Nonlocal models for image processing: properties and applications,
Eduardo Cuesta (Department of Applied Mathematics, Institute of Mathematics University of Valladolid, Spain)
23 May 2014, 14:30, Auditorium 1, Subunit 1 FMUC (Health Sciences Campus, at IBILI)
One of the alternatives for the mathematical formulation of image processing problems is based on local, nonlinear PDEs models. In the first part of the talk, a brief overview of them, with special regards to morphological and structural properties, will be done. In the second part, some recent results related to the extension of these properties to non-local evolutionary integral models, will be presented. Finally, the third part of the talk will be devoted to the practical implementation of these models and their application in different areas, including medical image processing and satellite image classification.
 E. Cuesta and J. Finat, Image processing by means of a linear integro-differential equation, IASTED 438-442 (2003).
 E. Cuesta, M. Kirane and S.A. Malik, Image structure preserve denoting using generalized fractional time integrals, Signal Processing 92 553-563 (2012).
 E. Cuesta, A. Durán and M. Kirane, On evolutionary integral models dor image restoration (submitted)
Joint work with: A. Durán, M. Kirane and C. Quintano.
Design and assembly of OCT systems,
Carla Carmelo Rosa (INESC Tec & Dep. FÝsica e Astronomia FCUP, Porto,
23 May 2014, 15:15, Auditorium 1, Subunit 1 FMUC (Health Sciences Campus, at IBILI)
In this talk important aspects of opto(mechanical) hardware design and signal processing algorithms development will be discussed, in the context of optical
coherence tomography systems, keeping in mind applications in the field of biomedical sciences and industry. Some results obtained with both multi-scan enface time-domain and fourier
domain OCT configurations developed in the lab will be presented.
Development of a DGTD Method for dispersive media with applications to bioelectromagnetics,
Stéphane Lanteri (INRIA Sophia Antipolis-Méditerranée, France)
31 October 2013, 14:30, Auditorium 1, Subunit 1 FMUC (Health Sciences Campus, at IBILI)
This study is concerned with the numerical modeling of the propagation of electromagnetic waves in dispersive media. Such propagation media are characterized by electromagnetic parameters (e.g. the electric permittivity) that depend on the frequency of the incident wave. There is a lot of practical problems that involve such propagation media as in particular situations for which one has to model the interaction of an electromagnetic wave with biological tissues. As a matter of fact, the numerical modeling of the propagation of electromagnetic waves through human tissues is at the heart of many biomedical applications such as breast imaging related to cancer tumor detection, the development of intelligent medical implants in the body or microwave based hyperthermia to kill cancer cells. For the numerical treatment of the propagation in dispersive media, methodological developments have focused for quite a long time on the Finite Difference Time Domain (FDTD) method. Numerical techniques based on the finite element method have also been investigated. These studies deal with NÚdÚlec elements and propose various proofs of convergence of semi-discrete schemes and in some cases of the fully discrete schemes with error estimates. In the present work we consider using a discontinuous Galerkin discretization method. The starting point of our study is the non-dissipative discontinuous Galerkin formulation presented in [Fezoui et al., 2005] for the Maxwell's equations in non-dispersive media. We propose an extension of this DGTD method to the case of a Debye type dispersive media but the proposed methodology can be extended to other dispersive models as well. We present some preliminary numerical results aiming at validating the accuracy of the resulting DGTD methodology.
[Fezoui et al., 2005] L. Fezoui, S. Lanteri, S. Lohrengel and S. Piperno, Convergence and stability of a Discontinuous Galerkin time-domain method for the 3D heterogeneous Maxwell equations on unstructured meshes ESAIM: Math. Model. and Numer. Anal., Vol. 39, No. 6, pp. 1149-1176 (2005)
Multiple Light Scattering & Radiative Transport (& Multiple Diffusions),
Eduardo Nunes-Pereira (Center of Physics (CFUM) & Department of Physics, University of Minho, Braga, Portugal)
31 October 2013, 15:15, Auditorium 1, Subunit 1 FMUC (Health Sciences Campus, at IBILI)
A stochastic theory for Multiple Light Scattering via Radiative Transport is reviewed. The model encompasses the regimes from weak to very strong scattering. Special emphasis is devoted to the description of the propagation of fluorescence in strongly scattering media. For incoherent radiative transport, space and time can be factored out and this is the main physical insight in the theory. Two cases are discussed: molecular fluorescence (radiative and combined radiative and radiationless transport mechanism) and atomic vapor fluorescence (anomalous diffusion; the the best knowledge of the author, currently the only case where the LÚvy Flight parameter can be computed a priori). The deviations from a diffusion equation model will be highlighted. The reviewed work is put into context by describing its links to anomalous diffusion models, LÚvy flights and walks, animal foraging, epidemics spreading and human population dynamics, fractional diffusion, imaging though turbid media, power and Pareto laws, Gaussian statistics and Bayesian inference.
