Automatic design of W-operators using membership functions: a case study in brain MRI segmentation

A W-operator is an image transformation that is locally defined inside a window W, invariant to translations. The automatic design of the W-operators consists of the design of functions, whose domain is a set of patterns or vectors obtained by translating a window through training images and the output of each vector is a class or label. The main difficulty to consider when designing W-operators is the generalization problem that occurs due to lack of training images. In this work, we propose the use of membership functions to solve the generalization problem in gray level images. Membership functions are defined from the training images to model regions that are often inaccurate due to ambiguous gray levels in the images. This proposal was applied to brain magnetic resonance image segmentation to test its performance in a field of interest in biomedical images. The experiments were carried out with different numbers of training and test images, windows sizes of \(3\times 3\), \(5\times 5\), \(7\times 7\), \(11\times 11\), and \(15\times 15\), and images with noise levels at 0, 1, 3, 5, 7, and 9\(\%\). To calculate the performance of each designed W-operator, the classification error, sensitivity, and specificity were used. From the experimental results, it was concluded that the best performance is achieved with a window of size \(3\times 3\). In images with noise levels from 1 to 5\(\%\), the classification error is less than 4\(\%\) and the sensitivity and specificity are greater than 94 and 98\(\%\), respectively.