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Functional Data Analysis Applied to Descriptors Generation of Multiscale Fractal Dimension Signatures.

João Batista Florindo

Instituto de Física de São Carlos - Universidade de São Paulo, 2009

This work studies the application of a statistical technique named Functional Data Analysis (FDA) for the generation of descriptors. These descriptors can be used for pattern recognition, more specifically, for the recognition of relevant objects in an image. These objects can be represented by features vectors, also known as signatures, obtained by a technique named Multi-scale Fractal Dimension (MFD). These vectors present a high dimensionality (number of elements), causing to be necessary the use of an approach for the reduction of this number of values, but without a large loss of information carried by the signature. In this context, several techniques for the extraction of a reduced set of signature descriptors are studied in the literature. Among these techniques, the most classic are Fourier and wavelets, both with simple presentation and providing satisfactory results. The proposal presented here is the use of FDA combined with MFD for the generation of pattern descriptors. The results obtained by the use of this approach for the generation of descriptors showed that this technique allows the obtention of good results, even in situations in wich is not possible the use of many descriptors. FDA was also applied to the extraction of descriptors of MFD texture signatures. Also in this case, the results were interesting. The experiments showed the FDA presents a good potential for the application to this type of problem, allowing the obtention of good results even by using a few descriptors. It is suggested future works in which FDA can be used, researching for still more efficient methods.

keywords: Functional data analysis, Multi-scale fractal dimension, Pattern recognition. Fractal descriptors