The International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences. Vol. XXXVII. Part B5. Beijing 2008 
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The global undulation and local diversity can be seen as the 
coefficients of the high frequency parts in different scale. We 
can take the high frequency coefficients as a reference of the 
terrain surface complexity. 
In the terrain visualization we can find that when the view point 
of the user grows higher, the terrain scale we saw will become 
bigger, and the terrain in the study region will become “flat”. 
So we can conclude that the terrain surface complexity is 
relevant with the terrain scale, when the terrain scale become 
large the terrain surface “seems” to become flat. 
Figure 3. The relation between flight height and terrain scale 
[Reddy 99] 
Figure 4. the relation between terrain surface complexity and 
terrain scale 
We use (/I 1 ,/ 2 ,/ 3 /¿./¿./¿) as 
a eigenvector to present the terrain surface complexity. M 
represents the maximum level number of wavelet 
decomposition. And fj , fj , represent the sum of 
coefficients in LHj, HLj, HHj. Then we adopt the formula to 
calculate terrain surface complexity: 
3.3 The improved SPIHT coding method adopted 
Set Partitioning in Hierarchical Trees (SPIHT) compression 
algorithm is promoted by Said and Pearlman in 1996. It is an 
improved method of EZW. The data structures and coding 
blocks used by SPIHT are wavelet coefficients grouped into 
trees. SPIHT provides a progressive ordering of data that 
enables us to determine which data are most important to the 
DEM quality. 
Figure 5. The zero-tree structure in SPIHT algorithm 
In this paper we make some improvements on SPIHT algorithm 
according to terrain surface complexity, and adopt it as the 
compression method in this paper. 
The following sets can represent the corresponding tree 
representations: 
0(i,j) is the set of coordinates of all offspring of node (i,j) 
D(i,j) is the set of all coordinates that are descendants (all nodes 
that are below) of the node (i j) 
L(ij) is the set of all coordinates that are descendants but not 
offspring of node (i j) 
The following are the lists that will be used to keep track of 
important pixels: 
LIS: List of Insignificant Sets, this list is one that shows us that 
we are saving work by not accounting for all coordinates but 
just the relative ones. 
LIP: List of Insignificant Pixels, this list keeps track of pixels to 
be evaluated 
LSP: List of significant Pixels, this list keeps track of pixels 
already evaluated and need not be evaluated again. 
A general procedure for the code is as follows: 
1. Initialization: threshold T=2 n , n = |jog 2 (max ( . y) (|C., |})J 
LSP is empty; add starting root coordinates to LIP and LIS. 
2. Sorting pass: (new n value) 
(D for entries in LIP: (Stop if the rest are all going to be 
insignificant) 
- decide if it is significant and output the decision result 
- if it is significant, move the coordinate to LSP and output 
sign of the coordinate 
(2) for entries in LIS: (Stop if the rest are all going to be