CONSTRUCTION OF DECISION RULES FOR FACE RECOGNITION BASED ON THE SQUARED MAHALANOBIS DISTANCE FOR NORMALIZED DATA
DOI:
https://doi.org/10.32782/IT/2023-2-6Keywords:
ace recognition, Mahalanobis distance, prediction ellipsoid, normalization, Dlib, multivariate normal distribution.Abstract
Face recognition is one of the tasks of pattern recognition, which is becoming more and more popular due to its wide application in computer vision, security systems, etc. The low probability of identifying a person by face can have negative consequences. Therefore, there is a need to develop and improve face recognition methods. One of the widely used pattern recognition methods is based on the application of decision rules based on the squared Mahalanobis distance. The squared Mahalanobis distance is used to construct the prediction ellipsoid. But a significant limitation of its use is the need to fulfill the assumption about the normality of the distribution of multidimensional data, the violation of which usually leads to a decrease in the probability of recognition. The aim of the work is to increase the probability of face recognition by building decision rules based on the squared Mahalanobis distance for ten-dimensional normalized data of face characteristics. A Python program was developed to obtain a vector of face characteristics using the Dlib library. The Mardia test was used to assess the deviation from the normal distribution of the data. It was investigated that the received samples of facial characteristics have a distribution that deviates from normal, so normalization was performed using the well-known one-dimensional transformation in the form of a decimal logarithm. Based on the squared Mahalanobis distance, decision rules are built in the form of ten-dimensional prediction ellipsoids for initial and normalized data. Decision rules built for normalized data showed a higher probability of recognizing faces. The results prove that normalization increases the probability of face recognition in case of significant deviation of the multidimensional distribution of face characteristics from normal. It was also found that in the case of high correlation between facial features, the application of one-dimensional normalizing transformations does not always lead to good recognition results. In this case, it is necessary to use multivariate normalizing transformations, such as Box-Cox or Johnson.
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