Full text: Proceedings, XXth congress (Part 7)

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International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Vol XXXV, Part B7. Istanbul 2004 
each pixel as a member of class. The probabilities are then con- 
verted to a posteriori probabilities of class membership, which 
are assessed as the probability density of a case for a class rela- 
tive to the sum of the densities. For each pixel, the a posteriori 
probabilities sum to 1.0. At each resolution, the highest a poste- 
riori probability and its related class are output for each pixel. 
With this approach, the feature layers obtained from coarse 
resolutions do not have to map back to the finest resolution 
specified and the computation cost is lower than that in the first 
strategy. 
The third approach is a top-town filtering approach. This multi- 
resolution procedure starts with the coarsest resolution image. 
The finer resolution images are used only when necessary. The 
posterior probabilities of the training data are used to determine 
the threshold at each resolution level. For pixels with maximum 
posterior probabilities greater than the threshold are assigned to 
their related classes and are excluded (masked) for subsequent 
processing. All pixels with maximum posterior probabilities 
less than the threshold are regarded as mixed pixels, or pixels 
that do not have identical signatures and cannot be identified at 
this resolution level. Their posterior probabilities are used as 
prior probabilities at next resolution level. 
More efficient classification algorithms can be used. This in- 
cludes the Fuzzy-set and neural net classifiers (Foody, 1999; 
2000), approximating the model by Markov, conditional inde- 
pendence or fractal structure obtained from multi-scale analysis 
(Solberg et al. 1996; Li et al. 2000). 
2.4 Error analysis 
At the same spatial resolutions, classification errors can be 
influenced by many factors, such as scheme selection, spatial 
autocorrelation among and within classes and classification 
techniques, to name a few. Traditionally classification error 
analysis is based on the use of an error matrix or contingency 
table to derive descriptive statistics such as overall accuracy, 
kappa coefficients, etc. The error models for area classification 
maps across scales are largely unsolved and little work has been 
done, although it is becoming more important with the 
increasing availability of multi-scale data (Tate and Atkinson 
2001). The emphasis in this framework is to explore how 
spatial autocorrelation of classification errors among and within 
classes changes with spatial resolutions. The variance loss from 
fine resolution to coarse resolution will be calculated. The 
relationship between these errors and spatial autocorrelation 
parameters obtained from the multi-scale analysis will be 
analyzed for each class. 
3. CASE STUDY 
The multi-resolution framework was tested using simulated 
multi-resolution images derived from IKONOS data for a por- 
tion of the western part of Kingston City, Ontario, Canada. The 
IKONOS image has a spatial resolution of 4 m with four spec- 
tral bands. Ten land cover classes were used, including resi- 
dential roof, industrial/commercial roof, Road, lawn, conifer 
tree, deciduous tree, bare/cleared land, water, new crop, and 
wetland. 
4 m IKONOS image was aggregated progressively into four 
nominal resolution levels (8 m, 12 m, 16 m, and 20 m) by an 
averaging method. Both single-resolution and multi-resolution 
classification were conducted. The single-resolution classifica- 
1189 
tion was used as a benchmark for evaluating various multi- 
resolution approaches. 
Initial exploratory data analysis was carried out as three trials. 
The first trial used histograms to determine the types of distri- 
bution exhibited by each band. The second trial included the 
mean and standard deviation to assess distribution properties. 
The final trial established if each band offers or similar or dif- 
ferent information, i.e. are they correlated? 
A set of sampling data was selected for each class. The semi- 
variogram was used in the case study to decide the spatial auto- 
correlation level in each class. Each value of a pixel was com- 
pared to its neighbors at varying distances (lags) and the differ- 
ences were calculated. The semivariance was then calculated by 
averaging the summation of squared differences for pixels. In 
most cases the semivariance tends to increase with spatial inter- 
vals. After reaching a maximum value, the semi-variogram flat- 
tens (called the sill). The lag at which the sill is reached is 
called the range. The range indicates the extent to which val- 
ues sampled from a spatial process are similar (spatially re- 
lated). Detailed theoretical and mathematical exploration of 
variograms can be found in Cressie (1991), and Woodcock et 
al. (1988a; 1988b). 
The non-directional or isotropic semi-variogram was calculated 
and plotted for to assess the degree of spatial autocorrelation in 
respective bands in the case study. The ranges were determined 
by visual examination and through a comparison of piecewise 
slopes. Table 1 lists the ranges for each class. 
  
  
  
  
  
  
  
  
  
  
  
  
Classes Range (m) 
Residential roof 16 
Commercial/industrial roof 28 
Road 8 
Lawn 14 
Conifer trees 6 
Deciduous trees 12 
Cleared/bare land 30 
Water 12 
New crop 24 
Wetland 8 
  
  
  
Tablel. The ranges obtained from semi-variogram 
The shape and range of each semi-variogram were useful for 
determining suitable sizes for training data, sampling interval, 
resolution or window sizes used for spatial feature extraction. 
Based on the discussion in previous section, when image reso- 
lution is close to or coarser than the range of a class, an L- 
resolution scene model is generally most appropriate for that 
class. Otherwise, spatial features that incorporate tex- 
ture/contexture information should be generated at H- 
resolution. 
Training data were selected by visually identifying and manu- 
ally digitizing blocks of pixels. As a general rule, the length and 
width of small blocks for each class were close to the range ob- 
tained from the semi-variogram, so that each block was big 
enough to represent the spectral and spatial properties of each 
class. Thus, the heterogeneity or autocorrelation within each 
class was included in the training data. The distance between 
any two blocks was greater than or equal to the range of the 
semi-variogram, so the pixels in one block were correlated, but 
not spatially autocorrelated with those in another block. 
 
	        
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