ArticlePDF Available

Current Trends for 4D Space-Time Topology for Semantic Flow Segmentation

December 2011

December 2011

DOI:10.1016/j.procs.2011.09.013

License
CC BY-NC-ND 3.0

Authors:

Krešimir Matković

VRVis Zentrum für Virtual Reality und Visualisierung Forschungs GmbH

Helwig Hauser

University of Bergen

Armin Pobitzer

SINTEF

Show all 10 authorsHide

Content uploaded by Ronald Peikert

Content may be subject to copyright.

Available via license: CC BY-NC-ND 3.0

Content may be subject to copyright.

Available online at www.sciencedirect.com

Procedia Computer Science 7 (2011) 253–255

The European Future Technologies Conference and Exhibition 2011

Current Trends for 4D Space-Time Topology for Semantic Flow

Segmentation

Kreˇ

simir Matkovi´

ca, Alan Leˇ

za, Helwig Hauserb, Armin Pobitzer b, Holger Theisel c,

Alexander Kuhn c, Mathias Ottoc, Ronald Peikertd, Benjamin Schindler d, Raphael Fuchs d

aVRVis Research Center, Vienna, Austria

bUniversity of Bergen, Norway

cUniversity of Magdeburg, Germany

dETH Zurich, Switzerland

1. Introduction

Recent advances in computing and simulation technology promote the simulation of time-dependent ﬂows, i.e., ﬂows

where the velocity ﬁeld changes over time. The simulation of time-dependent ﬂow is a more realistic approximation of

natural phenomena and it represents an invaluable tool for scientists and practitioners in multiple disciplines, including

meteorology, vehicle design, and medicine. Flow visualization, a subﬁeld of scientiﬁc visualization, is one of several

research areas which deal with the analysis of ﬂows. There are many methods for the analysis of steady ﬂows, but

the extension to the time-dependent case is not straight forward. The SemSeg project, a FET-Open project in the 7th

Framework programme, attempts to provide a solution for the semantic segmentation of time-dependent ﬂows. It aims

at the formulation of a sound theoretical mechanism to describe structural features in time-dependent ﬂow. In this

paper, we brieﬂy summarize recent research results from the SemSeg project. Several different approaches are pursued

in the project, including methods based on the ﬁnite-time Lyapunov exponent (FTLE), methods based on vector ﬁeld

topology (VFT), and interactive visual analysis (IVA) methods. Uncertainty visualization and the interactive evaluation

of methods are helping in evaluating the results.

2. Selected Current Research in SemSeg

Vector ﬁeld topology (VFT) is a well-established methodology for analyzing and visualizing velocity ﬁeld datasets.

Its power lies in the automatic and parameter-free extraction of ﬂow structures that have proven meaningful in a wide

range of application domains. Its limitation, however, is the restriction to steady ﬂow. This was addressed, in parts, by

using moving frames of reference for the local application of VFT, for example, based on optimality criteria [1].

Uncertain vector ﬁeld topology. Flow data is usually obtained either by measuring the actual physical process or

by simulation. In both cases the results contain an inherent uncertainty, that evolves from measurement inaccuracies

as well as from different parameter setting or using different simulation models. We present a technique to visualize

the global uncertainty in steady 3D vector ﬁelds using a topological approach. We start from an existing approach

for the 2D case and extend this into 3D space. In addition, we develop an acceleration strategy to detect sink and

source distributions. Having these distributions, we use overlaps of their corresponding volumes to identify separating

structures and saddles. As part of the approach, we introduce uncertain saddle and boundary switch connectors and

1877-0509/$ – see front matter © Selection and peer-review under responsibility of FET11 conference organizers and published by Elsevier B.V.

doi:10.1016/j.procs.2011.09.013

254 K. Matkovi´c et al. / Procedia Computer Science 7 (2011) 253–255

provide algorithms to extract them. For the visual representation, we use multiple direct volume renderings and test

our method on a number of synthetic as well as real-world datasets [2]. A popular alternative to VFT is based on the

ﬁnite-time Lyapunov exponent (FTLE). The ridges of this scalar quantity indicate ﬂow structures, so-called Lagrangian

coherent structures (LCS). These structures can be visualized without an explicit ridge extraction step. Analyzing LCS

and the related geometrical trajectory properties allows for a deeper insight into the structure of time dependent ﬂow

phenomena.

