In: Wagner W., Székely, B. (eds.): ISPRS TC VII Symposium - 100 Years ISPRS, Vienna, Austria, July 5-7, 2010, IAPRS, Vol. XXXVIII, Part 7B 
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processing image from study area wasn’t polluted by clouds. 
Figure 2 illustrates the processing image with ST values. 
Cordinate System: Universal Transverse Mercator 
Reference Elipsoid: Mayford 
Central Meridian; 51° WGr 
Figure 2. NOAA image processed with ST information from 
6/12/2003 on Rio dos Sinos Hydrographic Basin 
With the processing and georeferencing image was possible to 
put over it a digital elevation model obtained from isolines at 
vertical equidistant of 20m and georeferenced on Torres vertical 
datum. Next, for each pixel centroid was obtained the following 
information: east and north UTM coordinates, altitude and ST. 
2.3 Proposed neural network structure 
The ANN was structured on multilayer perceptron (MLP), 
whose algorithm principle is based on errorcorrection learning. 
When a pattern is presented to the network for the first time, it 
produces a random output. The difference between this output 
and the intended compose the error, that is calculated by the self 
algorithm. The backpropagation algorithm makes that the 
weights from output layer been the first to be adjusted and after 
the weights from residual layers, correcting them from back to 
front, with the objective of reduce the error. This process is 
repeated during the learning until the error become acceptable 
(Silva et al., 2004). 
The neurons utilized in the ANN were set based on the model 
proposed by Haykin (2001), as show the Figure 3. In the 
synaptic weights (Wkj) the k index refer to the neuron in 
question while the j index report to the synapse input signal 
which weight has relation. The function of the weight is 
multiply the synapse input signal connected to the neuron. 
ANNs can also present additional weights, called “bias”, that 
have the role in preventing error generation when all input data 
are null, because so the matrix of weights don’t suffer 
modifications in the training. Activation function is a function 
of internal order, been a decision made by self neuron over what 
do with the resultant value from the sum of pondered inputs. 
Transference function is a function of output or logic threshold. 
It controls the activation intensity to obtain the wanted 
performance from network. 
bias 
Figure 3. Artificial neuron structure utilized on ANN. Adapted 
from Haykin (2001) 
Mathematically, Figure 3 can be expressed in equations 5, 6 and 
7. 
j=\ 
(5) 
= u k +b k 
(6) 
= <p{v k ) 
(7) 
where: uk is the output from linear combinator (additive 
junction); 
• wkj are the synaptic weights; 
• Xj are the input variables; 
• is the activation potential; 
• b it the bias; 
• yk is the output signal of k neuron; 
• is the activation function. 
For the network was used a supervised training through the 
Levemberg-Maquardt algorithm, which used the Newton 
method that applies the minimum approximation for error 
function (Haykin, 2001). In this case, ANN was trained through 
pairs of input and output presentations, in others words, for each 
input provided for network exist an expected output that is also 
provided for the training. The network produces an output 
answer where it self is compared with the expected output (that 
was provided). The difference between network answer and 
expected answer (known), generate a residue (error). This 
obtained error is used to calculate the necessary adjust for 
synaptic weights from network, that will be corrected until the 
network answer coincide with expected output. Such is the 
minimization error process (Haykin, 2001). 
Continue talking about this learning type (Haykin, 2001), the 
necessary calculations to minimize the error are important and 
related to utilized algorithm, like on backpropagation, for 
example, where the consider parameters as interactions number 
by input pattern are used to get the minimum error value on 
training (network capability to escape from local minimums). 
Equation 8 shows the error function (MSE - Mean Squared 
Error) that will be minimized on training step: 
MSE = (8) 
n 
where:* dj is the expected output value from ANN; 
• yj is the obtained output value; 
With the objective to select an ANN that could supply a better 
performance, were realized many tests, modifying the number 
of intermediate layers, the number of neurons per layer and the 
activation function, enable the selection of the best ANN for ST 
estimation. 
The ANN variables from input and output layers were 
normalized inside the interval [0-1]. 
2.4 Results analysis 
ANN was trained by information extracted from processing 
NOAA thermal satellite image with a surface coverage from 
6/12/2003. Its pixel size of 1X1 Km provided a quantity of 3737 
points for the training process. The existing meteorological 
stations on BHRS enabled the temperature and averages of air 
relative humidity obtainment from satellite image period. 
To test the proposed model were collected in field ST 
information with a laser thermometer on 3/18/2008. With the 
assistance of a GPS receiver model Trimble Pocket were 
obtained the UTM coordinates (SIRGAS) for ST sample points. 
Temperature and averages of air relative humidity were taken