Histogram-Tensorial Gaussian Representations and its Applications to Facial Analysis

We present a tensorial framework based in Histograms of Gaussian Binary Maps for facial analysis. The chapter defines and discusses the different steps to build a tensorial representation taking into account the different possible dimensions as orientation, position and scale using the Gaussian derivatives and LBP (Local Binary Patterns). In this chapter, we also consider two different tensorial architectures, the first considers each one of derivative orders as a separate tensor and the second considers the correlation between derivatives when the order is added as supplementary dimension in the final tensor. In addition Multilinear Principal Component Analysis is presented as an algorithm to reduce the dimensions in a tensor without loss of 3-D structure due to vectorization and also as a statistical method for capturing the most discriminative information from each considered dimension in the tensors. Finally, we combine different machine learning methods with our tensorial representation for improving results in Face recognition and Age estimation. In this scope, face recognition is addressed as a classification problem using Kernel Discriminative Vectors to improve recognition rates. On the other hand, Age estimation is addressed as a regression problem using Relevance Vector Machines (RVM).

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