Studying separation structures based on FTLE. For a thorough analysis such as the study of bifurcations, ridges

are necessary. We compare several ridge deﬁnitions and developed a novel method [3] which exploits properties of

FTLE ﬁelds. It avoids one order of numerical differentiation and results in higher quality ridge surfaces. Coherent

ﬂow behavior, and separation, as its dual behavior, are important features in ﬂow ﬁelds. The currently most common

approach to detect such behavior makes use of the FTLE, which is, informally speaking, the maximal local separation

rate. We developed a ﬁlter that distinguishes between separation due to different ﬂow directions and from separation

due to different ﬂow speeds [4]. The ﬁlter follows the geometric intuition behind the original deﬁnition of FTLE.

Computing the FTLE without the ﬂow map gradient. Existing methods for the computation of FTLE either rely on an

approximation of the ﬂow map gradient, or they use frequent renormalization steps during the integration process. This

poses a number of challenges which are due to the fact that this gradient shows an exponential growing or shrinking

with integration time. We developed a novel method for computing FTLE of 2D unsteady vector ﬁelds which uses

exclusively measures that are linearly growing with integration time. Using this approach the evolving FTLE can be

reformulated as an ODE and obtained by a numerical integration of a 7D vector ﬁeld.

Scale-space aware analysis of time-dependent dynamics. Commonly used feature extraction methods tend to have

a rich response for complex, e.g., turbulent ﬂows. Using classical image processing approaches, based, e.g., on size or

the vicinity of two features, the output is reduced, which, however, does not necessarily respect the underlying physics.

We propose the use of Proper Orthogonal Decomposition (POD) to decompose the ﬂow ﬁeld according to its kinetic

energy to construct an approximation of the ﬁeld, representing the largest energy-scales, and apply feature extraction

in the sequel [5]. This guarantees that the large-scale dynamics of the ﬂow are represented in the ﬁnal output. By using

a scale-space approach to both FTLE computation and ridge extraction [6], we were able to address the dilemma of

either excessive computing time or error due to gradient underestimation.

Interactive Visual Analysis. Besides the above described automatic methods we also use interactive visual analysis

(IVA) in order to understand ﬂow phenomena. As simulation datasets get large, the fully automatic methods are no

longer sufﬁcient. We have developed a pathline explorer, a tool for the interactive visual analysis of time-dependent

ﬂows. The main idea is to compute pathlines and pathline attributes (some of them are scalar and others are functions

of time or of the position along the pathline), and then to interactively explore the new dataset. The ﬁrst tests were done

using an exhaust manifold case from automotive industry [7]. Interactive visual analysis will be also used to compare

results from various automatic ﬂow segmentation methods.

3. Outlook and Acknowledgments

Based on the here presented research, we are looking forward to new research questions, including the analysis of

tensors on unsteady ﬂows as well as streakline-based approaches.

The SemSeg project acknowledges the ﬁnancial support of the Future and Emerging Technologies (FET) programme

within the Seventh Framework Programme for Research of the European Commission, under FET-Open grant number

226042. More information about the SemSeg project is available from the URL www.SemSeg.eu.

References

[1] R. Fuchs, J. Kemmler, B. Schindler, F. Sadlo, H. Hauser, R. Peikert, Toward a Lagrangian Vector Field Topology, Computer Graphics Forum 29

(3) (2010) 1163–1172.

[2] M. Otto, T. Germer, H.-C. Hege, H. Theisel, Uncertain 2d vector ﬁeld topology, Computer Graphics Forum 29 (2).

