On Development of Land Cover Classification system using Remote Sensing Data in terms of Inverse Problem
The number of observed remote sensing data set is much smaller than the number of parameters , then the number of parameters, then estimation problems in remote sensing cab be dealt as ill-posed problems in inverse problem.
As ill-posed problems cannot produce a unique solution specific condition is required to solve them. For example, the general solution f equation (1) is expressed as following.
X=A
-Y (2)
Where A
- : generalized inverse matrix
A
- has various candidates. Given the mean square error minimum condition for example, for the equation (1), the unique inverse matrix among A
- and the unique solution cab be determined
As shown above, ill-posed problems cab be solved with generalized inverse matrix and conditions, but the unique solution doesn't always correspond with the true solution because te solution process for ill-posed problems is merely mathematical one.
When dealing with geographical data in equation (1), problems such as (I) multicollinearity and (II) spatial autoregressin should be considered. Multicolinearity means that independent variables show relatively high correlating and generalized inverse matrix cannot be estimated because of reduction of A's rank. Spatial autoregresion means that error in equation (1) shows autoregression . several strategies for the problems or regularization of ill-posed problems, are reported, and the strategies for (I) are shown s followings.
(I-1) Reduction of solution space by assuming conditions
(I-2) Singular value decomposition
(I-3) Tikhonov regularization
As for (I-3) , (3) is replaced by (5), and (4) by (6) as a result of adding he condition that norm of minimized.
Assumption of conditions in (I-1) and determination of parameter c in (I-3) are dependent on empirical "knowledge " about geographical characteristics. if such knowledge are formulated and used effectively , the never problem in remote sensing may have possibility to be solved, which leads to estimation of land cover with much higher confidence.
2-2 knowledge Handling
knowledge on land cover varies form socio-economics one to ecological or geographical characteristics, e.g. agriculture practices. In some cases, there's inconsistency between some knowledge. The processes below are thought to be necessary to involve such knowledge in the estimation system. Firstly, inconsistent knowledge should be discriminated. Second, as for inconsistent knowledge, confidence for each one should be given so that the inconsistency can be resolved in a rational manner. Then, the estimation process to unify both consistent and inconsistent knowledge should be composed. In the process, as shown in Section 2-1, certain conditions or parameters should be estimated with more accuracy or reasonability by involving such knowledge. The importance is how to express knowledge on the computers so that their inconsistency can be easily checked , and how to access the inconsistency between knowledge.
Figure 3. Classified System using TM and AVHRR Images
3. Land Cover Classification System using TM and AVHRR Images
Figure 3 shows a flow of classification system using TM and AVHRR images ( under development ) as an example in section 2. besides TM and AVHRR images, DEM data and ground truth data are considered as input data. And, data fusion model will function in the final part of the system to integrate both land cover candidates from TM and AVHRR more effectively. Knowledge in the object ( land cover ) model will be used opt extract some information for the inverse problem approach, s described n section 2-1.
4. Conclusions
in this paper, authors formulated estimation of geographical characteristics using remote sensing as an inverse problem, on showed that the estimation process can be supported by applying knowledge on geographical characteristics. In future, considering the importance of fusion of several remote sensing data, the estimation process should have wide generalization for allowing eh fusion of different types of sensors on satellites.
Reference:
-
Kubo, S., "Inveres Problem', Baifukan, 1992
- Matsuba, Y., "A Comparative Review on Countermeasures for Patameter Estimation
Problems in Regionla Modeling ", Master Thesis, Univ. of Tokyo, 1997.
-
Bijerhammar, A., "Theory of Error and Generalized matrix Inverses ", Elsevier, 1973.
