# Corrected landscapes

Mathematical method perfects interpretation of radar images

A forest, pastures and the outskirts of a city may all look the same when seen at a height of thousands of meters by radar in aircraft or satellites that monitor the surface of the Earth. The details that differentiate each kind of landscape are missed, because of the interference generated by the waves emitted by the radar meeting those reflected by the surface of the terrain.

Consequently, the sensor receives little clear information, and the result is maps with faults, which appear in the form of dots in the image, not always decipherable, even with the assistance of the techniques most widely used for the processing of images. The problem may be close to an end: a team of researchers from the Federal University of Pernambuco (UFPE) has developed a mathematical model, which, if it does not totally eliminate the noise, reduces it to the minimum and makes it possible to arrive at results that are close to reality.

After two years of work, the team from Recife has perfected a statistical method known as the bootstrap (meaning carrying out the task without outside assistance), much adopted in statistics for solving problems that cannot be resolved by means of simple mathematical expressions, but practically not used in the processing of images. The new bootstrap , as it is being called, is not just applicable to radar images of the SAR (Synthetic Aperture Radar) kind, like the ones used in the System for the Vigilance of the Amazon (Sivam), which uses electromagnetic radiation in the microwave band, which can successfully go through the clouds and the canopies of the trees to detect forest clearing, to map the use of the land, and to locate minerals in the subsoil.

According to one of the authors of this work, Francisco Cribari Neto, from UFPE’s Statistics Department, the new method can also be applied to improve the resolution and precision of examinations done with other kinds of radiation that makes it possible to detect volume, like the images from laser microscopes or from ultrasonography, used, for example, to see babies in the womb or the heart as it beats.

Pseudo-images
The original step for solving the problem of interpreting images arose from an idea of Cribari, of whom Alejandro Frery, from UFPE’s Information Technology Center, had asked for help in 1998, to solve a problem: the difficulty of processing images on account of the lack of information due to the interference from the waves of the Earth, seen as noise. Together, they went on to produce extra data about these regions, using mathematical calculations that were however based on the original information. In collaboration with Frery and with Michel Ferreira da Silva, studying for his master’s degree, Cribari developed computer calculations (algorithms) that made it possible to work with sectors of the original radar images and to reproduce thousands of copies with small variations – or pseudo-images. “It is like cloning a person and getting similar but not identical results”, Cribari explains.

In this way, the team went on to analyze about 2,000 pseudo-images, instead of one real image, to get the so-called maximum point of a mathematical function, which in this case indicates the rugosity of the surface. As a result, the researchers achieved much more precise information. “It is as if we broke down the image into various little bits and were to put them together side by side, with small alterations, like a jigsaw puzzle with various possible solutions, so that one spot need not necessarily be where it was before”, Cribari explains.

Testing in Germany
To see if the idea would work in practice, the researchers applied the new bootstrap and the traditional technique, known as the maximum likelihood method, to a radar image of the town of Oberpfaffenhofen, near to Munich, in Germany. It was supplied by the German aerospace center, where the specialists got to know the method and handed over the material to test its effectiveness. And it worked. While the data obtained from the maximum likelihood method indicated an area of forest on the outskirts of the town, the data from the new bootstrap indicated land covered by pastures in the same place.

Which was indeed reality: there was a pasture there, as attested in the article accepted for publication in the Computational Statistics and Data Analysis magazine. The results obtained vary from case to case. “The new technique has perfected the way how the numbers are translated into useful information”, says Frery. “This may lead some decisions to change completely”.

In spite of the improvement achieved, the new technique continued to be inefficient in those cases where there were few observations of a given region – less than 50 pixels (each pixel is the smallest graphic unit in the image and may correspond to 1 meter on the surface under observation). The team from UFPE has solved this problem as well. Working in partnership with Marcelo Souza, another student for a master’s degree, Cribari and Frery developed a way of tracking the surface being studied in search of the maximum point, which indicated the rugosity of the surface, altering the strategy of using known mathematical calculations.

Instead of scanning the area in a random fashion until finding this point, the program traces parallel straight lines, cut at right angles by other straight lines, forming squares on the surface. Next, these lines are followed, and the area is scanned more efficiently.

Prospects
The researchers tested the model on 80,000 images created by computers – with sizes varying from 3 by 3 pixels square to up to 11 by 11 pixels – and on a thousand segments of the radar image of the German town. The traditional model was unable to carry out the calculations in about half the cases – the smaller the area under observation, the greater the ratio of error, which varied from 30% to 60%. But the new method, called alternated algorithm, which improves the results of the new bootstrap , discovered the maximum point in all the real situations and failed in only 6 of the 80,000 artificial images, according to the study by the UFPE team presented at the Brazilian Symposium of Graphic Computing and Image Processing, held at the beginning of October in Fortaleza, Ceará.

Besides the Aerospace Center in Germany, the new bootstrap has reached the National Institute for Space Research (Inpe). “We have an interest in assessing the new method”, comments Corina da Costa Freitas, a researcher from the institute’s Image Processing Division. “If it proves to be efficient, it will most probably be incorporated into our works”.

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