Time Line Cell Tracking for the Approximation of Lagrangian Coherent Structures with Subgrid Accuracy

Kühn, Alexander; Engelke, Wito; Rössl, Christian; Hadwiger, Markus; Theisel, Holger

doi:10.1111/cgf.12269

Cited by 12 publications

(7 citation statements)

References 32 publications

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“…A variety of authors have proposed further schemes to investigate the extraction and use of LCS in a general context but independent from visualization; due to the limited space available here, we refer the reader to several recent works [PD10, HSW11, KER*14, MBESar] and recursive references therein for a more complete overview.…”

Section: State Of the Art – Vector Fieldsmentioning

confidence: 99%

A Survey of Topology‐based Methods in Visualization

Heine

Leitte

Hlawitschka³

et al. 2016

Computer Graphics Forum

137

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This paper presents the state of the art in the area of topology-based visualization. It describes the process and results of an extensive annotation for generating a definition and terminology for the field. The terminology enabled a typology for topological models which is used to organize research results and the state of the art. Our report discusses relations among topological models and for each model describes research results for the computation, simplification, visualization, and application. The paper identifies themes common to subfields, current frontiers, and unexplored territory in this research area.

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Section: State Of the Art – Vector Fieldsmentioning

confidence: 99%

A Survey of Topology‐based Methods in Visualization

Heine

Leitte

Hlawitschka³

et al. 2016

Computer Graphics Forum

137

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show abstract

“…To accurately compute streaklines and timelines, additional refinement procedures are required (i.e., inserting and integrating new seed points) to reproduce their geometry over longer integration intervals. In the literature, it has been shown that prominent Lagrangian features, can be extracted using pathlines [29], streaklines [30], and timelines [31]. In addition, time-dependent trajectories can be reformulated as streamlines in a higher-dimensional domain.…”

Section: Lagrangian Measures For Violent Video Detectionmentioning

confidence: 99%

Crowd Violence Detection Using Global Motion-Compensated Lagrangian Features and Scale-Sensitive Video-Level Representation

Senst¹,

Eiselein²,

Kühn³

et al. 2017

IEEE Trans.Inform.Forensic Secur.

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Lagrangian theory provides a rich set of tools for analyzing non-local, long-term motion information in computer vision applications. Based on this theory, we present a specialized Lagrangian technique for the automated detection of violent scenes in video footage. We present a novel feature using Lagrangian direction fields that is based on a spatio-temporal model and uses appearance, background motion compensation, and long-term motion information. To ensure appropriate spatial and temporal feature scales, we apply an extended bag-of-words procedure in a late-fusion manner as classification scheme on a per-video basis. We demonstrate that the temporal scale, captured by the Lagrangian integration time parameter, is crucial for violence detection and show how it correlates to the spatial scale of characteristic events in the scene. The proposed system is validated on multiple public benchmarks and non-public, real-world data from the London Metropolitan Police. Our experiments confirm that the inclusion of Lagrangian measures is a valuable cue for automated violence detection and increases the classification performance considerably compared to stateof-the-art methods.

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“…For FTLE, the probably most widespread implementation (and the one we used) is to seed particles close to one another and approximate the flow map gradient by taking finite differences of their reached destinations, as in Haller and Yuan [HY00, Hal01]. The flow visualization community proposed alternative methods, such as localized FTLE [KPH*09], streak surface‐based extraction [ÜSE13] and timeline tracking [KER*14]. A benchmark comparison of further computation methods was compiled by Kuhn et al [KRWT12].…”

Section: Related Workmentioning

confidence: 99%

“…FTLE computations can be accelerated, e.g., by adaptive refinement of the flow map by Catmull‐Rom interpolation [GGTH07], by the observation of filtered height ridges [SP07] or around automatically detected geometric structures [BT13]. Further, higher order flow map approximation [ÜSK*12] and timeline refinement [KER*14] schemes have been proposed. There exist several integral curve approximation schemes, such as hierarchical lines [HSW11], interpolation [COJ15, AOGJ15] and edge maps [BJB*12], which can be used to speed up any Lagrangian analysis technique.…”

Section: Related Workmentioning

confidence: 99%

MCFTLE: Monte Carlo Rendering of Finite‐Time Lyapunov Exponent Fields

Günther¹,

Kühn

Theisel³

2016

Computer Graphics Forum

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samples: 2 × 10 11 , 82.4 hrs (10 k it.) FTLE samples: 3.88 × 10 11 , 103.9 hrs (6.2 k it.) Figure 1: High-quality FTLE visualization of a European Centre for Medium-Range Weather Forecasts (ECMWF) reanalysis simulation of the wind velocity field of the northern hemisphere at April, 10th in 2010. The three-dimensional FTLE field emphasizes the spatial turbulence structure in the wind field and illustrates differences above land masses of North America (left and detail region), the North Atlantic region (center) and Europe (right). Integration duration (GPU): τ = 10, majorant extinctionσt = 1, FTLE range R = [0.35, 0.61],σt grid: 100 × 50 × 10, left: 1600 × 600, right: 1400 × 800 pixels. AbstractTraditionally, Lagrangian fields such as finite-time Lyapunov exponents (FTLE) are precomputed on a discrete grid and are ray casted afterwards. This, however, introduces both grid discretization errors and sampling errors during ray marching. In this work, we apply a progressive, view-dependent Monte Carlo-based approach for the visualization of such Lagrangian fields in time-dependent flows. Our approach avoids grid discretization and ray marching errors completely, is consistent, and has a low memory consumption. The system provides noisy previews that converge over time to an accurate high-quality visualization. Compared to traditional approaches, the proposed system avoids explicitly predefined fieldline seeding structures, and uses a Monte Carlo sampling strategy named Woodcock tracking to distribute samples along the view ray. An acceleration of this sampling strategy requires local upper bounds for the FTLE values, which we progressively acquire during the rendering. Our approach is tailored for high-quality visualizations of complex FTLE fields and is guaranteed to faithfully represent detailed ridge surface structures as indicators for Lagrangian coherent structures (LCS). We demonstrate the effectiveness of our approach by using a set of analytic test cases and real-world numerical simulations.

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Time Line Cell Tracking for the Approximation of Lagrangian Coherent Structures with Subgrid Accuracy

Cited by 12 publications

References 32 publications

A Survey of Topology‐based Methods in Visualization

A Survey of Topology‐based Methods in Visualization

Crowd Violence Detection Using Global Motion-Compensated Lagrangian Features and Scale-Sensitive Video-Level Representation

MCFTLE: Monte Carlo Rendering of Finite‐Time Lyapunov Exponent Fields

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