction 
scheme is shown in Figure 1. The monoplotting mode based on 
wavelet transform and dynamic programming has been well 
demonstrated and documented in our previous publications 
(Gruen, Li, 1995). We will focus here on the multi-image mode 
based on LSB-Snakes, which provides for a robust and 
mathematically sound fully 3-D approach. 
In general, the snakes or active contour models feature extraction 
algorithm integrates both photometric and geometric constraints, 
with an initial estimate of the location of the feature, by an 
integral measure referred to as the total energy of snakes (Kass, et 
al., 1988). The local minimum of this energy defines the feature 
266 
International Archives of Photogrammetry and Remote Sensing. Vol. XXXI, Part B3. Vienna 1996 
of interest. It has two advantages: Geometric constraints are 
directly used to guide the search for the feature, and global 
information is used through integration of the energy along the 
whole length of the curve (Fua, Leclerc, 1990). The 
mathematical basis of the existing optimization approaches, 
however, is not well formulated and we diagnose a lack of 
investigations on issues with regard to optimality, existence and 
uniqueness of the solution (Amini, et al., 1990), and the balance 
between different part of the energy (Samadani, 1991). Also, the 
internal quality assessment of the results is not possible. 
In this paper, active contour models are formulated in a least 
squares approach and extended to integrate multiple images for 
feature extraction in a fully 3-D mode. With such a development, 
the various tools of least squares estimation with their familiar 
and well established mathematical formulations can be 
favourably utilized for the statistical analysis of the obtained 
results and the realistic evaluation of its performance, e. g. 
through the use of the covariance matrix of the estimated 
parameters. This is in clear contrast to conventional snakes, 
which due to their particular theoretical background and 
formulation, do not provide any measures for the qualitative 
control of their results. At the same time, it can be considered as 
a new application and extension of the least squares template 
matching (LSM) technique (Gruen, 1985). Also, through the 
integration of camera models and a multiple-image approach 
redundant image information becomes available, which 
stabilizes the solution and allows to deal with partial occlusions 
and similar distortions. 
     
   
  
  
  
  
  
  
  
  
  
    
  
   
  
  
  
  
  
  
  
  
  
  
  
    
    
     
   
   
    
   
  
    
   
   
   
   
    
    
   
   
   
   
   
   
   
    
   
    
  
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