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Discrete entropy is used to measure the content of an image, where a higher value indicates an image with richer details. Infrared images are capable of revealing important hidden targets. The disadvantage of this type of image is that their low contrast and level of detail are not consistent with human visual perception. These problems can be caused by variations of the environment or by limitations of the cameras that capture the images. In this work we propose a method that improves the details of infrared images, increasing their entropy, preserving their natural appearance, and enhancing contrast. The proposed method extracts multiple features of brightness and darkness from the infrared image. This is done by means of the multiscale top-hat transform. To improve the infrared image, multiple scales are added to the bright areas and multiple areas of darkness are subtracted. The method was tested with 450 infrared thermal images from a public database. Evaluation of the experimental results shows that the proposed method improves the details of the image by increasing entropy, also preserving natural appearance and enhancing the contrast of infrared thermal images.

Interaction between variables is often found in statistical models, and it is usually expressed in the model as an additional term when the variables are numeric. However, when the variables are categorical (also known as nominal or qualitative) or mixed numerical-categorical, defining, detecting, and measuring interactions is not a simple task. In this work, based on an entropy-based correlation measure for n nominal variables (named as Multivariate Symmetrical Uncertainty (MSU)), we propose a formal and broader definition for the interaction of the variables. Two series of experiments are presented. In the first series, we observe that datasets where some record types or combinations of categories are absent, forming patterns of records, which often display interactions among their attributes. In the second series, the interaction/non-interaction behavior of a regression model (entirely built on continuous variables) gets successfully replicated under a discretized version of the dataset. It is shown that there is an interaction-wise correspondence between the continuous and the discretized versions of the dataset. Hence, we demonstrate that the proposed definition of interaction enabled by the MSU is a valuable tool for detecting and measuring interactions within linear and non-linear models.