International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Vol XXXV, Part B3. Istanbul 2004 
  
more general case, it often leads to more fragmented results due 
to disturbances like cars, shadows, trees etc. which perturbate 
the ridge structure. In addition, there is an added difficulty 
when using the detected road segments for performing change 
detection on a road vector layer. The road segments from the 
image are represented by connected chains of pixels, whereas 
the vector data consists out of polvlines. Moreover the chains 
can be fragmented or contain small disturbances which make a 
good comparison with the polylines difficult. Therefore, as a 
first phase in our work we concentrate on the detection of road 
junctions. 
2. ROAD DETECTION 
Lines in an image can be seen as narrow valleys or ridges in the 
intensity surface if one views the image as a terrain model. 
Steger (1998) reviewed different approaches to line detection. 
In this work, line detection is performed based on polynomial 
interpolation to determine pixels belonging to road structures in 
the image, the "facet model" (cfr. Haralick and Watson, 1981). 
This is a standard method for ridge detection. The image is 
regarded as a function /(ij). Lines are detected as ridges and 
ravines in this function by localy approximating the image 
function by its second order Taylor polynomial. The 
polynomial is used to approximate first and second order 
derivatives of the image function in each pixel. The direction of 
the line can be determined from the Hessian matrix of the 
Taylor polynomial. The gradient and curvature information in 
each pixel are used to classify a pixel in a number of 
topological classes based on their sign or magnitude. Line 
points are mainly characterized by a high second directional 
derivative, i.e. a high curvature perpendicular to the line 
direction. 
The calculation of the partial derivatives can be done in various 
ways. The facet model determines a least squares fit of a 
polynomial F to the image data / over a window of size N=w? 
with window size w. The origin is chosen in the central pixel of 
the window. The value of the polynomial F in pixel (ij) is 
given by: 
:2 
F(i,j,0) =a, + a,i+a,j+a,i’ + aij + a,j 
=m 0 
7 1 
a= jf y T (D 
def ud 
The facet model for line detection searches the least-squares 
solution 6, given the image data ¥ containing the intensity 
value /(i,j) in each pixel (i,j): 
argmin (0) with (0) = [276 _ “| 
0 
1 #1 A 4 + hr 
Msi: : ez (2) 
b diy ud den dv 
. US 2 > 7 yNxl 
€ z[10.7) E. Kis 4l eR 
where w,,- | w/2 | : 
This leads to the linear system M^MÓ - M^X with the 
solution 6, given by. Ó, -(M' M) 'M'x.. The matrix M is 
independent of the position of the window within the image, 
meaning that the calculation of (M" M) ' M' needs to be 
816 
IG 
  
  
  
Ar An class 
0 0 flat 
- - peak 
+ valley 
0 ridge 
0 'alley 
0 slope 
- - slope 
slope 
  
++ +S6000C0C 
N 
© + 1 
+ 
+ 
  
Table 1. Classification of the image structure based on gradient 
and eigenvalues of the Hessian. 
o 
performed only once for the processing of an image with a fixed 
window size w. On the basis of the parameters O of the 
interpolated surface F, the gradient and Hessian in a certain 
pixel can be calculated: 
T : . 
ol oI ét, +2ui+a.j 
  
  
  
gradient(1)=| —, = ; 
Ox y a +ai+2a ) 
Bp. He 
Prio 3) 
OU — x6y 2a, a; 
Hessian(I)=| . = 
al 0 / a 26 
Gyex Oy 
Based on the gradient and eigenvalues of the Hessian, each 
pixel in the image can be assigned a topological class based on 
the sign and magnitude of the gradient and eigenvalues (cfr. 
Table 1). For road detection, we are interested in the ridge and 
valley class. Figure 2 shows an example of ridge detection 
performed on an extract of a IKONOS panchromatic scene 
above Ghent. Detection is performed using a window size w=9. 
A morphological thinning operator is performed on the raw 
detection result to produce lines of single pixel width (cfr. 
Arcelli et.al., 1981). 
  
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