Instrumentation & Measurement Magazine 23-6 - 27

performance. In this context, we introduce the confusion matrix that contains information about measures, accuracy, and
precision. A Confusion Matrix [9] or contingency table is a tool
for measuring the performance of a Machine Learning model,
by checking how often its predictions are correct compared to
reality in classification problems. To calculate a confusion matrix, it is necessary to have a set of test data (test dataset) or a
set of validation data (validation dataset) with the expected result values. We then make a prediction for each line of the test
dataset. From the expected results and predictions, the matrix
indicates the number of correct predictions for each class and
the number of incorrect predictions for each class, organized
according to the predicted class. Each row of the table corresponds to a predicted class, and each column corresponds to
an actual class. The k-nearest neighbors (kNN) [10] test is also
included for verifying the closest elements within both images.
The resulting matrix verifies the exact overlapping between
both SAR images. The results of Fig. 7 illustrate that both SAR
images come from the same sensor and the processing is accurate and precise. Moreover, the confusion matrix takes into
account metrics [11] used in measurement science:
	

accuracy 

y tpp  y tn
p
yp

recall 

y tpp
y ptp  y pfn

y tpp
ytpp  y pfp

	(5)

Since we have two measures (precision and recall), it helps
to have a measurement that represents both. We calculate an FMeasure [12] which uses harmonic mean in place of arithmetic
mean as it punishes the extreme values more. The F-Measure
will always be nearer to the smaller value of precision or recall:
	

2 * Recall * precision
	(6)
FF-Measure
 Measure 
Recall  precision

Comparison of Performances
In this section, we propose a method of confirming and comparing the proposal. We decide to use a method based on
convolution and kernel determination [13] to extract features
from SAR images. By convolution we intend to implement a
mathematical operation on two functions: f and g to produce a
third function which corresponds of the area under the curve
of the product of the two functions f and g. The definition of
convolution in a discrete expression is given by:

	(3)
	

where the accuracy is the classification rate, y is the positive sum of the quantity under test (for example, surface of a
given item in the map such as forest reflectance), the subscript
p stands for positive, tp is the true positive, and tn is the true
negative. Recall (see (4)), can be defined as the ratio of the total number of correctly classified positive examples divided
by the total number of positive examples. High Recall indicates
the class is correctly recognized as a small number of false negative (FN):
	

precision 

	

( f * g)[n
]









 f [m] g[n  m]  f [n  m] g[m]	(7)

	(4)

To get the value of precision (5), we divide the total number
of correctly classified positive examples by the total number of
predicted positive examples. High Precision indicates that an
example labelled as positive is indeed positive (a small number of positive (FP)).

Fig. 7. Confusion matrix: percentage and absolute values, respectively.
September 2020	

Fig. 8. Convolution and Kernel algorithm for feature extraction.

IEEE Instrumentation & Measurement Magazine	27



Instrumentation & Measurement Magazine 23-6

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