811 
3 VALIDATION OF THE METHOD 
Table 1. Data analysis model. 
g texture. It 
ler than the 
tures. The 
e of the 
tructed and 
because there 
e of slightly 
in the texture 
noccupied areas, 
on, which gives 
rentiated from 
xture 
nds on the 
minating 
nd, by means of 
iscriminating 
ecution of this 
Iso specific 
m. 
This validation consists of verifying if the 
residential sectors of different textures also 
includes groups of inhabitants different with respect 
to given socioeconomic variables. 
Such activity was carried out within determined 
restrictions due to the impossibility of executing 
another flight over the test area, of redefining the 
homogeneous town-areas using new photographic 
products, as well as of executing a specifically 
planned field survey, in order to obtain the 
validation. 
In view of the impossibility, dictated by budgetary 
restrictions, aerial photographs, taken in 1977 of 
the urban area of Sao José dos Campos, were used, as 
well as the residential sectors of the same texture 
then defined (Oliveira et al., 1978), and the field 
survey effectuated for a research by DalBianco and 
Netto Jr (1979), based upon the division of the town 
into sectors. 
In order to adjust the available material to the 
current interests, some residential sectors were 
eliminated from the study. This was done because, in 
some cases, the number of sample elements 
(residences) typifiying it was very small, or because 
there was no demonstrative difference between its 
texture and the texture of the neighboring sector, 
although the division had appeared to be coherent 
when it was proposed. 
While the data collecting was done sector by 
sector, in the data analysis the sectors were 
compared by pairs. 
Two sets of pairs of sectors of homogeneous 
texture were constructed: a) the first contained 
pairs of neighboring sectors, the comparison of 
which aimed at validating the process by which such 
geographic units were delineated. In this case 46 
pairs of sectors were analysed; b) the second 
contained some pairs of sectors, defined by the 
photointerpretation, nonneighboring, and of a 
markedly differentiated texture. In this case the 
objective was the validation of the differentiation 
in texture as a standard for the differentiation of 
the residential population segments, as far as their 
position in the social structure of the city has 
concerned. 
The processes used to analyse each of the sets of 
residences contained in each pair of sectors 
studied were the following: 
Using the K MEANS algorithm implemented by 
Cappelletti (1982), in an adaptation of the algorithm 
introduced by Hartigan (1975), the residences of 
both sectors were reassembled according to field data 
referring to variables used as indicators of the 
social position: habitation standard, main 
householder's income and his schooling. 
Hence for each set of two residential sectors, a 
data matrix was used with dimensions N x M, where N 
stood for the number of residences researched and M 
for the number of variables considered. 
The algorithm aims at minimizing the sum of the 
squares of the Euclidean distances between units of a 
"cluster" and its center. 
To the variables of habitation standard and 
schooling were associated the numbers 1, 2, 3 and 4, 
from the worst to the best habitation as well as 
from the lowest to the highest schooling. 
The results of the utilization of the K MEANS 
algorithm determined the number of residences of each 
of the two sectors classified in each of the two 
clusters. The referring proportions being 
determined subsequently, according to the model 
presented in table 1, in which p. ij. stands for a 
proportion of elements of the sector i (defined 
through the photograph texture), assembled into 
cluster j (through the use of the algorithm). 
1 St Cluster 2 nc ^ Cluster 
Sector 1 
P- 
11 
P- 
12 
Sector 2 
P- 
21 
P- 
22 
Based upon this table, a statistical test was 
carried out to verify if there was an expressive 
difference between the proportions of elements in 
each of the sectors classified in one of the 
clusters. This difference would mean that the 
populations of the sectors, where samples came from, 
were different with regard to their social position 
in the structure of the local urban society. 
4 RESULTS 
The differences between the proportions of elements 
in both clusters were examined in 46 pairs of 
neighboring sectors. The results showed an expressive 
difference among 29 of these neighboring sectors, at 
a significance level of a = 0.20 and among 33 at a 
significance level of a = 0.30. 
During a new examination of the aerial photographs, 
it was discovered that those pairs of sectors, in which 
this difference did not prove to be expressive, were 
generally related to the pairs of sectors with less 
evident visual discrimination of the texture. There < 
was only one exception that occurred in the case 
of one of those pairs. 
In relation to the tests carried out with, 
nonneighboring sectors having an outstandingly 
differentiated photograph texture, it was found that 
all of the 8 pairs compared showed a statistically 
expressive difference at a level of a= 0-01 among 
the proportions of their elements classified in both 
clusters defined by the K MEANS algorithm. Six of 
them were expressively different at a level of 
<*= 0.0007. 
Sucn results lead to the acceptance of the 
photograph texture differentiation of the residential 
areas as an appropriate standard for discriminating 
the different segments of the urban population 
according to their socioeconomic level. 
Furthermore, it is to be emphasized that the 
sucess of this method will depend on the screening 
of only clearly differentiated textures. 
5 CONCLUSIONS 
The results in this study demonstrate that the visual 
photograph texture discrimination is an appropriate 
process for delineating residential town-sectors so 
as to become geographic references suitable to the 
purposes of urban planners. 
Once, by means of the definition of these sectors, 
a set of geographic units sensitive not only to the 
physical differentiation of the residential 
environment, but also to the socioeconomic 
differentiation of the inhabitants, is obtained. 
These sectors may become a useful planning 
instrument. This may be possible specially if we take 
into account that the method involves a relatively 
simple process that can be carried out by a 
photointerpreter qualified for this task. 
REFERENCES 
Cappelletti, C.A. 1982. An application of cluster 
analysis for determining homogeneous subregions: 
the agroclimatological point of view. Sao José dos 
Campos: INPE (INPE-2490-PRE/173).