Deep Learning Approaches for PDE-based Image Analysis and Beyond: From the Total Variation Flow to Medieval Paper Analysis
type: CreativeWork
description: Partial differential equations (PDEs) play a fundamental role in the mathematical modelling of many processes and systems in physical, biological and other sciences, as well as in engineering and computer science. Image analysis is a prime example for a field where PDEs have triggered many innovations. One such PDE that has gained considerable attention in the last few years is the total variation (TV) flow. The TV flow generates a scale-space representation of an image based on the TV functional. This gradient flow has desirable features for images such as sharp edges and enables spectral, scale, and texture analysis. Based on the solution to the TV flow, a non-linear spectral decomposition can be derived. Due to its ability to extract spectral components corresponding to objects of different size and contrast, such decompositions enable filtering, feature transfer, image fusion and other applications. However, obtaining the spectral TV decomposition involves solving multiple non-smooth optimisation problems to solve the governing PDE - the TV flow - and is therefore computationally highly intensive. In the first part of the thesis, we present a supervised neural network approximation of the spectral TV decomposition which significantly speeds up its numerical solution. We report up to four orders of magnitude speedup in processing of mega-pixel size images, compared to classical GPU implementations of spectral TV. Our proposed network, the TVspecNET, is able to implicitly learn the underlying PDE and, despite being entirely data-driven, inherits equivariances of the model-based transform. To the best of our knowledge, this is the first approach towards learning a non-linear spectral decomposition of images. The TVspecNET, however, is designed as a supervised learning approach and in that relies on ground truth data. It is additionally constrained to produce fixed spectral bands of the image. We therefore extend the work to learn the TV flow solution in the third p…
abstract: Partial differential equations (PDEs) play a fundamental role in the mathematical modelling of many processes and systems in physical, biological and other sciences, as well as in engineering and computer science. Image analysis is a prime example for a field where PDEs have triggered many innovations. One such PDE that has gained considerable attention in the last few years is the total variation (TV) flow. The TV flow generates a scale-space representation of an image based on the TV functional. This gradient flow has desirable features for images such as sharp edges and enables spectral, scale, and texture analysis. Based on the solution to the TV flow, a non-linear spectral decomposition can be derived. Due to its ability to extract spectral components corresponding to objects of different size and contrast, such decompositions enable filtering, feature transfer, image fusion and other applications. However, obtaining the spectral TV decomposition involves solving multiple non-smooth optimisation problems to solve the governing PDE - the TV flow - and is therefore computationally highly intensive. In the first part of the thesis, we present a supervised neural network approximation of the spectral TV decomposition which significantly speeds up its numerical solution. We report up to four orders of magnitude speedup in processing of mega-pixel size images, compared to classical GPU implementations of spectral TV. Our proposed network, the TVspecNET, is able to implicitly learn the underlying PDE and, despite being entirely data-driven, inherits equivariances of the model-based transform. To the best of our knowledge, this is the first approach towards learning a non-linear spectral decomposition of images. The TVspecNET, however, is designed as a supervised learning approach and in that relies on ground truth data. It is additionally constrained to produce fixed spectral bands of the image. We therefore extend the work to learn the TV flow solution in the third p…
author: Großmann, Tamara
language: eng
keywords: Deep Learning, Finite Element Method, Image Analysis, Image Processing, Medieval Paper Analysis, Neural Networks, Partial Differential Equations, Physics-Informed Neural Networks, Spectral Total Variation Decomposition, Total Variation Flow
license: https://apollo8-f-pro.lib.cam.ac.uk/bitstreams/ed4f9d89-96ff-48ca-a424-3df455024dd0/download
license: https://www.rioxx.net/licenses/all-rights-reserved/
date published: 2023-09-02
date modified: 2026-07-22T22:24:31Z
provider: Cambridge University
publisher: Networked Digital Library of Theses and Dissertations
type: WebPage
source organization: University of Cambridge

PropertyValue
property ID: DOI
value: 10.17863/CAM.106705