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Efficient generation of 3D surfel maps using RGB-D sensors

Artur Wilkowski, Tomasz Kornuta, Maciej Stefańczyk, Włodzimierz Kasprzak (2016)

International Journal of Applied Mathematics and Computer Science

The article focuses on the problem of building dense 3D occupancy maps using commercial RGB-D sensors and the SLAM approach. In particular, it addresses the problem of 3D map representations, which must be able both to store millions of points and to offer efficient update mechanisms. The proposed solution consists of two such key elements, visual odometry and surfel-based mapping, but it contains substantial improvements: storing the surfel maps in octree form and utilizing a frustum culling-based...

Employing different loss functions for the classification of images via supervised learning

Radu Boţ, André Heinrich, Gert Wanka (2014)

Open Mathematics

Supervised learning methods are powerful techniques to learn a function from a given set of labeled data, the so-called training data. In this paper the support vector machines approach is applied to an image classification task. Starting with the corresponding Tikhonov regularization problem, reformulated as a convex optimization problem, we introduce a conjugate dual problem to it and prove that, whenever strong duality holds, the function to be learned can be expressed via the dual optimal solutions....

Enhanced electrical impedance tomography via the Mumford–Shah functional

Luca Rondi, Fadil Santosa (2001)

ESAIM: Control, Optimisation and Calculus of Variations

We consider the problem of electrical impedance tomography where conductivity distribution in a domain is to be reconstructed from boundary measurements of voltage and currents. It is well-known that this problem is highly illposed. In this work, we propose the use of the Mumford–Shah functional, developed for segmentation and denoising of images, as a regularization. After establishing existence properties of the resulting variational problem, we proceed by demonstrating the approach in several...

Enhanced Electrical Impedance Tomography via the Mumford–Shah Functional

Luca Rondi, Fadil Santosa (2010)

ESAIM: Control, Optimisation and Calculus of Variations

We consider the problem of electrical impedance tomography where conductivity distribution in a domain is to be reconstructed from boundary measurements of voltage and currents. It is well-known that this problem is highly illposed. In this work, we propose the use of the Mumford–Shah functional, developed for segmentation and denoising of images, as a regularization. After establishing existence properties of the resulting variational problem, we proceed by demonstrating the approach in several...

EuDML—Towards the European Digital Mathematics Library

Sylwestrzak, Wojtek, Borbinha, José, Bouche, Thierry, Nowiński, Aleksander, Sojka, Petr (2010)

Towards a Digital Mathematics Library. Paris, France, July 7-8th, 2010

The paper describes the background, the expected functionalities, and the architecture design goals of the European Digital Mathematics Library (Eu-DML), an infrastructure system aimed to integrate the mathematical contents available online throughout Europe, allowing for both extensive and specialized mathematics resource discovery. The three years long project to build the EuDML, partially funded by the European Commission, started in February 2010.

Explicit integration of equations of motion solved on computer cluster

Rek, Václav (2019)

Programs and Algorithms of Numerical Mathematics

In the last decade the dramatic onset of multicore and multi-processor systems in combination with the possibilities which now provide modern computer networks have risen. The complexity and size of the investigated models are constantly increasing due to the high computational complexity of computational tasks in dynamics and statics of structures, mainly because of the nonlinear character of the solved models. Any possibility to speed up such calculation procedures is more than desirable. This...

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