Kernel density estimation via diffusion

Botev, Zdravko I.; Grotowski, Joseph F.; Kroese, Dirk P.

doi:10.1214/10-aos799

Cited by 1,636 publications

(1,345 citation statements)

References 41 publications

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“…This is accomplished by backtracking streamlines in time from x to the injection location. The resulting statistics of the TOF are needed to determine the distribution of Z( x,t) by means of kernel density estimation (KDE) (Botev et al, 2010). The TOF can also be estimated by solving an elliptic steady-state equation in Eulerian coordinates (Shahvali et al, 2012).…”

Section: Saturation Distribution Estimation Via Stochastic Travel Andmentioning

confidence: 99%

An efficient distribution method for nonlinear two-phase flow in highly heterogeneous multidimensional stochastic porous media

Ibrahima

Meyer

2017

Comput Geosci

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In the context of stochastic two-phase flow in porous media, we introduce a novel and efficient method to estimate the probability distribution of the wetting saturation field under uncertain rock properties in highly heterogeneous porous systems, where streamline patterns are dominated by permeability heterogeneity, and for slow displacement processes (viscosity ratio close to unity). Our method, referred to as the frozen streamline distribution method (FROST), is based on a physical understanding of the stochastic problem. Indeed, we identify key random fields that guide the wetting saturation variability, namely fluid particle times of flight and injection times. By comparing saturation statistics against full-physics Monte Carlo simulations, we illustrate how this simple, yet accurate FROST method performs under the preliminary approximation of frozen streamlines. Further, we inspect the performance of an accelerated FROST variant that relies on a simplification about injection time statistics. Finally, we introduce how quantiles of saturation can be efficiently computed within the FROST framework, hence leading to robust uncertainty assessment.

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Section: Saturation Distribution Estimation Via Stochastic Travel Andmentioning

confidence: 99%

An efficient distribution method for nonlinear two-phase flow in highly heterogeneous multidimensional stochastic porous media

Ibrahima

Meyer

2017

Comput Geosci

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“…Mean annual cumulative precipitations of 481 mm and temperature of 16.9°C were recorded during the period 1981-2010(Climate-Data 2016. The drought periods range from 3 to 5 months, with few rainy days.…”

Section: Study Areamentioning

confidence: 99%

“…d, e Seismic refraction profiles made on and along the slope. Notice that the vertical and horizontal scales of P-1 and P-2 profiles are different in both plots identifies and defines the different planar discontinuities of the rock mass slope surface by applying an analysis based on a neighbouring points coplanarity test, finding principal orientations by the non-parametric technique Kernel Density Estimation (Botev et al 2010) and identifying clusters by the density-based scan algorithm with noise (Ester et al 1996). This information has allowed the identification of the most important discontinuity sets affecting the slope from the available 3DPC corresponding to 2011 (i.e.…”

Section: Identification Of Discontinuities From 3dpcmentioning

confidence: 99%

A multidisciplinary approach for the investigation of a rock spreading on an urban slope

et al. 2017

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Landslides are very complex processes controlled by multiple factors. The knowledge and characterization of these factors is essential for a comprehensive understanding of the mechanisms and kinematics of the instabilities and for an efficient design of corrective measures. The aim of this work is to combine traditional geological and geotechnical techniques with geophysical, remote sensing and forensic techniques for obtaining a whole picture of an active lateral spreading affecting the Finestrat municipality in Alicante, SE Spain. Geomorphological, geotechnical and geophysical techniques (i.e. ground penetrating radar and refraction seismic) have provided essential information about the geometry, structure and petro-physical properties of the slope. A Terrestrial Laser Scanner was used for recognizing the most important sets of discontinuities affecting the rock mass and to evaluate the activity of the landslide slope. Complementarily, a forensic analysis of the building damage completed the available datasets, yielding very useful kinematic information of the landslide. Finally, a sensitivity analysis of the stability of the rock slope has been performed considering both block toppling and block sliding models. Therefore, the multisource analysis performed in this work has allowed the identification and characterization of a complex lateral spreading, highlighting its effectiveness for a comprehensive understanding of this type of landslide.

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“…and we use a Gaussian kernel with an automatically adapted bandwidth parameter H [20]. The shape KDE is estimated on sparse points and can be sampled densely to obtain a dense confidence map, S map .…”

Section: Shape-location Cuesmentioning

confidence: 99%

Online Learning for Fast Segmentation of Moving Objects

Ellis

Zografos

2013

Computer Vision – ACCV 2012

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Abstract. This work addresses the problem of fast, online segmentation of moving objects in video. We pose this as a discriminative online semi-supervised appearance learning task, where supervising labels are autonomously generated by a motion segmentation algorithm. The computational complexity of the approach is significantly reduced by performing learning and classification on oversegmented image regions (superpixels), rather than per pixel. In addition, we further exploit the sparse trajectories from the motion segmentation to obtain a simple model that encodes the spatial properties and location of objects at each frame. Fusing these complementary cues produces good object segmentations at very low computational cost. In contrast to previous work, the proposed approach (1) performs segmentation on-the-fly (allowing for applications where data arrives sequentially), (2) has no prior model of object types or 'objectness', and (3) operates at significantly reduced computational cost. The approach and its ability to learn, disambiguate and segment the moving objects in the scene is evaluated on a number of benchmark video sequences.

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Kernel density estimation via diffusion

Cited by 1,636 publications

References 41 publications

An efficient distribution method for nonlinear two-phase flow in highly heterogeneous multidimensional stochastic porous media

An efficient distribution method for nonlinear two-phase flow in highly heterogeneous multidimensional stochastic porous media

A multidisciplinary approach for the investigation of a rock spreading on an urban slope

Online Learning for Fast Segmentation of Moving Objects

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