Implementação de um método para cálculo das frações de área de componentes homogêneos de uma imagem usando análise linear de histogramas

Abstract

In the present work an implementation of a tool to determine the area fractions of homogeneous components of an image by linear analysis of histograms is described. In this method the histogram of the entire image is expressed as a linear combination of the histograms of all its components. The linear coeficients, or weights, assigned to each component form the solution set of the problem. Since the histograms of the components are not known, the program offers a user-friendly interface to extract representative samples that are treated as approximate histograms. The area fractions are estimated as the coefficients that minimize the square difference between the linear combination of histograms and the histogram of the entire image. As compared to previous implementations of this method, the tool introduces the constraint of unitary sum of area fractions through the Lagrange multipliers technique. The tool was implemented in the Java language using the JAMA library (Java Matrix Package) and was added to Arthemis image processing and analysis software, developed by LACA/UFSM the research group.