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In: Wagner W., Szekely, B. (eds.): ISPRS TC VII Symposium - 100 Years ISPRS, Vienna, Austria, July 5-7, 2010, IAPRS, Vol. XXXVIII, Part 7B 
2. DUAL DIRECTIONAL SLOPE-BASED FILTER 
2.1 Slope-Based Filter 
with along forward and backward, it is called dual-directional in 
this paper. 
The slope-based filter was firstly proposed by Vosselman 
(2000). This filter is designed by a kernel function which is 
composed of two parameters, slope and searching scope( d), 
expressed in eq. (1). 
(a) diagram of adaptive-slope filtering 
k(Ax,Ay) = -A.h (d) = slope* d 
(1) 
Figure 1 shows the diagram of the kernel function and indicates 
the principle of filtering. The cone-like searching window is 
determined by the kernel function. To decide a measured point 
is a ground point or not, the algorithm checks any other points 
locate under the cone window. If yes, the point will be labelled 
as a non-ground point, or it is labelled as a ground point. 
break line 
(b) diagram of over-filtering near break line 
break line 
slope 
Figure 1. Diagram of a kernel function 
It is obvious that the slope threshold should be properly 
determined based on the terrain type. An adaptive slope-based 
filter(ASF)(Sithole, 2001; Tseng et al., 2004) is therefore 
designed to determine the slope threshold before running the 
slope-based filter. 
The adaptive slope-based filter work well either for a flat 
surface or an oblique surface. However, areas near terracing 
fields and cliff areas may result in unreliable estimation of slope. 
Classification errors would occur in this kind of areas. Figure 2 
indicates an unwanted filtering situation. Figure 2(a) shows the 
filtering processing using an adaptive slope-based filter and 
some points near the break line would be eliminated. This 
situation is called over-filtering and the missing points will 
result in a smoother DEM than the true DEM(Figure 2(c)). 
2.2 Dual Directional Slope-Based Filter 
To overcome over-filtering, a dual-directional adaptive slope- 
based filter(DDASF) is presented in this paper. The basic idea 
is to divide original filter into two filters(see Figure 3). If we 
reconsider the over-filtering problem and perform the two 
filters, the missing points will be retained in the filtering result 
by alternative one of the two filters (see Figure 4(b)). The final 
filtering result can be the union of the two results. In other 
words, any point which as long as passes one of the two filters 
will be labelled as a ground point. Since the shape of ASF is 
symmetric, ASF is non-directional. The filtering results will be 
the same if we rotate ASF. However DDASF is designed to deal 
(c) unwanted smoothed areas due to over-filtering 
Figure 2. Diagram of over-filtering 
Figure 3. Diagram of dual-directional slope-based filter 
• •• •• • * *• 
(a) Diagram of point clouds 
tsr--' 
(b) filtering results of DDASF 
(c) Union of the two filtering results 
Figure 4. Diagram of DDASF filtering