Introducing elements of fractal geometry into deep convolutional neural networks: an application to the recognition and categorization of lung cancer

Abstract

This project proposes the study and development of a computational methodology for the analysis of images introducing elements of fractal theory into deep convolutional neural networks. Although these networks have become ubiquitous in computer vision, and in particular in the analysis of medical images, classical theories such as fractal geometry can still be very useful, among other reasons, for allowing a modeling with more direct interpretation and not need so much data for training. In this context, we propose the introduction of theoretical and technical concepts of fractal geometry into the pipeline of convolutional neural networks. The process takes place under three perspectives: the input, output and the network architecture. As for the input, a multifractal transformation is applied to the original image. At the output, the fractal dimension and/or multifractal spectrum of the convolutional layer feature maps will be calculated. Both solutions will be implemented directly in the network layers, through convolutions and other operators. With regards to the architecture, self-similar information flows will be used replacing residual architectures. The developed methodology will be applied to a problem in the medical area, which is the identification and categorization of lung cancer sub-types from microscopic images, using both histological and cytological samples. We expect that the results obtained will represent important theoretical and practical advances. In theoretical terms, the proposal aims to investigate the possibility of improvements in automatic learning algorithms for image classification, both in the classification accuracy, as well as in the lower sensitivity to a smaller amount of training data. In practical terms, useful implications for society are expected, through a better understanding of carcinogenic processes in this way promoting possibilities for both an earlier diagnosis and more effective treatment, improving the life quality and expectancy of the patient . (AU)