Construction of smooth maps with mean value coordinates

Bernstein polynomials are a classical tool in Computer Aided Design to create smooth maps with a high degree of local control. They are used for the construction of B\'ezier surfaces, free-form deformations, and many other applications. However, classical Bernstein polynomials are only defined for simplices and parallelepipeds. These can in general not directly capture the shape of arbitrary objects. Instead, a tessellation of the desired domain has to be done first. We construct smooth maps on arbitrary sets of polytopes such that the restriction to each of the polytopes is a Bernstein polynomial in mean value coordinates (or any other generalized barycentric coordinates). In particular, we show how smooth transitions between different domain polytopes can be ensured

Power assignment problems in wireless communication

A fundamental class of problems in wireless communication is concerned with the assignment of suitable transmission powers to wireless devices/stations such that the resulting communication graph satisfies certain desired properties and the overall energy consumed is minimized. Many concrete communication tasks in a wireless network like broadcast, multicast, point-to-point routing, creation of a communication backbone, etc. can be regarded as such a power assignment problem. This paper considers several problems of that kind; for example one problem studied before in (Vittorio Bil{\`o} et al: Geometric Clustering to Minimize the Sum of Cluster Sizes, ESA 2005) and (Helmut Alt et al.: Minimum-cost coverage of point sets by disks, SCG 2006) aims to select and assign powers to $k$ of the stations such that all other stations are within reach of at least one of the selected stations. We improve the running time for obtaining a $(1+\epsilon)$-approximate solution for this problem from $n^{((\alpha/\epsilon)^{O(d)})}$ as reported by Bil{\`o} et al. (see Vittorio Bil{\`o} et al: Geometric Clustering to Minimize the Sum of Cluster Sizes, ESA 2005) to $O\left( n+ {\left(\frac{k^{2d+1}}{\epsilon^d}\right)}^{ \min{\{\; 2k,\;\; (\alpha/\epsilon)^{O(d)} \;\}} } \right)$ that is, we obtain a running time that is \emph{linear} in the network size. Further results include a constant approximation algorithm for the TSP problem under squared (non-metric!) edge costs, which can be employed to implement a novel data aggregation protocol, as well as efficient schemes to perform $k$-hop multicasts

GPU point list generation through histogram pyramids

Image Pyramids are frequently used in porting non-local algorithms to graphics hardware. A Histogram pyramid (short: HistoPyramid), a special version of image pyramid, sums up the number of active entries in a 2D image hierarchically. We show how a HistoPyramid can be utilized as an implicit indexing data structure, allowing us to convert a sparse matrix into a coordinate list of active cell entries (a point list) on graphics hardware . The algorithm reduces a highly sparse matrix with N elements to a list of its M active entries in O(N) + M (log N) steps, despite the restricted graphics hardware architecture. Applications are numerous, including feature detection, pixel classification and binning, conversion of 3D volumes to particle clouds and sparse matrix compression

A framework for natural animation of digitized models

We present a novel versatile, fast and simple framework to generate highquality animations of scanned human characters from input motion data. Our method is purely mesh-based and, in contrast to skeleton-based animation, requires only a minimum of manual interaction. The only manual step that is required to create moving virtual people is the placement of a sparse set of correspondences between triangles of an input mesh and triangles of the mesh to be animated. The proposed algorithm implicitly generates realistic body deformations, and can easily transfer motions between human erent shape and proportions. erent types of input data, e.g. other animated meshes and motion capture les, in just the same way. Finally, and most importantly, it creates animations at interactive frame rates. We feature two working prototype systems that demonstrate that our method can generate lifelike character animations from both marker-based and marker-less optical motion capture data

A neighborhood-based approach for clustering of linked document collections

This technical report addresses the problem of automatically structuring linked document collections by using clustering. In contrast to traditional clustering, we study the clustering problem in the light of available link structure information for the data set (e.g., hyperlinks among web documents or co-authorship among bibliographic data entries). Our approach is based on iterative relaxation of cluster assignments, and can be built on top of any clustering algorithm (e.g., k-means or DBSCAN). These techniques result in higher cluster purity, better overall accuracy, and make self-organization more robust. Our comprehensive experiments on three different real-world corpora demonstrate the benefits of our approach

Axiomatic systems and topological semantics for intuitionistic temporal logic

We propose four axiomatic systems for intuitionistic linear temporal logic and show that each of these systems is sound for a class of structures based either on Kripke frames or on dynamic topological systems. Our topological semantics features a new interpretation for the `henceforth' modality that is a natural intuitionistic variant of the classical one. Using the soundness results, we show that the four logics obtained from the axiomatic systems are distinct. Finally, we show that when the language is restricted to the `henceforth'-free fragment, the set of valid formulas for the relational and topological semantics coincide

Combining linguistic and statistical analysis to extract relations from web documents

Search engines, question answering systems and classification systems alike can greatly profit from formalized world knowledge. Unfortunately, manually compiled collections of world knowledge (such as WordNet or the Suggested Upper Merged Ontology SUMO) often suffer from low coverage, high assembling costs and fast aging. In contrast, the World Wide Web provides an endless source of knowledge, assembled by millions of people, updated constantly and available for free. In this paper, we propose a novel method for learning arbitrary binary relations from natural language Web documents, without human interaction. Our system, LEILA, combines linguistic analysis and machine learning techniques to find robust patterns in the text and to generalize them. For initialization, we only require a set of examples of the target relation and a set of counterexamples (e.g. from WordNet). The architecture consists of 3 stages: Finding patterns in the corpus based on the given examples, assessing the patterns based on probabilistic confidence, and applying the generalized patterns to propose pairs for the target relation. We prove the benefits and practical viability of our approach by extensive experiments, showing that LEILA achieves consistent improvements over existing comparable techniques (e.g. Snowball, TextToOnto)