Towards a virtual retina - a multidisciplinary approach,
Miguel Morgado (IBILI/DFUC, University of Coimbra, Portugal)
20 June 2012, 14:30, Auditorium 1, Subunit 1 FMUC (Health Sciences Campus, at IBILI)
On the separability of clusters,
Jorge Orestes Cerdeira (ISA/UTL, Technical University of Lisbon, Portugal)
20 June 2012, 15:00, Auditorium 1, Subunit 1 FMUC (Health Sciences Campus, at IBILI)
Separability of clusters is an issue that arises in many different
areas, and is often used in a rather vague and subjective manner.
We introduce a combinatorial notion of interiority to derive a global view
on separability of a set of entities.
We develop this approach further to evaluate the overall
separability of a partition in the context of cluster analysis.
Our approach captures combinatorial
and geometrical aspects of data and provides, in addition to
numerical evaluations, graphical representations
particularly useful when data can not be easily visualized.
We illustrate the methodology on some real and simulated datasets.
Joint work with MJ Martins and PC Silva
Sampling in 2D: specificities, difficulties and applications,
José Manuel Rebordão (DF/FCUL, University of Lisbon, Portugal)
20 June 2012, 16:00, Auditorium 1, Subunit 1 FMUC (Health Sciences Campus, at IBILI)
Sampling strategies are a fundamental part of any measurement process. In the signal framework (one-dimensional, 1D - usually the time), sampling is a well-controlled process. For two (images, 2D) and three (volumes, 3D) spatial dimensions, one is frequently faced with unknown objects or objects whose symmetries only become evident as the spatial resolution increases, being easy to get results that can either describe the reality or just be a set of artifacts resulting from the measurement process.
On the other hand, one increasingly deals with information brought to us through "displays" based on several techniques or produced by dynamic scanning processes. Due to its periodic or quasi-periodic nature, such mathematical objects do not always make possible the natural application of the Shannon theorem, confronting us with the need of different analysis methods.
This seminar aims to draw the attention to a variety of artifacts emerging when processing images, from which several applications arise, profiting both from their stability, or from their singular nature and instability.
Anomalous diffusion imaging through fractional order calculus,
Ercília Sousa (CMUC, Department of Mathematics, University of Coimbra, Portugal)
14 December 2011, 10:00, Auditorium 1, Subunit 1 FMUC (Health Sciences Campus, at IBILI)
Recently, non-Gaussian diffusion techniques have been used to investigate water diffusion in the human and the animal brain, providing evidence that a new kind of contrast can be obtained, which can be related to specific tissue features. One of the models developed to describe the anomalous diffusion consists of considering the Bloch-Torrey equation with fractional order derivatives, where a new set of parameters are considered to describe this anomalous process. Although, several issues remain to be clarified, to be certain of the success of using these models to describe diffusion in biologic tissues, they suggest a possible fractional order dynamic, in the observed diffusion-induced magnetization changes, and therefore anomalous diffusion can be a powerful tool to characterize tissue microstructures. We present a three-dimensional fractional Bloch-Torrey model and in order to give a more clear and detailed idea on how the solutions of such type of models can be computed numerically, we analyze a one dimensional version of the fractional model.
Applications of retinal imaging with photoreceptor resolution,
SÚrgio Nascimento (Center of Physics (CFUM), University of Minho, Braga, Portugal)
14 December 2011, 11:00, Auditorium 1, Subunit 1 FMUC (Health Sciences Campus, at IBILI)
Support vector machines in medical image analysis,
João Duarte (IBILI, University of Coimbra, Portugal)
13 May 2011, 14:30, room 5.5, DMUC
Support Vector Machines (SVM) are a classification tool with broad applications. The process is based on the representation of each element of the set in a multidimensional feature space.This machine learning method relies then on optimization to find a set of splitting hyperplanes that separate each class elements on a given labeled training set with maximum margin. This originates a classification on the feature space that is then used to classify other elements whose classification is unknown. The aim of this talk is to discuss the use of SVM in medical imaging, namely in image data acquired from optical coherence tomography (OCT) and magnetic resonance imaging (MRI). We are interested in image segmentation and image classification and will show some applications of SVM on current work developed at our institute.
Afonso Bandeira (Department of Mathematics, University of Coimbra, Portugal)
15 July 2010, 14:30, Auditorium JJ Pedroso de Lima IBILI, Subunit 1 FMUC (Health Sciences Campus, at IBILI)