.E FILTER 
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70 state-of-the-art 
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right line sides 
e two filters in a 
ler, et al., 1995). 
ntre line or ridge. 
g the image with 
a quadratic polynomial of image convolutions with Gaussian 
derivatives(Steger, 1998). Steger's method can detect centre line 
with subpixel precision. Similarly, Jang and Hong extracted 
ridge points from the distance map generated by performing 
Euclidean distance transform on the edge map, but distance 
transform is slow for a large image (Jang & Hong, 2002). 
Generally speaking, existing line detection approaches either 
suffer from heavy computational cost or fail to obtain robust 
feature detection performance. Some so-called "real-time" line 
detection methods often generate too many false positives while 
the object semantics have seldom been considered. In this paper, 
we have evaluated several state-of-the-art line detection 
algorithms for power line detection from aerial imagery. A new 
real-time power line detection algorithm is proposed by using 
steerable filters as well as prior knowledge of objects 
surrounding the environment where the power line is. 
2. THE STEERABLE FILTER 
2D oriented filters, such as Gaussian filter and Gabor filter, 
have been widely used for robust edge and ridge detection 
(Casasent & Smokelin, 1994;Liu & Dai, 2006;Mehrotra, et al., 
1992). One approach is to convolve the oriented filter with the 
image at each orientation and analyse each filter response. 
Rotating filters at many directions is time consuming, 
especially if one filter is different from another by some small 
rotations. To address this computational cost, Steger proposed 
steerable filters (Steger, 1998). In this section, the idea of 
steerable filter is briefly introduced. 
Steerable filters are based on a small number of basis filters 
defined at pre-specified orientations, the filter response rotated 
at arbitrary direction is synthesized from the linear combination 
of these basis filters. These filters can be rotated efficiently by 
the proper interpolation of basis filters. Given f(x,y) as the 
filter response, and f'? (x, y) as the filter response rotated at the 
angle 6, the steerable filters can be written in Equation 1. 
M 
8 z : 6; 
f(x, y)= > Of xy) (1) 
where — 0; = the i" basis angle, i € 1,2,...,M 
k; (6) = the it" interpolation function 
f? (x, y) = the i*" basis function 
M = the number of basis filters 
Gaussian derivatives are widely used in computer vision due to 
their desirable properties such as steerability. Additionally they 
are band-pass filters which reinforces the response along its 
direction while suppress the response orthogonal to its 
orientation. Generally odd-order filters are used for edge 
detection, while even-order filters are for ridge detection, the 
second-derivative Gaussian is chosen as we focus on ridge 
detection for power line detection. The filters are formed by 
steerable quatrature pair filters - a second-derivative Gaussian 
and its Hilbert transform. This is able to determine the line type 
and direction. 
Let G, be the steerable filter, its quadrature pair steerable 
quadrature filter H, is the approximation to the Hilbert 
transform of G,. H, is achieved by finding the least squares fit 
to a polynomial times a Gaussian in (x,y). It is found that the 
satisfactory approximation could be achieved by using a third 
    
   
    
  
  
   
   
      
   
   
  
   
   
  
  
  
   
   
  
   
    
   
  
   
   
  
   
   
    
     
   
    
  
   
   
   
    
  
  
   
  
   
  
    
    
  
   
  
  
   
  
   
   
   
    
    
     
order, odd parity polynomial. It means that four basis filters 
suffice to steer the quadrature filter H, at any arbitrary 
orientation, and G, requires three basis functions. Figure 1 
illustrates the basis filters of G, and H, . The steerable 
quadrature filter pairs at any direction 0 are implemented: 
3 4 
G-5. king? Hi-5. K'(0H? Q) 
= i= 
where  G§,HY = G, and H, rotated by an angle 0 
kË(0) = the i** interpolating function for the 
steerable filter, they are cos? (8), —2 cos(0) sin(0), sin? (0) 
G?' — the i*^ basis filters for the steerable filter. 
kF (8) - the i*^ interpolating function for quadrature 
filter, cos? (8), —3cos? ()sin(0), 3cos(0)sin? (0), sin? (0) 
Hut ! — the i^^ basis filters for the quadrature filter 
  
(a) G? 
  
(b) Hy 
Figure 1. The basis filters of G, and H, 
In the implementation of steerable quadrature pair filters, the 
first step is to create 2D basis filters. Gaussian function G (x,y) 
is the unique rotationally symmetric function with the linearly 
separable property, i.e. G(x,y) = g(x) * g(¥). To facilitate the 
computation, the first and second derivatives of Gaussian 
function and their Hilbert transform is calculated in one 
dimension as well as the polynomial fitting of Hilbert 
transformation. 
2D filter convolution with the image is implemented by 
convolving each row in the image with the horizontal projection, 
and then convolving each column with the vertical projection. 
3. POWERLINE DETECTION ALGORITHM 
In this section, the proposed power line detection algorithm is 
presented. The main idea is to obtain the ridge points rather 
than edges based on the energy functions of the steerable 
oriented filter, and then extract linear features by grouping the 
collinear ridge points. In addition, knowledge is used to 
distinguish power lines from surrounding linear objects. The 
characteristics are summarized as follows: 1) symmetry: 
geometry similarity along the main axis. The left and right sides 
have similar magnitude. 2) elongation: average length >> 
average width. 3) parallelism: the left and right borders 
should be locally parallel. 4) homogeneity: the region should be 
homogeneous, and the profile of the region intensities 
resembles a Mexican hat. 
3.1 Ridge Points Identification 
Power line segments can be identified by detecting the ridge 
points of the linear patterns. Most previous power line detection 
methods used edge detection-based method, which we believe 
are not appropriate because: 1) a thick power line segment 
represented with more than two pixels in an image will be