Article
Exploring protein folding trajectories using geometric spanners.
Computer Science Department, Stanford, CA 94305, USA.
Pacific Symposium on Biocomputing. Pacific Symposium on Biocomputing 02/2005; DOI: 10.1142/9789812702456_0005 Source: PubMed

Conference Paper: Balls hierarchy: Image segmentation by graph spanner
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ABSTRACT: We propose a novel approach for solving the image segmentation and grouping problem. Our approach focuses on color and regional proximity relations in the image data. We treat image pixels as nodes in the graph so that proximity relations among both pixel's color and position are kept in geometric spanners. Geometric spanners for both color and position are created in hierarchical data structure socalled balls hierarchy. Balls hierarchy creates a multiresolution hierarchical subgraph that reflects a great deal about the original graph while maintaining all the existing proximity information in the image. We show that balls hierarchy can be used for image segmentation and grouping problems. We have applied our novel approach to several exemplary images such as histopathologic images and found results encouraging.Biomedical Imaging: From Nano to Macro, 2009. ISBI '09. IEEE International Symposium on; 08/2009 
Article: Modeling time and topology for animation and visualization with examples on parametric geometry
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ABSTRACT: a b s t r a c t The art of animation relies upon modeling objects that change over time. A sequence of static images is displayed to produce an illusion of motion. Even for simple cases, a careful analysis exposes that formal topological guarantees are often lacking. This absence of rigor can result in subtle, but significant, topological flaws. A new modeling approach is proposed to integrate topological rigor with a continuous model of time. Examples will be given for Bézier curves, while indicating extensions to a richer class of parametric curves and surfaces. Applications to scientific visualization for molecular modeling are discussed. Prototype animations are available for viewing over the web.Theoretical Computer Science 01/2008; 405:4149. · 0.49 Impact Factor  [Show abstract] [Hide abstract]
ABSTRACT: The greedy algorithm produces highquality spanners and, therefore, is used in several applications. However, even for points in ddimensional Euclidean space, the greedy algorithm has nearcubic running time. In this paper, we present an algorithm that computes the greedy spanner for a set of n points in a metric space with bounded doubling dimension in O(n2logn)\ensuremath {\mathcal {O}}(n^{2}\log n) time. Since computing the greedy spanner has an Ω(n 2) lower bound, the time complexity of our algorithm is optimal within a logarithmic factor. KeywordsSpannerDilationStretch factorGreedy algorithmDoubling dimensionAlgorithmica 02/2008; 58(3):711729. · 0.49 Impact Factor
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