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edge width 
IC) 
A 
   
  
edge intensity 
» 
> 
X 
(I DE EE min{DE, EE} 
  
  
Figure 1 Concepts of dilalion- erosion-residual edge 
(DE:dilation-residual edge, EE:erosion-residual edge) 
opening : o(x)=((f{©k)@k) (x) (3) 
closing : c(x)=(({9k) Ok) (x). (4) 
Since the erosion in opening is firstly computed, it 
has a feature that deletes small noises. Similarly 
closing can extract the small gradients by 
calculating dilation in the first step. 
3. MORPHOLOGICAL EDGE DETECTION 
Conventional simple morphological edge detector 
is the dilation-residual edge image (dilation-type) 
is as follows: 
dilation-type : DE(x)=d(x)-f(x) (5) 
or DE' (x) 7c (x)-f(x) 
Similarly the erosion-residual edge image 
(erosion-type) is as follows: 
erosion-type : EE(x)=f(x)-e(x) (6) 
or EE'(x)=f(x)-o(x) 
Even though DE and EE are simple and robust, they 
are not effective for images which have extremely 
noisy pixels. In the case of using these detectors, 
the outputs may introduce spurious edges. For the 
original image, DE extracts higher (value) side 
edges and EE extracts lower side edges. 
Figure 1 shows concepts of edge detection for DE 
and EE. As shown in the figure, the extreme points 
of overlapped pixels are considered the real edge 
pixels. To detect the real edge pixels the 
minimization of dilation- erosion-residual edge 
pixels are introduced. Lee et al. designed BMM 
(Blur Minimization Morphological) operator (Lee, 
1987) and Feehs et al. showed ATM (Alpha 
  
edge width 
f(x) 
A 
edge intensity 
  
  
  
  
Ope Cee Bf © wep 
  
  
International Archives of Photogrammetry and Remote Sensing. Vol. XXXI, Part B3. Vienna 1996 
Figure 2 Concept of WNED 
Trimmed Multidimensional Morphological) edge 
detector (Feehs, 1987). BMM is shown as follows: 
BMM(x)2min(fa(x)-e (x), d(x)-fa(x)) (7) 
where fa(x) is a blurred image. BMM operator blurs 
the original image by averaging the pixel values 
spanned by the structuring element. Dilation and 
erosion image for blurred image are computed in 
the first step. Erosion- and dilation-residual images 
are created using these images. The edge intensity 
at coordinate x is given by the minimum of the 
dilation-residual and erosion-residual images. ATM 
is shown as follows: 
ATM(x)=min{o(x)-e (x), d(x)-c(x)} (8) 
where the original image for dilation and erosion is 
initially blurred. 
BMM has been proven to perform better than the 
spatial-based and  differential-based edge 
detectors and ATM has also proven statistically that 
performs better than BMM. These operators, 
however, are unable to extract the weak gradients. 
For increased structuring element sizes, weak 
gradients are extracted, along with other spurious 
edge pixels which are difficult to isolate. 
To improve the problem, we show WNED 
(Wide-Narrow Edge Detection) algorithm which is 
combined two minimization (maximization) 
algorithm. As shown in Figure 2 the edge intensity 
of WNED is larger than the minimum based edge 
detectors’. If the structuring element sizes are 
increased, minimum based operators such as BMM 
and ATM extract the weak gradients. In contrast to 
such operators, WNED can separate the edge 
pixels and the other pixels. This possibly could be 
because the edge intensity of WNED is more 
significant" than “the minimum based edge 
detectors. Symbolically WNED is written as: