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of agricultural areas and the process of deforestation. Two main approaches for hypothesis generation about the shape 
of forest/non-forest objects are: 
First, in the absence of GIS data, a method of automatic shape hypothesis generation of RS data by means of local 
maximum likelihood (LML) classification is used as a shape hypothesis generator for LBSC (Abkar 1999). Fig. 4-b 
shows the forest and non-forest cover map obtained from the automatic shape hypothesis generator by means of LML 
classification of the 1989 TM image, which contains small-patched and sparsely distributed deforested areas. 
Second, based on the availability of data and/or knowledge from the GIS the initial hypothesis with an irregular shape 
was generated. Rules for the development and change of the irregularly shaped forest/non-forest objects from simple 
morphological parameters are formulated to generate shape hypotheses. After which the parameters are determined 
based on the RS data. Given an initial state of non-forest class (or forest cover) the "isotropic expand" operation is used 
to predict the next state of the non-forest class (see Fig. 5). The expand hypothesis is parameterized by using the 
number of successive "pixel" expands applied to the reference map of 1977. Isotropic expansion is selected optionally 
as 4 nearest neighbor expansion. 
The assumption underlying the isotropic expand operation (people cut trees at the forest boundary at the same rate), was 
not reasonable, as appeared in the (residual) error maps, with error patterns indicating an incomplete geometric 
hypothesis. Adding constraints such as soil to the deforestation process significantly improved the isotropic expansion 
of the non-forest area (see Fig. 6). The soil map is resampled to the coordinate system of the Landsat-TM sensor (Fig. 
2-d) and then the soil suitability map for agriculture is derived. Next, this constraint map, are crossed with the 
deforestation hypothesis map to generate constraint hypothesis maps. Therefore, the prior knowledge in this case, 
consists of an initial state represented in a reference map of 1977 and the underlying assumption for the generation 
process is the process of expansion constrained by, for example, soil and land form. This is called “soil-constrained 
isotropic expand" but the generated constraint hypotheses maps are non-isotropic, i.e. the generated result is non- 
isotropic (e.g. Fig. 6-b). 
Using global geometric hypothesis such as unconstraint and soil constraint isotropic expends have the disadvantages 
that the generated hypothesis boundaries are artificial and cannot account for local changes. Consequently, the method 
of isotropic and soil-constrained isotropic expands were extended to “non-isotropic expand" by using local radiometric 
constraints for application of expand in the framework of hypothesis generation and parameter estimation; this is in 
contrast with the pixel-based approaches. The method is capable of dealing with regular, irregular and small-patched 
and sparsely distributed deforested areas (Fig. 7). 
3.4 Hypothesis Evaluation & Error Analysis 
In this section the model results are evaluated by the minimum cost solution of hypotheses. The graph of the cost 
function and the representation of the residual error maps are used for the evaluation of the model to measure the 
outcomes from the geometric hypotheses. Then, the results are evaluated by the minimum cost solution of hypotheses. 
Figures 4-b, 5-b, 6-b, and 7-b show the forest and non-forest cover map obtained from the various models of hypothesis 
generation using Landsat-TM images and GIS data and knowledge. The graphs of the costs are also shown in Figures 4- 
a, 5-a, 6-a, and 7-a. The deforestation maps can be determined by comparing the classification results with the land 
use/cover map of 1997 (see Figures 4-c, 5-c, 6-c, and 7-c). 
Figure 4. Forest and non-forest cover 
map obtained from the automatic shape 
hypothesis generator. 
(a) the graph of the cost as a function of the 
number of shrink operations (Local min) for 
LML classification. The graph has a min- 
cost of 0.306451 at Local-min-parameter = 8. 
(b) the. best result of the IML 
classification 
(c) deforestation map of Phrao between 
1977 and 1989. 
  
cost 0.3217 
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International Archives of Photogrammetry and Remote Sensing. Vol. XXXIII, Part B3. Amsterdam 2000. 13