[3] B. Schindler, R. Peikert, R. Fuchs, H. Theisel, Ridge Concepts for the Visualization of Lagrangian Coherent Structures, in: R. Peikert, H. Hauser,

H. Carr, R. Fuchs (Eds.), Topological Methods in Data Analysis and Visualization II, Springer, 2011.

[4] A. Pobitzer, R. Peikert, R. Fuchs, H. Theisel, H. Hauser, Filtering of FTLE for Visualizing Spatial Separation in Unsteady 3D Flow, in: R.

Peikert, H. Hauser, H. Carr, R. Fuchs (Eds.), Topological Methods in Data Analysis and Visualization II, Springer, 2011.

K. Matkovi´c et al. / Procedia Computer Science 7 (2011) 253–255 255

[5] A. Pobitzer, M. Tutkun, Ø. Andreassen, R. Peikert, R. Fuchs, H. Hauser, Energy-scale aware feature extraction for ﬂow visualization, Computer

Graphics Forum 30 (3).

[6] R. Fuchs, B. Schindler, R. Peikert, Scale-Space Approaches to FTLE Ridges, in: R. Peikert, H. Hauser, H. Carr, R. Fuchs (Eds.), Topological

Methods in Data Analysis and Visualization II, Springer, 2011.

[7] A. Lez, A. Zajic, K. Matkovic, A. Pobitzer, M. Mayer, H. Hauser, Interactive exploration and analysis of pathlines in ﬂow data, in: in: WSCG

2011 Full Papers Proceedings, 2011.

ResearchGate has not been able to resolve any citations for this publication.

Interactive Exploration and Analysis of Pathlines in Flow Data

Article

Full-text available

Jan 2011

The rapid development of large-scale scientific computing nowadays allows to inherently respect the unsteady character of natural phenomena in computational flow simulation. With this new trend to more regularly consider time-dependent flow scenarios, an according new need for advanced exploration and analysis solutions emerges. In this paper, we now present three new concepts in pathline analysis which further improve the abilities of analysis: a multi-step analysis which helps to save time and space needed for computation, direct pathline brushing, and usage of pre-configured view arrangements. We have found that clever combining of these three concepts with already existing methods creates very powerful tool for pathline analysis. The coordinated multiple views (CMV) tool used supports iterative composite brushing which enables a quick information drill-down. We illustrate the usefulness using an example from the automotive industry. We have analyzed an exhaust manifold time-dependent simulation data set.

Ridge Concepts for the Visualization of Lagrangian Coherent Structures

Conference Paper

Full-text available

Nov 2012

The popularity of vector field topology in the visualization community is due mainly to the topological skeleton which captures the essential information on a vector field in a set of lines or surfaces separating regions of different flow behavior. Unfortunately, vector field topology has no straightforward extension to unsteady flow, and the concept probably most closely related to the topological skeleton are the so-called Lagrangian coherent structures (LCS). LCS are material lines or material surfaces that separate regions of different flow behavior. Ideally, such structures are material lines (or surfaces) in an exact sense and at the same time maximally attracting or repelling, but practical realizations such as height ridges of the finite-time Lyapunov exponent (FTLE) fulfill these two requirements only in an approximate sense. In this paper, we quantify the deviation from exact material lines/surfaces for several FTLE-based concepts, and we propose a numerically simpler variants of FTLE ridges that has equal or better error characteristics than classical FTLE height ridges.

Scale-Space Approaches to FTLE Ridges

Conference Paper

Full-text available

Nov 2012

The finite-time Lyapunov exponent (FTLE) is useful for the visualization of time-dependent velocity fields. The ridges of this derived scalar field have been shown to correspond well to attracting or repelling material structures, so-called Lagrangian coherent structures (LCS). There are two issues involved in the computation of FTLE for this purpose. Firstly, it is often not practically possible to refine the grid for sampling the flow map until convergence of FTLE is reached. Slow conversion is mostly caused by gradient underestimation. Secondly, there is a parameter, the integration time, which has to be chosen sensibly. Both of these problems call for an examination in scale-space. We show that a scale-space approach solves the problem of gradient underestimation. We test optimal-scale ridges for their usefulness with FTLE fields, obtaining a negative result. However, we propose an optimization of the time parameter for a given scale of observation. Finally, an incremental method for computing smoothed flow maps is presented.

