Laboratory for Computational Mathematics

Advances in Image Processing and Inverse Problems: Applications in Medical and Earth Observation Imagery, and Biomathematics


Problem Description

This project focuses on the design and development of image processing and inverse methods for the solution of different problems arising in a variety of important applications, like medical and earth observation imagery, and biomathematics. The problems involve image segmentation, image registration, image denoising, as well as, parameter estimation, for which the intention is to apply partial differential equations and variational based methods, combined with methodologies from numerical mathematics and scientific computing (Starting date: July 01, 2013; Duration 24 months).

Modelling & Computational Challenges

Biomathematics goals: modeling and numerical simulation of the dynamics of some lesions, related to colorectal cancer, as well as, the estimation of physiologic parameters, impossible to be measured in vivo.

Image Processing goals:  development of fully automatic image processing and analysis tools, for medical and earth observation imagery. The main challenges consist in devising fast computerized methods with twofold objectives: i) to assist physicians as auxiliary screening/diagnosis/prognosis tools, ii) to assess, for safety and environment monitoring, industrial equipments, as well as, biomass quantification and evolution.

Research at LCM

For the biomathematics problems, convection-diffusion equations, combined with homogenization and multiscale methods will be used for handling periodic or oscillatory structures and microstructures. These will be linked with PDE constrained optimization methods for estimating some physiologic parameters.

For the image processing problems the main objective is to develop accurate lesion detectors in medical images, namely for identifying bleeding regions (in the small bowel) or colonic polyps (in the large bowel), in wireless capsule endoscopy images, or micro-aneurysms in ophthalmological images. 

Moreover efficient change detector functions for particular earth observation imagery (including satellite and radar images) will be studied.

Left: Original medical image showing two bleeding regions in the small bowel  (the two red spots). Image obtained with the wireless endoscopic capsule PillCam SB. Right: The corresponding processed image sequence,  where the two bleeding regions are clearly detected.

Original retinal fundus image (left) and the corresponding vessel network (extracted from its green channel texture component)

Papers & Reports

    [1] Isabel N. Figueiredo and Carlos Leal, Physiologic Parameter Estimation Using Inverse Problems, SIAM Journal on Applied Mathematics 73(3), (2013) 1164–1182

    [2] Isabel N. Figueiredo, Sunil Kumar, Carlos Leal and Pedro N. Figueiredo, Computer-assisted bleeding detection in wireless capsule endoscopy images, Computer Methods in Biomechanics and Biomedical Engineering: Imaging & Visualization (2013).

    [3] Isabel N. Figueiredo, Giuseppe Romanazzi, Carlos Leal and Bjorn Engquist, A Multiscale Model for Aberrant Crypt Foci, Procedia Computer Science 18 (2013) 1026 – 1035. 

    [4] Alexander V. Mamonov, Isabel N. Figueiredo, Pedro N. Figueiredo and Yen-Hsi Richard Tsai, Automated Polyp Detection in Colon Capsule Endoscopy, (submitted)

    [5] Isabel N. Figueiredo, Sunil Kumar and Pedro N. Figueiredo, An Intelligent System for Polyp Detection in Wireless Capsule Endoscopy Images, (submitted) 

    [6] Isabel N. Figueiredo, Sunil Kumar, Carlos Leal and Pedro N. Figueiredo, An Automatic Blood Detection Algorithm for Wireless Capsule Endoscopy Images, (submitted) 

    [7] Isabel N. Figueiredo, Júlio S. Neves, Susana Moura, Carlos M. Oliveira and João D. Ramos, Pattern Classes in Retinal Fundus Images Based on Function Norms, (submitted)


    • Lesion detectors - under  preparation (Matlab codes).

    Project Team

    • Isabel M. Narra de Figueiredo (LCM/CMUC, Project’s Principal Investigator, University of Coimbra)

    • Carlos M. Franco Leal (LCM/CMUC, University of Coimbra)

    • Ercília Cristina da Costa e Sousa (LCM/CMUC, University of Coimbra)

    • Gabriel Falcão Paiva Fernandes (Department of Electrical and Computer Engineering, University of Coimbra)

    • Gil Rito Gonçalves (Department of Mathematics, University of Coimbra)

    • Giuseppe Romanazzi (LCM/CMUC, University of Coimbra)

    • Júlio Severino das Neves (CMUC, University of Coimbra)

    • Pedro M. Narra de Figueiredo (Faculty of Medicine, University of Coimbra)

    • Sunil Kumar (PostDoctoral Fellow, Department of Mathematics, University of Coimbra)

    • Susana Margarida Pereira da Silva Domingues de Moura (CMUC, University of Coimbra)

    Project Reference

    FCT Research Project - PTDC/MAT-NAN/0593/2012