S.A.B. Kim 
  
31 COG 
COG aims at removing interpolated values if the interpolants are unevenly distributed. COG is defined as 
coc . 3&9) +6} 
max. dist 
where Ax and Ay are the mean of the distance between a scattered input and interpolated point. max dist is the 
maximum of the distance. Evenly scattered input gives 0 for COG and unevenly distributed input gives high COG. To 
determine the threshold of COG, COG is computed over a 35 km x 30 km area. This computation produces about 
471,000 samples and their distribution is shown in 
Fig. 3. The mean COG is 0.28 with peak at 0.20. The mean is not zero because the distribution of scattered input is not 
uniform with respect to the distance from the interpolated point. Equalisation of the distribution was tried but then the 
performance of COG was not good. The COG thresold is determined empirically by applying various values to the 
DEM in Fig. 1. COG threshold of 0.6 gives the best result in terms of removing the artifacts along the coast. The result 
is in Fig. 4a, which shows significant improvement over the DEM by the simple interpolation in Fig. 1a. 
  
  
  
  
  
Fig. 4 Results of applying (a) COG and (b) ECI to the DEM by simple interpolation in Fig. 1a. 
32 ECI 
The DEM obtained after applying COG criterion is still incomplete. There are thread-like features inside holes (marked 
by loops in Fig. 4a). These occur because at the center of a hole COG is 0 and an interpolated value is not rejected. The 
normalised ECI defined below would be able to remove such thread-like features: 
N 
npa, JW aad (r, ) ECI 
ECI = moo and normalised ECI = E dist 
S pa, )w © ©) max dist 
k=l 
where r, is the distance from an output grid. p(r) is the distribution function of scattered input when the search area is 
full. w,, equalises the distribution of p(r) thus is an inverse to p(r). Therefore S Wa pi, )=1. Consideration is 
given so that w,, may not reach singularity. 
The threshold of ECI is determined empirically as described for COG threshold in § 3.1. The mean ECI is 0.69 ( 
Fig. 3). Ideally ECI should be 0.5 while anti-singularity measure adds a bias of 1/max_dist. max_dist of 5 pixels 
results in a bias of 0.2 thus such size for max_dist is realistic. The ECI thresold is determined by applying various 
values to the DEM in Fig. 1a. ECI of 0.8 gives the best result in terms of removing the threadlike features while still 
minimising any undesirable removal (Fig. 4b). 
  
498 International Archives of Photogrammetry and Remote Sensing. Vol. XXXIII, Part B3. Amsterdam 2000.