High-Level Hessian-Based Image Processing with the Frangi Neuron

Abstract

The Frangi neuron proposed in this work is a complex element that allows high-level Hessian-based image processing. Its adaptive parameters (weights) can be trained using a minimum number of training data. In our experiment, we showed that just one image is enough to optimize the values of the weights. An intuitive application of the Frangi neuron is to use it in image segmentation process. In order to test the performance of the Frangi neuron, we used diverse medical datasets on which second-order structures are visualized. The Frangi network presented in this paper trained on a single image proved to be significantly more effective than the U-net trained on the same dataset. For the datasets tested, the network performed better as measured by area under the curve receiver operating characteristic (ROC AUC) than U-net and the Frangi algorithm. However, the Frangi network performed several times faster than the non-GPU implementation of Frangi. There is nothing to prevent the Frangi neuron from being used as part of any other network as a component to process two-dimensional images, for example, to detect certain second-order features in them.