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Progressive Wasserstein Barycenters of Persistence Diagrams
This paper presents an efficient algorithm for the progressive approxima...
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Localized Topological Simplification of Scalar Data
This paper describes a localized algorithm for the topological simplific...
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Topological Regularization via Persistence-Sensitive Optimization
Optimization, a key tool in machine learning and statistics, relies on r...
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Topologically Controlled Lossy Compression
This paper presents a new algorithm for the lossy compression of scalar ...
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Lifted Wasserstein Matcher for Fast and Robust Topology Tracking
This paper presents a robust and efficient method for tracking topologic...
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Topological Interpretation of Interactive Computation
It is a great pleasure to write this tribute in honor of Scott A. Smolka...
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A Progressive Approach to Scalar Field Topology
This paper introduces progressive algorithms for the topological analysis of scalar data. Our approach is based on a hierarchical representation of the input data and the fast identification of topologically invariant vertices, for which we show that no computation is required as they are introduced in the hierarchy. This enables the definition of efficient coarse-to-fine topological algorithms, which leverage fast update mechanisms for ordinary vertices and avoid computation for the topologically invariant ones. We instantiate our approach with two examples of topological algorithms (critical point extraction and persistence diagram computation), which generate exploitable outputs upon interruption requests and which progressively refine them otherwise. Experiments on real-life datasets illustrate that our progressive strategy, in addition to the continuous visual feedback it provides, even improves run time performances with regard to non-progressive algorithms and we describe further accelerations with shared-memory parallelism. We illustrate the utility of our approach in (i) batch-mode and (ii) interactive setups, where it respectively enables (i) the control of the execution time of complete topological pipelines as well as (ii) previews of the topological features found in a dataset, with progressive updates delivered within interactive times.
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