Filtering of FTLE for Visualizing Spatial Separation in Unsteady 3D Flow

Chapter

Full-text available

Nov 2012

In many cases, feature detection for flow visualization is structured in two phases: first candidate identification, and then filtering. With this paper, we propose to use the directional information contained in the finite-time Lyapunov exponents (FTLE) computation, in order to filter the FTLE field. Thereby we can focus on those separation structures that delineate flow compartments which develop into different spatial locations, as compared to those that separate parallel flows of different speed. We provide a discussion of the underlying theory and our related considerations. We derive a new filtering scheme and demonstrate its effect in the context of several selected fluid flow cases, especially in comparison with unfiltered FTLE visualization. Since previous work has provided insight with respect to the studied flow patterns, we are able to provide a discussion of the resulting visible separation structures.

Toward a Lagrangian Vector Field Topology

Article

Jun 2010

In this paper we present an extended critical point concept which allows us to apply vector field topology in the case of unsteady flow. We propose a measure for unsteadiness which describes the rate of change of the velocities in a fluid element over time. This measure allows us to select particles for which topological properties remain intact inside a finite spatio-temporal neighborhood. One benefit of this approach is that the classification of critical points based on the eigenvalues of the Jacobian remains meaningful. In the steady case the proposed criterion reduces to the classical definition of critical points. As a first step we show that finding an optimal Galilean frame of reference can be obtained implicitly by analyzing the acceleration field. In a second step we show that this can be extended by switching to the Lagrangian frame of reference. This way the criterion can detect critical points moving along intricate trajectories. We analyze the behavior of the proposed criterion based on two analytical vector fields for which a correct solution is defined by their inherent symmetries and present results for numerical vector fields.

Energy-scale Aware Feature Extraction for Flow Visualization

Article

Jun 2011

In the visualization of flow simulation data, feature detectors often tend to result in overly rich response, making some sort of filtering or simplification necessary to convey meaningful images. In this paper we present an ap-proach that builds upon a decomposition of the flow field according to dynamical importance of different scales of motion energy. Focusing on the high-energy scales leads to a reduction of the flow field while retaining the un-derlying physical process. The presented method acknowledges the intrinsic structures of the flow according to its energy and therefore allows to focus on the energetically most interesting aspects of the flow. Our analysis shows that this approach can be used for methods based on both local feature extraction and particle integration and we provide a discussion of the error caused by the approximation. Finally, we illustrate the use of the proposed approach for both a local and a global feature detector and in the context of numerical flow simulations.

Uncertain 2D Vector Field Topology

Article

May 2010

Abstract We introduce an approach to visualize stationary 2D vector fields with global uncertainty obtained by considering the transport of local uncertainty in the flow. For this, we extend the concept of vector field topology to uncertain vector fields by considering the vector field as a density distribution function. By generalizing the concepts of stream lines and critical points we obtain a number of density fields representing an uncertain topological segmentation. Their visualization as height surfaces gives insight into both the flow behavior and its uncertainty. We present a Monte Carlo approach where we integrate probabilistic particle paths, which lead to the segmentation of topological features. Moreover, we extend our algorithms to detect saddle points and present efficient implementations. Finally, we apply our technique to a number of real and synthetic test data sets.

Interactive exploration and analysis of pathlines in flow data

Jan 2011

A Lez
A Zajic
K Matkovic
A Pobitzer
M Mayer
H Hauser

A. Lez, A. Zajic, K. Matkovic, A. Pobitzer, M. Mayer, H. Hauser, Interactive exploration and analysis of pathlines in flow data, in: in: WSCG 2011 Full Papers Proceedings, 2011.