3 research outputs found

    A parallel Homological Spanning Forest framework for 2D topological image analysis

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    In [14], a topologically consistent framework to support parallel topological analysis and recognition for2 D digital objects was introduced. Based on this theoretical work, we focus on the problem of findingefficient algorithmic solutions for topological interrogation of a 2 D digital object of interest D of a pre- segmented digital image I , using 4-adjacency between pixels of D . In order to maximize the degree ofparallelization of the topological processes, we use as many elementary unit processing as pixels theimage I has. The mathematical model underlying this framework is an appropriate extension of the clas- sical concept of abstract cell complex: a primal–dual abstract cell complex (pACC for short). This versatiledata structure encompasses the notion of Homological Spanning Forest fostered in [14,15]. Starting froma symmetric pACC associated with I , the modus operandi is to construct via combinatorial operationsanother asymmetric one presenting the maximal number of non-null primal elementary interactions be- tween the cells of D . The fundamental topological tools have been transformed so as to promote anefficient parallel implementation in any parallel-oriented architecture (GPUs, multi-threaded computers,SIMD kernels and so on). A software prototype modeling such a parallel framework is built.Ministerio de Educación y Ciencia TEC2012-37868-C04-02/0

    Eight Biennial Report : April 2005 – March 2007

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    Component Trees For The Exploration Of Macromolecular Structures In Biology

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    Understanding the three-dimensional structure of a macromolecular complex is essential for understanding its function. A component tree is a topological and geometric image descriptor that captures information regarding the structure of an image based on the connected components determined by different grayness thresholds. This dissertation presents a novel interactive framework for visual exploration of component trees of the density maps of macromolecular complexes, with the purpose of improved understanding of their structure. The interactive exploration of component trees together with a robust simplification methodology provide new insights in the study of macromolecular structures. An underlying mathematical theory is introduced and then is applied to studying digital pictures that represent objects at different resolutions. Illustrations of how component trees, and their simplifications, can help in the exploration of macromolecular structures include (i) identifying differences between two very similar viruses, (ii) showing how differences between the component trees reflect the fact that structures of mutant virus particles have varying sets of constituent proteins, (ii) utilizing component trees for density map segmentation in order to identify substructures within a macromolecular complex, (iv) showing how an appropriate component tree simplification may reveal the secondary structure in a protein, and (v) providing a potential strategy for docking a high-resolution representation of a substructure into a low-resolution representation of whole structure
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