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...
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....
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...
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...
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.