On Box-Cox Transformation for Image Normality and Pattern Classification

Abstract: A unique member of the power transformation family is known as the Box-Cox transformation. The latter can be seen as a mathematical operation that leads to finding the optimum lambda ({\lambda}) value that maximizes the log-likelihood function to transform a data to a normal distribution and to reduce heteroscedasticity. In data analytics, a normality assumption underlies a variety of statistical test models. This technique, however, is best known in statistical analysis to handle one-dimensional data. Herein, this paper revolves around the utility of such a tool as a pre-processing step to transform two-dimensional data, namely, digital images and to study its effect. Moreover, to reduce time complexity, it suffices to estimate the parameter lambda in real-time for large two-dimensional matrices by merely considering their probability density function as a statistical inference of the underlying data distribution. We compare the effect of this light-weight Box-Cox transformation with well-established state-of-the-art low light image enhancement techniques. We also demonstrate the effectiveness of our approach through several test-bed data sets for generic improvement of visual appearance of images and for ameliorating the performance of a colour pattern classification algorithm as an example application. Results with and without the proposed approach, are compared using the AlexNet (transfer deep learning) pretrained model. To the best of our knowledge, this is the first time that the Box-Cox transformation is extended to digital images by exploiting histogram transformation.