Multidimensional and fuzzy sample entropy (SampEnMF) for quantifying H&E histological images of colorectal cancer.

In this study, we propose to use a method based on the combination of sample entropy with multiscale and multidimensional approaches, along with a fuzzy function. The model was applied to quantify and classify H&E histological images of colorectal cancer. The multiscale approach was defined by analysing windows of different sizes and variations in tolerance for determining pattern similarity. The multidimensional strategy was performed by considering each pixel in the colour image as an n-dimensional vector, which was analysed from the Minkowski distance. The fuzzy strategy was a Gaussian function used to verify the pertinence of the distances between windows. The result was a method capable of computing similarities between pixels contained in windows of various sizes, as well as the information present in the colour channels. The power of quantification was tested in a public colorectal image dataset, which was composed of both benign and malignant classes. The results were given as inputs for classifiers of different categories and analysed by applying the k-fold cross-validation and holdout methods. The derived performances indicate that the proposed association was capable of distinguishing the benign and malignant groups, with values that surpassed those results obtained with important techniques available in the Literature. The best performance was an AUC value of 0.983, an important result, mainly when we consider the difficulties of clinical practice for the diagnosis of the colorectal cancer.