The shadow removal transforms the non-standard illumination 
condition to the standard and defines the grey value in standard. 
So the key is to estimate the standard light source condition. 
According to Von Kries model: 
R'] [k, 0 OTR R 
G|z|0 Kk, 0 ||G|=DIG (1) 
5) 0 0 à 2% B 
Where R',G', B' are the three bands tristimulus values after 
calibration. K,, K.., k, are gain, which is defined by standard 
illumination condition, and is key for shadow removal. 
There are several algorithms based on color constancy used for 
light source color estimation. These algorithms are divided into 
two types. 
One estimate light source method is based on low-level features 
in images; it uses the Gray-World (Buchsbaum, 1980), Max- 
RGB (Land, 1971), and Gray-Edge algorithms (Weijer, 2007). 
In order to estimate light source color, they have different 
assumptions; Gray-World algorithm supposes the average of 
scene reflectance is achromatic in the image, Max-RGB 
supposes the maximum RGB band value is light source color, 
and Gray-Edge supposes differential mean value of scene 
reflectance is achromatic in the image. All these algorithms can 
do better in light source color estimating when their 
assumptions are satisfied. Other estimate light source methods 
exist based on statistics, the typical one being Color by 
Correlation algorithm (Finlayson, 2001). This algorithm has 
good general advantages, but needs a lot of a priori knowledge, 
and the result is not of high precision. 
On the basis of these studies, G Finlayson and Trezzi proposed 
a Color Constancy algorithm: the Shades of Gray algorithm 
(SoG) (Finlayson, 2004). It assumes that the shadow and the 
non-shadow region of image should meet the Minkowski norm. 
Minkowski norm (Equation (2)): 
Jf axay MN 
(2) 
Where, e is the light source value of one current scene, f' is the 
grey value of each image band, and Æ is scale factor. p is the 
exponential parameter of the norm; it can be an arbitrary integer 
of [1,00). p determines the weight of each grey value in the 
light source being estimated. The larger the value of p is, the 
more effect from high brightness pixels (When po», SoG 
turns into Max-RGB one ). The smaller the value of p is, the 
weight of different brightness pixels is more scattered (When 
p — 1, SoG turns into Gray-World one). This method is easy in 
calculation and does not need a priori statistics models. For 
some normal nature scene images, it results in best shadow 
removal when y — 6, according to the experiment (Finlayson, 
2004). 
Aerial remote sensing images have a large imaging area, which 
include different types of landmarks and landforms. Especially 
in the downtown area of a megalopolis, the shadow of high-rise 
buildings will cause a very significant light condition difference 
in adjacent ground objects. So we should study whether the 
  
algorithms developed for general scene images are suitable for 
aerial remote sensing images, especially for color infrared aerial 
images; and their applicability for aerial images. Since the Gray- 
World and Max-RGB are a special case of the Shades of Gray 
algorithm, we focus on the SoG algorithm and propose this 
method to remove shadow on urban aerial images, and analyze 
the suitability and effect for high-resolution aerial images. After 
the experiment, we draw a conclusion. 
3. SHADOW REMOVAL METHOD BASED ON COLOR 
CONSTANCY 
The process of shadow removal in this paper is depicted here as 
Figure 1: 
  
Original 
aerial images 
Le Shadow detection 
  
  
  
  
  
  
  
  
Yv Yv 
Shadowed non-shadowed 
regions regions 
  
  
  
  
  
  
  
e Calculation of color 
constancy 
light source light source 
color of color of non- 
shadowed shadowed 
region: ei region: e» 
= 
Rate 
constants 
ei/e» 
i 
Calculate the grey of 
shadowed region in 
the case of non- 
shadowed region 
light condition 
g h(x,y) 
y 
  
  
  
  
  
  
  
  
  
  
  
  
  
  
Figure 1. Shadow removal processing 
3.1 Shadow detection 
Since shadow detection is the basis in shadow removal 
processing, shadow detection accuracy directly affects the effect 
of shadow removal. There are two types of shadow detection 
methods: 
(DA method based on object geometric features, which requires 
sensor attitude, illumination conditions, as well as a digital 
surface model (DSM) of the object. Because it is not easy to get 
building geometric information or DSM in metropolitan area, 
this method of shadow detection is difficult. 
@ A method based on the image grey characteristics in the 
shadow region, which does not need other information except 
the grey value; because of this it is applied more commonly. 
The traditional method is based on a histogram, but this is not 
suitable for the vast majority of remote sensing images; it is 
especially not suited for color infrared aerial images. 
   
  
    
    
   
   
    
      
   
     
  
  
  
  
  
   
    
   
      
   
   
     
  
   
     
   
  
  
   
   
    
    
     
    
   
    
     
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