method. In this technique we use a blurred transparent 
positive as the mask, and overlay the positive with the 
negative by outlines to get a photo with low contrast and 
even optical density. We then print on the rigid printing paper 
to enhance the overall contrast and finally obtain the optical 
photo(Li et al., 2006). 
According to the Mask dodging principle, we use the 
following mathematical model to depict an optical image 
with uneven lightness(Sun, 2008): 
LG y) 2 I y) + B(x, y) (1) 
Where I (x, y) denotes the original image, that is, the image 
with uneven lightness, I(x, y) denotes the image with even 
lightness in the ideal conditions, and B(x,y) denotes the 
background image. According to the formula above, the 
image with uneven lightness can be regarded as the result of 
overlapping the ideal image with the background image, so 
the reason for uneven lightness of the image is that the 
lightness of the background image is uneven. Therefore, we 
can process the original image using the low-pass filter to get 
the background image, and then the image with even 
lightness can be obtained by subtracting the background 
image from the original one. 
3. THE IMPROVED IMAGE DODGING ALGORITHM 
BASED ON MASK TECHNIQUE 
In the process of image dodging with the algorithm based on 
Mask technique, there are some defects and problems. First, 
it smoothes the whole image using the same filter. 
Theoretically, the degree of smoothing should depend on the 
definition of image, so we should process the image regions 
with different lightness and contrast using different filters. 
Second, the algorithm doesn't overcome the uneven contrast 
phenomenon. The contrast of the regions which are darker in 
the original image is still lower, and vice versa. 
The following will elaborate the improved algorithm from 
four parts: producing the background image, subtraction, 
removing the border lines between image blocks, and 
processing the contrast. 
3.1 Producing the Background Image 
Producing the background image is a very critical step, 
because its quality will directly affect the final dodging effect. 
Due to the irregular distribution of uneven lightness and 
contrast in an image, which is difficult to be depicted by a 
simple mathematical model, we usually produce the 
background image with a low-pass filter to reflect the 
background lightness variation. By comparison, the Gaussian 
low-pass filter in frequency domain can get a satisfactory 
background image. 
We first divide the original image into blocks, and make sure 
there are overlapped pixels between adjacent blocks, which 
can avoid the obvious border lines between adjacent blocks 
and can make these border lines be removed simply after 
dodging. According to the Mask dodging algorithm, the 
selection of the smoothing operator should depend on the 
definitions of regions with different lightness and contrast. 
The regions with higher definition should be smoothed to a 
    
greater degree, and the regions with lower definition to a less 
degree. 
In the object field, the straight edges of ground objects will 
be blurred after being imaged by a degrading system, as 
showed in Figurel (Hu, et al.,2004). 
Joa) gi y) 
  
object field image field 
i 
| 
i 
| 
Ê 
| 
  
  
  
Figure 1. Edge curve of the object with straight edge 
The slope of edge curve reflects the blurriness of the edge, so 
we can measure the definitions of image regions by the slope 
of the edge curve. This paper adopted the calculation method 
of the definition of image regions which Hu et al. (2004) 
proposed. 
Based on the general shape of the edge curve, we adopt the 
following cosine function to simulate the edge curve (Zhou, 
1999). 
f(x) 2 Acos Bx - C (2) 
Where x is the pixel coordinate, f(x) is the gray value of the 
pixel, and A, B and C are the three parameters. In order to 
solve out for A, B, and C, at least three pairs of data (f(x), x) 
are needed. Edge is reflected in the digital image to be a 
series of pixels whose gray values are in increasing or 
decreasing order. Therefore, we can extract some feature 
edge values in the image blocks to simulate the edge curve. 
Then we differentiate the function of the edge curve to get 
the definition. 
F(x) = —ABsin Bx (3) 
Use the mid-point of the edge curve to calculate F(x), let 
Bx = % so F(i) = E : 
Set the cut-off frequency of the low-pass filter according to 
the definition of each image block. If the definition of an 
image block is lower, the image block should be smoothed 
with the Gaussian low-pass filter with the higher cut-off 
frequency, and inversely so. The calculation steps of the cut- 
off frequency of the Gaussian filter are as follows: 
(1) Calculate the definition of each image block, F;. The 
value range of i is [1,n], where n is the number of image 
blocks. 
(2) Acquire the maximum and minimum definitions, Fax 
and Fmin- 
(3) According to the size of the image block, set the 
maximum and minimum cut-off frequency of the Gaussian 
low-pass filter, Domax and Do,,, , to get the cut-off 
frequency of Gaussian filter of each image block. 
   
    
  
   
    
    
    
    
    
   
    
     
    
    
    
   
     
    
  
     
   
     
   
   
     
  
     
  
      
   
     
   
     
    
    
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