Related papers: Three-dimensional alpha shapes
Traditional problems in computational geometry involve aspects that are both discrete and continuous. One such example is nearest-neighbor searching, where the input is discrete, but the result depends on distances, which vary continuously.…
Triangular decomposition is one of the standard ways to represent the radical of a polynomial ideal. A general algorithm for computing such a decomposition was proposed by A. Szanto. In this paper, we give the first complete bounds for the…
This paper defines, for each convex polytope $\Delta$, a family $H_w\Delta$ of vector spaces. The definition uses a combination of linear algebra and combinatorics. When what is called exact calculation holds, the dimension $h_w\Delta$ of…
This paper uses clustering algorithms to introduce a shape framework for deformable objects. Until now, the shape detection of the deformable objects has faced several challenges: 1) unable to form a unified framework for multiple shapes;…
Measurement is a fundamental building block of numerous scientific models and their creation. This is in particular true for data driven science. Due to the high complexity and size of modern data sets, the necessity for the development of…
This work studies path planning in two-dimensional space, in the presence of polygonal obstacles. We specifically address the problem of building a roadmap graph, that is, an abstract representation of all the paths that can potentially be…
What is the shape of the Universe? Is it curved or flat, finite or infinite ? Is space "wrapped around" to create ghost images of faraway cosmic sources? We review how tessellations allow to build multiply-connected 3D Riemannian spaces…
Forest automata (FA) have recently been proposed as a tool for shape analysis of complex heap structures. FA encode sets of tree decompositions of heap graphs in the form of tuples of tree automata. In order to allow for representing…
Metrizable spaces are studied in which every closed set is an $\alpha$-limit set for some continuous map and some point. It is shown that this property is enjoyed by every space containing sufficiently many arcs (formalized in the notion of…
3D image processing constitutes nowadays a challenging topic in many scientific fields such as medicine, computational physics and informatics. Therefore, development of suitable tools that guaranty a best treatment is a necessity.…
We introduce the Voronoi functional of a triangulation of a finite set of points in the Euclidean plane and prove that among all geometric triangulations of the point set, the Delaunay triangulation maximizes the functional. This result…
Three-dimensional (3D) point cloud analysis has become one of the attractive subjects in realistic imaging and machine visions due to its simplicity, flexibility and powerful capacity of visualization. Actually, the representation of scenes…
The universal-algebraic approach has proved a powerful tool in the study of the complexity of CSPs. This approach has previously been applied to the study of CSPs with finite or (infinite) omega-categorical templates, and relies on two…
This article proposes a new discrete framework for approximating solutions to shape optimization problems under convexity constraints. The numerical method, based on the support function or the gauge function, is guaranteed to generate…
Plotting solution sets for particular equations may be complicated by the existence of turning points. Here we describe an algorithm which not only overcomes such problematic points, but does so in the most general of settings. Applications…
Existing online 3D shape repositories contain thousands of 3D models but lack photorealistic appearance. We present an approach to automatically assign high-quality, realistic appearance models to large scale 3D shape collections. The key…
What is computable with limited resources? How can we verify the correctness of computations? How to measure computational power with precision? Despite the immense scientific and engineering progress in computing, we still have only…
This paper describes the design and implementation of mechanisms for light-weight inclusion of formal mathematics in informal mathematical writings, particularly in a Web-based setting. This is conceptually done in three stages: (i) by…
The Shapley value, and its broader family of semi-values, has received much attention in various attribution problems. A fundamental and long-standing challenge is their efficient approximation, since exact computation generally requires an…
Because of their strong theoretical properties, Shapley values have become very popular as a way to explain predictions made by black box models. Unfortuately, most existing techniques to compute Shapley values are computationally very…