Università degli studi di Modena e Reggio Emilia

Image segmentation is a key topic in image processing and computer vision and several approaches have been proposed in the literature to address it. The formulation of the image segmentation problem as the minimization of the Mumford-Shah energy has been one of the most commonly used techniques in the last past decades. More recently, deep learning methods have yielded a new generation of image segmentation models with remarkable performance. In this paper we propose an unsupervised deep learning approach for piece-wise image segmentation based on the so called Deep Image Prior by parameterizing the Mumford-Shah functional in terms of the weights of a convolutional neural network. Several numerical experiments on both biomedical and natural images highlight the goodness of the suggested approach. The implicit regularization provided by the Deep Image Prior model allows to also consider noisy input images and to investigate the robustness of the proposed technique with respect to the level of noise.

It is well known that biomedical imaging analysis plays a crucial role in the healthcare sector and produces a huge quantity of data. These data can be exploited to study diseases and their evolution in a deeper way or to predict their onsets. In particular, image classification represents one of the main problems in the biomedical imaging context. Due to the data complexity, biomedical image classification can be carried out by trainable mathematical models, such as artificial neural networks. When employing a neural network, one of the main challenges is to determine the optimal duration of the training phase to achieve the best performance. This paper introduces a new adaptive early stopping technique to set the optimal training time based on dynamic selection strategies to fix the learning rate and the mini-batch size of the stochastic gradient method exploited as the optimizer. The numerical experiments, carried out on different artificial neural networks for image classification, show that the developed adaptive early stopping procedure leads to the same literature performance while finalizing the training in fewer epochs. The numerical examples have been performed on the CIFAR100 dataset and on two distinct MedMNIST2D datasets which are the large-scale lightweight benchmark for biomedical image classification.