Diffusion models and their accelerated solution in image and surface processing.
Discrete approximation of the Mumford-Shah functional in dimension two
Discrete approximation of the Mumford-Shah functional in dimension two
The Mumford-Shah functional, introduced to study image segmentation problems, is approximated in the sense of vergence by a sequence of integral functionals defined on piecewise affine functions.
Efficient generation of 3D surfel maps using RGB-D sensors
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...
Efficient reductions of picture words
Einige geometrische Aspekte der Bildverarbeitung
Electrical Impedance Tomography: from topology to shape
Employing different loss functions for the classification of images via supervised learning
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
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
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
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.
Fingerprint identification based on dermatological features.
Finite nondense point set analysis
The paper deals with the decomposition and with the boundarz and hull construction of the so-called nondense point set. This problem and its applications have been frequently studied in computational geometry, raster graphics and, in particular, in the image processing (see e.g. [3], [6], [7], [8], [9], [10]). We solve a problem of the point set decomposition by means of certain relations in graph theory.
Finite volume schemes for the generalized subjective surface equation in image segmentation
In this paper, we describe an efficient method for 3D image segmentation. The method uses a PDE model – the so called generalized subjective surface equation which is an equation of advection-diffusion type. The main goal is to develop an efficient and stable numerical method for solving this problem. The numerical solution is based on semi-implicit time discretization and flux-based level set finite volume space discretization. The space discretization is discussed in details and we introduce three...
Finite-differences discretizations of the Mumford-Shah functional
Finite-differences discretizations of the mumford-shah functional
About two years ago, Gobbino [21] gave a proof of a De Giorgi's conjecture on the approximation of the Mumford-Shah energy by means of finite-differences based non-local functionals. In this work, we introduce a discretized version of De Giorgi's approximation, that may be seen as a generalization of Blake and Zisserman's “weak membrane” energy (first introduced in the image segmentation framework). A simple adaptation of Gobbino's results allows us to compute the Γ-limit of this discrete functional...
Fourth-order partial differential equations for effective image denoising.
Fractal image coding by multi-scale selection based on block complexity.
Fractional regularization term for variational image registration.
Free Discontinuity problems with unbounded Data: the two dimensional case.