Introduction
Convolutional neural networks (CNNs) have been successfully applied to many image recognition/segmentation tasks. However, there are two main limitations of CNN. The first is that CNNs usually require a large amount of labelled image data, which might not be met in many applications. The second is that for large scale datasets, the training of CNNs is very time consuming. There is therefore need for further improvement of the efficiency of CNNs. This project aims to enhance the performance of CNNs for image analysis by exploring effective local descriptors of an image to accompany the data in CNNs, using rough paths theory and space-filling curves.
Explaining the science
A key step to improve the accuracy and efficiency of the CNN algorithm in image analysis is to find effective low-dimensional descriptors to summarise local information around each pixel as a feature set for consumption by a CNN. The signature of a path is a mathematical concept originated from rough paths theory (RPT) – a non-linear generalization of classical control theory with a control being very oscillatory in stochastic (random) analysis. The signature transformation can be used to summarise unparameterised data streams effectively with significant dimension reduction. As an example, for online Chinese handwritten character recognition, by combining the signature feature of pen trajectories over the sliding window and CNN, it's possible to increase accuracy significantly compared with CNN with raw data input.
See the related project 'Capturing complex data streams' for more information about rough path signatures.
Apart from online handwritten character recognition, the hybrid approach of combining the signature feature with machine learning methods has achieved state-of-the-art results in other applications, including mental health and action classification. Those successful applications empirically showed that the effectiveness of the signature feature is generic in capturing the order information in sequential data, ignoring time re-parameterisation.
By adding the signature feature as an extra layer of a CNN, it can boost performance of the learning algorithm. However, using the signature feature with image data is challenging as there is no generic time order. In order to tackle this problem, this work proposes the use of space-filling curves to transform image data into sequential data.
Project aims
The core objective of this project aims to design the effective 'signature feature' of image data for machine learning algorithms, using space-filling curves and rough paths theory, and build the theoretical foundation of the proposed method, i.e. the universality of the proposed feature - the so-called 'spatial signature' and its rotational invariant. In parallel to this, the project aims to apply the proposed methodology to enhance the accuracy and efficiency of deep-learning-based image segmentation methods in medical applications, which has significant potential impact in biomedical image analysis.
Applications
The proposed research can be applied to the medical imaging domain. For example, it is known that atrial fibrillation (AF) is the most common chronic cardiac dysrhythmia and causes considerable morbidity and mortality. Late gadolinium enhanced magnetic resonance imaging (LGE-MRI) is a safe, non-invasive and radiation free technique that can provide scar information prior to the ablation procedure, and scar detection is important for the treatment of AF. Fully automated segmentation of the atrial scarring is a difficult task due to variable LGE-MRI image quality and limited sample size.
The proposed algorithm in the project will be applied to LGE-MRI so as to improve the accuracy of scar segmentation. The datasets used in this project have been acquired as part of an NIHR funded clinical trial (Catheter Ablation Versus Thoracoscopic Surgical Ablation in Long Standing Persistent Atrial Fibrillation).
Recent updates
November 2019
The project team have organised a workshop on 19 November 2019 on mathematical and computational modelling for clinical data analysis, featured with the latest development of machine learning methods for medical image data analysis. More details of the workshop can be found here.