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- Models on variational methods for image processingPublication . Rodrigues, José AlbertoVariational image-processing models offer high-quality processing capabilities for imaging. They have been widely developed and used in the last two decades, enriching the fields of mathematics as well as information science. Mathematically, several tools are needed: energy optimization, regularization, partial differential equations, level set functions, and numerical algorithms. With this work we analyze some variational imageprocessing models.
- Multiscale stress analysis in CFRC using microscope image data of carbon fibresPublication . Graça, R. J. R.; Rodrigues, José Alberto; Loja, Amélia; Jorge, PedroComposite materials, are known as strong candidates to improve different kinds of structures. The micromechanical study of these materials is very important, because it may define the best composite characteristics to be used and/or predict more accurately its response. In the present work a multi-stage procedure comprising different fibre contour modelling strategies and a sequent hierarchic multiscale analysis is performed. With this study it is intended to achieve a more realistic characterization of the stresses maximum values for a set of case studies, through the use of fibre geometry data obtained from microscope images of carbon fibre laminated composites. The theoretical circular cross-section is also considered to enable a comparative study among the different situations.
- Using the finite element method to understand calculusPublication . Rodrigues, José Alberto; Loja, Amélia; Barbosa, JoaquimThis paper presents a complementary, alternative teaching and learning methodology based on the use of the finite element method to illustrate mathematical models and to explore their (numerical) solutions in the context of vector calculus properties understanding. This methodology is illustrated via a set of examples focused on specific engineering problems, but its scope can also be widened to other scientific areas. The examples presented on this paper allow concluding that this approach may be an interesting way to re-think and complement the perspective usually considered in the transmission of mathematical concepts. The use of a freeware finite element method computational package, FreeFEM++ may also be an important issue to stimulate the dissemination of this phenomena modelling and comprehension approach.
- Numerical modeling of cardiomyocytes using Finite Element MethodPublication . Oliveira, Joana; Rodrigues, José AlbertoIn recent years, the use of mathematical and geometrical models has been enabling the simulation of biological complex systems. Models of cardiac cells provide the possibility to understand the biochemistry and biomechanics of cardiac cells and cardiovascular diseases. The main objective of this work is to simulate the calcium flux and contractile activity of the cardiomyocyte, resorting on the Finite Element Method, and to develop a modelling tool with which we can simulate the key physiological aspects of the cardiac myocytes: Calcium concentration and contraction potential (% of shortening). To test our model's performance several tests were applied varying the local active cellular tension driven by the intracellular calcium concentration (Tu), and the position of T-tubules in the cell, from left to right and up to bottom. Our results show that the behaviour of our model is faithful to what is known to be true with the cell's physiology and pathological conditions.
- Developments on finite element methods for medical image supported diagnosticsPublication . Almeida, Ana; Barbosa, Joaquim; Carvalho, André; Loja, Amélia; Portal, Ricardo; Rodrigues, José Alberto; Vieira, Lina OliveiraVariational image-processing models offer high-quality processing capabilities for imaging. They have been widely developed and used in the last two decades, enriching the fields of mathematics as well as information science. Mathematically, several tools are needed: energy optimization, regularization, partial differential equations, level set functions, and numerical algorithms. For this work we consider a second-order variational model for solving medical image problems. The aim is to obtain as far as possible fine features of the initial image and identify medical pathologies. The approach consists of constructing a regularized functional and to locally analyse the obtained solution. Some parameters selection is performed at the discrete level in the framework of the finite element method. We present several numerical simulations to test the efficiency of the proposed approach.
- Models on variational methods for image processingPublication . Rodrigues, José AlbertoVariational image-processing models offer high-quality processing capabilities for imaging. They have been widely developed and used in the last two decades, enriching the fields of mathematics as well as information science. Mathematically, several tools are needed: energy optimization, regularization, partial differential equations, level set functions, and numerical algorithms. With this work we analyze some variational imageprocessing models.
- Finite element techniques for medical image processingPublication . Almeida, A.; Barbosa, Joaquim; Carvalho, A.; Loja, Amélia; Portal, Ricardo; Rodrigues, José Alberto; Vieira, L.We consider some second-order variational model for solving medical image problems. The aim is to obtain as far as possible fine features of the initial image and identify medical pathologies. The approach consists of constructing a family of regularized functionals and to select locally and adaptively the regularization parameters. The parameters selection is performed at the discrete level in the framework of the finite element method. We present several numerical simulations to test the efficiency of the proposed approach.