The Mumford-Shah conjecture in image processing
The outlook for mathematics on the web.
The polar form of a polynomial surface.
The Rooted Tree Embedding Problem into Points in the Plane.
The structure-from-motion reconstruction pipeline – a survey with focus on short image sequences
The problem addressed in this paper is the reconstruction of an object in the form of a realistically textured 3D model from images taken with an uncalibrated camera. We especially focus on reconstructions from short image sequences. By means of a description of an easy to use system, which is able to accomplish this in a fast and reliable way, we give a survey of all steps of the reconstruction pipeline. For the purpose of developing a coherent reconstruction system it is necessary to integrate...
The tree of shapes of an image
In [30], Kronrod proves that the connected components of isolevel sets of a continuous function can be endowed with a tree structure. Obviously, the connected components of upper level sets are an inclusion tree, and the same is true for connected components of lower level sets. We prove that in the case of semicontinuous functions, those trees can be merged into a single one, which, following its use in image processing, we call “tree of shapes”. This permits us to solve a classical representation...
The tree of shapes of an image
In [CITE], Kronrod proves that the connected components of isolevel sets of a continuous function can be endowed with a tree structure. Obviously, the connected components of upper level sets are an inclusion tree, and the same is true for connected components of lower level sets. We prove that in the case of semicontinuous functions, those trees can be merged into a single one, which, following its use in image processing, we call “tree of shapes”. This permits us to solve a classical representation problem...
The Upper Envelope of Piecewise Linear Functions: Algorithms and Applications.
The Upper Envelope of Voronoi Surfaces and Its Applications.
Tight Upper Bounds for the Discrepancy of Half-Spaces.
Tiling Polygons with Parallelograms.
Time Stamping Preprint and Electronic Journal Server Environment
The exchange of preprints and journals plays an important role to communicate new research ideas and results in many academic fields. Distribution of preprints and journal articles by electronic file via the Internet has become a primary method in addition to paper publication. Electronic preprints and articles in the paperless era should be certified in terms of existence proof and tamper resistance because they are easily modified by their site administrator. We developed a secure preprint and...
Time-delay regularization of anisotropic diffusion and image processing
We study a time-delay regularization of the anisotropic diffusion model for image denoising of Perona and Malik [IEEE Trans. Pattern Anal. Mach. Intell 12 (1990) 629–639], which has been proposed by Nitzberg and Shiota [IEEE Trans. Pattern Anal. Mach. Intell 14 (1998) 826–835]. In the two-dimensional case, we show the convergence of a numerical approximation and the existence of a weak solution. Finally, we show some experiments on images.
Time-delay regularization of anisotropic diffusion and image processing
We study a time-delay regularization of the anisotropic diffusion model for image denoising of Perona and Malik [IEEE Trans. Pattern Anal. Mach. Intell12 (1990) 629–639], which has been proposed by Nitzberg and Shiota [IEEE Trans. Pattern Anal. Mach. Intell14 (1998) 826–835]. In the two-dimensional case, we show the convergence of a numerical approximation and the existence of a weak solution. Finally, we show some experiments on images.
Time-delayed Perona-Malik type problems.
Towards a Digital Mathematical Library
The workshop’s objectives were to formulate the strategy and goals of a global mathematical digital library and to summarize the current successes and failures of ongoing technologies and related projects. There is already some experience with building smaller DMLs and/or building big thematical scientific digital libraries. Why there are already big fulltext digital library in some domains like PubMed in biomedical one, but none in others? We try to pose such and other questions, and try to find...
Towards a Digital Mathematics Library. On the Crossroad
The DML workshop’s objectives were to formulate the strategy and goals of a global mathematical digital library and to summarize the current successes and failures of ongoing technologies and related projects. There is already experience with building regional DMLs or building big thematic scientific digital libraries. EuDML project reached it halflife period. While there are already big fulltext digital libraries in some domains like PubMed Central in the biomedical domain, Inspire in high-energy...
Towards a Flexible Author Name Disambiguation Framework
In this paper we propose a flexible, modular framework for author name disambiguation. Our solution consists of the core which orchestrates the disambiguation process, and replaceable modules performing concrete tasks. The approach is suitable for distributed computing, in particular it maps well to the MapReduce framework. We describe each component in detail and discuss possible alternatives. Finally, we propose procedures for calibration and evaluation of the described system.
Towards Reverse Engineering of PDF Documents
We present a progress report on our ongoing project of reverse engineering scientific PDF documents. The aim is to obtain mathematical markup that can be used as source for regenerating a document that resembles the original as closely as possible. This source can then be a basis for further document processing. Our current tool uses specialised PDF extraction together with image analysis to produce near perfect input for parsing mathematical formula. Applying a linear grammar and specific drivers...
Towards Sub-cellular Modeling with Delaunay Triangulation
In this article a novel model framework to simulate cells and their internal structure is described. The model is agent-based and suitable to simulate single cells with a detailed internal structure as well as multi-cellular compounds. Cells are simulated as a set of many interacting particles, with neighborhood relations defined via a Delaunay triangulation. The interacting sub-particles of a cell can assume specific roles – i.e., membrane sub-particle, internal sub-particle, organelles, etc –,...