The International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences. Vol. XXXVII. Part Bl. Beijing 2008 
344 
processing [Tabb, et al., 2002]. Forest height is then estimated 
from the complex coherence of a volume-dominated 
polarization by inverting Equation (1) with the assumption of 
m=0. This volume-dominated polarization can be the one 
corresponding to the high phase centre from phase optimization 
or alternatively, by using HV as an approximation. 
We examine three approaches that have been proposed in the 
literature for forest height estimation: 1) DEM differencing, 2) 
2-D search, and 3) Combined approach: 
2.1 DEM Differencing 
In the DEM differencing approach, the forest height h v is 
estimated directly from the phase difference between the 
ground phase and the volume-dominated polarization phase 
[Cloude and Papathanassiou, 1998]. This approach enjoys the 
light computational load and simple implementation effort. 
However, as pointed out by Yamada et al. [2001], this approach 
tends to underestimate height because the phase centre of the 
selected volume-dominated polarization is seldom on the top of 
the canopy. 
2.2 2-D Search 
Cloude and Papathanassiou (2003) introduced the 2-D search 
approach, in which, a look-up table (LUT) of complex 
interferometric coherences as calculated in Equation (1) is 
established, using a set of extinction coefficient values and 
forest height values. By finding the closest element in the LUT 
to the observed complex coherence, we can estimate extinction 
coefficient and forest height at the same time. Figure 1 
illustrates the basic idea of this approach. 
Complex Coherunc« (90,74) 
Figure 1. 2-D search approach for tree height estimation (see 
text). 
In Figure 1, the green curves are estimated complex 
interferometric coherence according to Equation (1) assuming 
no ground return (m=0) with <7=0,0.1,...,1.0db/m from centre to 
outer and /zv=0-40m with 0.5m as step. Red plus marks 
correspond to tree heights of: 10, 20, 30, and 40m. The 
black/blue pluses form the coherence region with the green star 
as the high phase end, which is used for tree height inversion. 
The closest point on the set of green curves is found by a 2-D 
array search and the corresponding tree height and the 
corresponding extinction rate are the inversion results. 
One of the disadvantages of this approach is that it is very time 
consuming especially if a blind search is used and an accurate 
estimate is desired. A fine LUT (small step size for hv and a) 
can increase the estimate accuracy but at the same time will 
significantly increase the computation time. To this end, some 
information can be used to guide the search and help reduce the 
searching time. For example, the knowledge of forest height 
range or the knowledge of extinction rate range, can narrow 
down the search space. 
Another disadvantage of this approach is, if the selected 
coherence is not volume dominant (i.e. m = 0), then it will not 
be intersected by one of the LUT curves and the method will 
fail. 
2.3 Combined Approach 
An approach which combines elements of the previous 
approaches was proposed in [Cloude, 2006]. The estimated 
forest height consists of two terms. The first is from the DEM 
differencing approach, which tends to underestimate height. 
The second term provides an adjustment based on the forest 
height estimated from a zero extinction scenario, which can be 
directly achieved by inverting a sine function (Equation (4)). 
/n ._ ar gQv)-^o , „2sine- 1 ([/,[) (4) 
K z K z 
In Equation (4), the first element is just the DEM differencing 
term, while the second term is an inversion using the coherence 
magnitude only for the zero extinction case. The second term is 
weighted by a factor £ which has a constrained range as argued 
in Cloude (2006). 
3. RESULTS 
In this research, the forest height estimation results from the 
three approaches are compared first on PolSARproSim 
[Williams, 2006] simulated L-Band data and then on repeat- 
pass L-Band PolInSAR data acquired by German Aerospace 
Center (DLR) E-SAR system in the European Space Agency 
(ESA)-sponsored INDREX-II campaign [Hjansek, et al., 2005a]. 
The INDREX-II campaign was conducted in November 2004 
as an experimental airborne radar experiment campaign over 
Indonesian tropical forest. Some results of forest height 
estimation from this dataset have been reported in [Hjansek, et 
al., 2005b; Kugler, et al., 2006; Cloude, et al., 2007]. DEM 
extraction beneath the forest canopy using this dataset has also 
been presented in [Mercer, et al., 2007]. 
3.1 Results from Simulated Data 
The PolSARproSim simulator developed by Dr. Mark Williams 
(Williams, 2006) is used to generate L-Band polarimetric SAR 
data over a forested area. PolSARproSim is a fully polarimetric- 
interferometric coherent SAR scattering and imaging simulator. 
It is distributed as part of ESA’s PolSARpro, a polarimetric 
SAR data processing and educational toolbox. Detailed design