CNN for Efficient Objects Classification with Embedded Vector Fields

Classification methods use image object features to distinguish between objects and assign them to classes. In the present study we develop a convolutional neural network (CNN) optimized to classify images with embedded vector fields (VFs), generated on the solution \(\hat{u}(x,y)\) of the Poisson equation, which contains the image function in its right-hand side. The embedded VF features subject to extraction, by our CNN, are trajectories and singular points (SP), which augment the image object features. The aim of this paper is to validate that the set of augmented image features increases the separability of the image objects and improves the classification statistics. To reach the aim, we implement our CNN along with four contemporary CNNs to classify two public image databases COIL100 and ISIC2020 as well as their derivatives with embedded VFs. The obtained results are presented in the paper and confirm that embedding VFs with real and complex SPs increases the classification statistics.