Year: 2022
Type: preprint
Abstract: The total variation (TV) flow generates a scale-space representation of an image based on the TV functional. This gradient flow observes desirable features for images, such as sharp edges and enables spectral, scale, and texture analysis. Solving the TV flow is challenging; one reason is the the non-uniqueness of the subgradients. The standard numerical approach for TV flow requires solving multiple non-smooth optimisation problems. Even with state-of-the-art convex optimisation techniques, this is often prohibitively expensive and strongly motivates the use of alternative, faster approaches. Inspired by and extending the framework of physics-informed neural networks (PINNs), we propose the TVflowNET, an unsupervised neural network approach, to approximate the solution of the TV flow given an initial image and a time instance. The TVflowNET requires no ground truth data but rather makes use of the PDE for optimisation of the network parameters. We circumvent the challenges related to the non-uniqueness of the subgradients by additionally learning the related diffusivity term. Our approach significantly speeds up the computation time and we show that the TVflowNET approximates the TV flow solution with high fidelity for different image sizes and image types. Additionally, we give a full comparison of different network architecture designs as well as training regimes to underscore the effectiveness of our approach.
Source: arXiv (Cornell University)
Institutions: University of Cambridge, University of Bremen, University of Bath
Language: English
Subfield: Computer Vision and Pattern Recognition
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
Awards: Predicting Dementia: Optimising and translating AI to improve prognosis and clinical pathways, All in one cancer imaging optimisation using an integrated mathematical and deep learning approach, G2522634756, Robust and Efficient Analysis Approaches of Remote Imagery for Assessing Population and Forest Health in India, The Mathematics of Deep Learning, Regularisation theory in the data driven setting, G6084690111, EPSRC Centre for Mathematical and Statistical Analysis of Multimodal Clinical Imaging, All in one cancer imaging optimisation using an integrated mathematical and deep learning approach, G7293733238, G751609732, Combining Knowledge And Data Driven Approaches to Inverse Imaging Problems, G81539058, Predicting Dementia: Optimising and translating AI to improve prognosis and clinical pathways, G8402139738
OpenAlex ID: W4281843039