Abordagens computacionais para calcular componentes principais ponderadas com aplicações em análise de imagens de faces humanas

• Autor(a) principal: Miranda, Laura Costa Pereira
• Data de Publicação: 2023
• Tipo de documento: Dissertação
• Idioma: por
• Título da fonte: Biblioteca Digital de Teses e Dissertações do LNCC
• Texto Completo: https://tede.lncc.br/handle/tede/383
• topic: Processamento de imagens - Modelos matemáticos; Reconhecimento de faces; Análise de componentes principais; CNPQ::ENGENHARIAS

Despite the efficiency of principal components analysis (Principal Components Analysis - P CA) as an unsupervised method for dimensionality reduction, its algorithm does not incorporate prior information extracted from the specific domain corresponding to the data. One way to address this limitation of P CA is to use spatial weights computed from the data itself, generating weighting maps, which we also call computational maps. In this context, the main objective of this work is to investigate the efficiency of weighting techniques for the design of principal components in gender and facial expression experi- ments, considering classification and reconstruction problems. Specifically, the methodology consists of generating spatial weights to weight the pixels of the input images, translated in relation to the global average of the data. Then, the weighted data is used as input for the traditional P CA algorithm. The method thus obtained is called weighted P CA. Such a data-driven approach has been employed in the literature through the calculation of linear classifiers and discriminant analysis techniques. In this dissertation, we propose other alternatives and analyze the results obtained in the problems of interest. We consider the following techniques for calculating spatial weights: (a) Shannon entropy computed pixel-by-pixel (H); (b) Inverse of Shannon Entropy (̂H); (c) Jensen-Shannon divergence (JS); (d) Student’s t-test (T ); (e) Hyperplanes computed using Smooth Support Vector Machine (W ). The technique (e) is known in the literature for the method in focus, being chosen as a reference for comparison with our proposals. The maps obtained by method (d) are used in face analysis, however, in different methodologies from that addressed in this dissertation. The application of Student’s t-test, Shannon entropy and its inverse, and Jensen-Shannon divergence to calculate spatial weights to compute the weighted P CA for face recognition is the main contribution of this work. The evaluation of the efficiency of the different principal components obtained from each technique is done through visualization, analysis of image reconstruction results and classification. For the latter, the following classifiers were used: Mahalanobis Distance (DM ) and K-Nearest Neighbors (KN N ), with K = 1. The computed weights may form a noisy weight map, which can introduce artifacts in the reconstruction and interfere with the classification. In order to reduce such effects, the computational maps were processed using a methodology based on quadtree, generating new maps, Hqt,̂ Hqt, JSqt, Tqt e Wqt, to reduce small local variations. The use of quadtree in the processing of spatial maps to compute the weighted P CA is another contribution of this work. The computational experiments were carried out using the FEI face image database, which consists of 400 images, 200 of men and 200 of women, where each subject is pictured with facial expressions of smiling and neutral. Another database used was the FERET one, consisting of 400 images, 214 of men and 186 of women, where each subject is pictured with facial expressions smiling and neutral. The results demonstrated the efficiency of the weighted versions of P CA especially when we applied the KN N classifier. In this case, the T ,̂ H, Hqt and̂ Hqt methods achieve the best results. In the case of reconstruction, there is a predominance of superior results for P CA in relation to the others, followed by the JS and W methods. The experiments were reworked with the statistical maps obtained after processing via quadtree, showing improved classification results for thê H and H methods, and showing improved reconstruction results for the W method.