Spatial Organization Approach

Principles
Given a studied area, the principle is to organize it spatially, following the type and state on one hand, and the heterogeneity on the other hand, of the environment. The creation of these categories are based on the two aspects of the environment that is potentially and at first sight approachable with remote sensing, namely:

• the types and states, for instance : type is water – state is turbid
• the spatial organization, precisely the heterogeneity, ranging from very disturbed to not-disturbed.

The approach is in two steps:

• first: the space is organized following the “types and states” characteristics
• second: each of these “types and states” are re-organized following the “disturbance” characteristics

In such a way, we are able to extract and propose from remotely sensed images, a very detailed typology of any area, under the actual spectral and spatial resolutions of the sensor used. For instance, from this model, it would now be possible to obtain 5 to 6 types, in fact easily even more, of such class as “Urban”. What is stressed is that, medical and epidemiologist researchers are not anymore bounded by the “poor” usual spatial categories used routinely, when remote sensing is not defined as the essential model providing the actual categories of environment existing in the given studied area. But in consequence, there will be a phase where and when this “plethora” of spatial classes will have to be qualified, at least to give “common” understandings and meanings to them. Which is assumed through knowledge based sounding approach in remote sensing, followed by a survey, whose frame is constrained by remote sensing, and whose questionnaire is open to medico-epidemiological issues.

Classification algorithm
Methodologically speaking, it is using the K-Means statistical algorithm to classify the pixels. This algorithm is organizing the pixels in what is sometimes called “natural” classes, as it is working by minimizing the within-variance (intra-classes : W), against the between-variance (Between-classes : B) in the general equation of the variance : T = B + W (T: Total variance). One question is: how many classes to use. This question is here considered only under the aspect of “how many maximum number of classes should be used, knowing that the area under study is composed of n pixels ?”. Which is meaning we are not discussing such questions as “what should be the optimum number of classes ?”

For this is applied the formula (Andrianasolo, 1990) decomposing an histogram in k classes:

k = 5 Log (n)
k : the number of classes
n : the size of the area in pixels Classification by types and states (spectral features).
The application of the above mentioned approach results in : k = 6 classes.


Spectral based - Organization
Classification by heterogeneity (textural features)
Using the method of grey value co-occurrence matrix with a window 7*7, 3 texture features are calculated on the basis of the 6 spectral features of the Thematic Mapper sensor: Variance = S_i S_j (i - m)² p(i,j).
Contrast = S^Ng-1 _n=0 n² {S^Ng_i=1 S^Ng_j=1 p(i,j)}
Entropy = -S_iS_j p(i,j) log (p(i,j)) Where:
p(i,j) : (i,j)^th entry in a normalized grey-tone spatial-dependence matrix.
N_g : Number of distinct grey levels in the quantized image.
m: mean of p.

18 textural features are obtained which are used to classify the area in k = 6 classes of “disturbance”.


Textural based - Organization