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Level sets of continuous functions increasing with respect to each variable

100%

Sajbura K.

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

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2005

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tom 25

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nr 1

19-26

EN

We are going to prove that level sets of continuous functions increasing with respect to each variable are arcwise connected (Theorem 3) and characterize those of them which are arcs (Theorem 2). In [3], we will apply the second result to the classical linear functional equation φ∘f = gφ + h (cf., for instance, [1] and [2]) in a case not studied yet, where f is given as a pair of means, that is so-called mean-type mapping.

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Integrated region-based segmentation using color components and texture features with prior shape knowledge

88%

Emambakhsh M., Ebrahimnezhad H., Sedaaghi M.

International Journal of Applied Mathematics and Computer Science

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2010

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tom 20

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nr 4

711-726

EN

Segmentation is the art of partitioning an image into different regions where each one has some degree of uniformity in its feature space. A number of methods have been proposed and blind segmentation is one of them. It uses intrinsic image features, such as pixel intensity, color components and texture. However, some virtues, like poor contrast, noise and occlusion, can weaken the procedure. To overcome them, prior knowledge of the object of interest has to be incorporated in a top-down procedure for segmentation. Consequently, in this work, a novel integrated algorithm is proposed combining bottom-up (blind) and top-down (including shape prior) techniques. First, a color space transformation is performed. Then, an energy function (based on nonlinear diffusion of color components and directional derivatives) is defined. Next, signeddistance functions are generated from different shapes of the object of interest. Finally, a variational framework (based on the level set) is employed to minimize the energy function. The experimental results demonstrate a good performance of the proposed method compared with others and show its robustness in the presence of noise and occlusion. The proposed algorithm is applicable in outdoor and medical image segmentation and also in optical character recognition (OCR).

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Optimal internal dissipation of a damped wave equation using a topological approach

88%

Münch A.

International Journal of Applied Mathematics and Computer Science

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2009

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tom 19

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nr 1

15-37

EN

We consider a linear damped wave equation defined on a two-dimensional domain Ω, with a dissipative term localized in a subset ω. We address the shape design problem which consists in optimizing the shape of ω in order to minimize the energy of the system at a given time T . By introducing an adjoint problem, we first obtain explicitly the (shape) derivative of the energy at time T with respect to the variation in ω. Expressed as a boundary integral on ∂ω, this derivative is then used as an advection velocity in a Hamilton-Jacobi equation for shape changes. We use the level-set methodology on a fixed working Eulerian mesh as well as the notion of the topological derivative. We also consider optimization with respect to the value of the damping parameter. The numerical approximation is presented in detail and several numerical experiments are performed which relate the over-damping phenomenon to the well-posedness of the problem.

Ograniczanie wyników

2 International Journal of Applied Mathematics and Computer Science

1 Discussiones Mathematicae, Differential Inclusions, Control and Optimization

1 Ebrahimnezhad H.

1 Emambakhsh M.

1 Münch A.

1 Sajbura K.

1 Sedaaghi M.

1 2010

1 2009

1 2005

Level sets of continuous functions increasing with respect to each variable

Integrated region-based segmentation using color components and texture features with prior shape knowledge

Optimal internal dissipation of a damped wave equation using a topological approach