removal and the atmospheric correction follows, while others 
apply the procedures vice-versa (Kay et al., 2009). 
2.1 Sun glint removal 
The available sun glint removal methods are categorized 
depending on the water area applied, i.e. open ocean or shallow 
waters. Kay et al. (2009) provide a thorough review of 
deglinting methodologies. A popular one for shallow waters 
deglinting was proposed by Hochberg et al. (2003) and it was 
based on the exploitation of the linear relationships between 
NIR and every other band in a linear regression by using 
samples of two isolated pixels from the whole image. Hedley et 
al. (2005) simplified the implementation of this method and 
made it more robust by using one or more samples of image 
pixels. The linear regression runs between the sample pixels of 
every visible band (y-axis) and the corresponding pixels of NIR 
band (x-axis). All the image pixels are deglinted according to 
the following equation (Hedley et al., 2003): 
R, - R, - b (Ry — Ming) (1) 
where  R;- the deglinted pixel value 
R;= the initial pixel value 
b;- the regression line slope 
Ruir = the corresponding pixel value in NIR band 
Miny = the min NIR value existing in the sample 
The effectiveness of the method relies on the appropriate choice 
of the pixel samples from an image region that is relatively dark, 
reasonably deep, and with evident glint (Green et al. 2000, 
Hedley et al., 2005, Edwards, 20102). 
2.2 Atmospheric correction 
There is a wide variety of methods for atmospheric correction 
above the sea surface. However, they usually require some input 
parameters concerning atmospheric and sea water conditions 
that are difficult to be obtained (Kerr, 2011). For this reason the 
simplified method of dark pixel subtraction is usually preferred 
for this kind of application (Benny and Dawson, 1983;Green et 
al., 2000; Mishra et al., 2007). The atmospherically corrected 
pixel value R,, is then: 
R47 Ri - Ra (2) 
where R;= the initial pixel value 
Rap = the dark pixel value 
According to Benny and Dawson (1983) the dark pixel value 
subtraction is valid if the atmospheric behaviour is constant for 
the whole study area. The disadvantage of this crude method is 
the fact that the dark pixel value can be determined in various 
ways (e.g. Lyzenga, 1981, Benny and Dawson, 1983, Green et 
al. 2000, Edwards, 2010b) that result in different correction 
values. An unsuccessful determination of Ry, may affect the 
depth estimation (Stumpf et al., 2003). An additional drawback 
appears in cases where the bottom reflectance is lower than the 
dark pixel value, for instance when the bottom is covered with 
sea grass, and the difference in equation (2) becomes negative. 
International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Volume XXXIX-B8, 2012 
XXII ISPRS Congress, 25 August — 01 September 2012, Melbourne, Australia 
Consequently equation (4) in $3 cannot be satisfied as the 
natural logarithm of a negative quantity is not defined. 
3. THE LINEAR BATHYMETRIC MODEL 
Lyzenga (1978) described the relationship between an observed 
reflectance Ry, and the corresponding water depth z and bottom 
reflectance A, as: 
R,7(A4- R,)exp(-gz) * Raj (3) 
where — Rgj- dark pixel value 
g = a function of the attenuation coefficients. 
Rearranging equation (3) depth z can be described as (Stumpf et 
al., 2003): 
z- g [In(Aa- R,) - In(R,, - Raj)] (4) 
where Rı,- Rıp>=0 
This single band method for depth estimation assumes that the 
bottom is homogeneous and the water quality is uniform for the 
whole study area. Lyzenga (1978, 1985) showed that using two 
bands could correct the errors coming from different bottom 
types provided that the ratio of the bottom reflectance between 
the two bands for all bottom types is constant over the scene. 
The proposed model is (Lyzenga, 1985): 
z= ay + aX; + aX; (5) 
where X; = In(Rwi-Rapi) 
X; = In(Ry;-Rap)) 
ag, a, a = coefficients determined through multiple 
regression using known depths and the corresponding 
reflectances. 
If imagery data have already been atmospherically corrected, 
according to §2.2, then X; = In(R,;) and Xj = In(R,;), where Ry; 
and R,; are the corrected reflectances (Green et al., 2000). In 
1983 Paredes and Spero proved that if there are at least as many 
bands as the existing bottom types in a study area, an 
independent from bottom types depth can be estimated. 
Lyzenga et al. (2006) proved that the n-band model 
z=a,+Y, aX, (6) 
where X; is described above, although derived under the 
assumption that the water optical properties are uniform 
(Lyzenga 1978, 1985) gives depths that are not influenced by 
variations in water properties and/or bottom reflectance. This 
means that the more the available bands are, the better the depth 
estimation. According to Bramante et al. (2010) imagery data 
with multiplicity of bands, e.g. Worldview-2, should produce 
better results over heterogeneous study areas. 
    
   
   
    
    
   
    
    
    
  
    
  
    
   
   
    
   
    
     
   
   
    
   
    
    
   
    
    
    
   
  
    
    
      
     
   
    
   
   
   
   
   
   
   
    
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