Using Topological Statistics to Detect Determinism in Time Series

Statistical differentiability of the measure along the reconstructed trajectory is a good candidate to quantify determinism in time series. The procedure is based upon a formula that explicitly shows the sensitivity of the measure to stochasticity. Numerical results for partially surrogated time series and series derived from several stochastic models, illustrate the usefulness of the method proposed here. The method is shown to work also for high--dimensional systems and experimental time seriesComment: 23 RevTeX pages, 14 eps figures. To appear in Physical Review

Crisp Boundary Detection Using Pointwise Mutual Information

Detecting boundaries between semantically meaningful objects in visual scenes is an important component of many vision algorithms. In this paper, we propose a novel method for detecting such boundaries based on a simple underlying principle: pixels belonging to the same object exhibit higher statistical dependencies than pixels belonging to different objects. We show how to derive an affinity measure based on this principle using pointwise mutual information, and we show that this measure is indeed a good predictor of whether or not two pixels reside on the same object. Using this affinity with spectral clustering, we can find object boundaries in the image – achieving state-of-the-art results on the BSDS500 dataset. Our method produces pixel-level accurate boundaries while requiring minimal feature engineering.National Science Foundation (U.S.) (Award 1212849)Shell ResearchNational Science Foundation (U.S.). Graduate Research Fellowshi