“Variational Feature Extraction in Scientific Visualization” by Daßler and Günther
Conference:
Type(s):
Title:
- Variational Feature Extraction in Scientific Visualization
Presenter(s)/Author(s):
Abstract:
Feature extraction is a common approach to analyze large scientific data sets. At present, many extraction techniques exist in different application domains. Using variational calculus, we phrase common feature definitions in a consistent mathematical language. We apply our framework in fluid dynamics, geophysics, atmospheric sciences, and oceanography.
References:
[1]
Ryan Abernathey and George Haller. 2018. Transport by Lagrangian Vortices in the Eastern Pacific. Journal of Physical Oceanography 48, 3 (2018), 667 — 685.
[2]
Robin Bader, Michael Sprenger, Nikolina Ban, Stefan R?dis?hli, Christoph Sch?r, and Tobias G?nther. 2020. Extraction and Visual Analysis of Potential Vorticity Banners around the Alps. IEEE Transactions on Visualization and Computer Graphics (Proc. IEEE Scientific Visualization) 26, 1 (2020), 259–269.
[3]
Irene Baeza Rojo and Tobias G?nther. 2019. Vector field topology of time-dependent flows in a steady reference frame. IEEE Transactions on Visualization and Computer Graphics 26, 1 (2019), 280–290.
[4]
David C. Banks and Bart A. Singer. 1995. A Predictor-Corrector Technique for Visualizing Unsteady Flow. IEEE Transactions on Visualization and Computer Graphics 1 (1995), 151–163.
[5]
Lukas B?siger, Michael Sprenger, Maxi Boettcher, Hanna Joos, and Tobias G?nther. 2022. Integration-based extraction and visualization of jet stream cores. Geoscientific Model Development 15, 3 (2022), 1079–1096.
[6]
Roxana Bujack. 2022. Discussion and Visualization of Distinguished Hyperbolic Trajectories as a Generalization of Critical Points to 2D Time-dependent Flow. In 2022 Topological Data Analysis and Visualization (TopoInVis). IEEE, IEEE, Oklahoma City, OK, USA, 59–69.
[7]
Roxana Bujack, Lin Yan, Ingrid Hotz, Christoph Garth, and Bei Wang. 2020. State of the Art in Time-Dependent Flow Topology: Interpreting Physical Meaningfulness Through Mathematical Properties. Computer Graphics Forum 39, 3 (2020), 811–835.
[8]
Brian Cabral and Leith Leedom. 1993. Imaging Vector Fields Using Line Integral Convolution. Computer Graphics (Proc. SIGGRAPH) 27 (1993), 263–272.
[9]
Simone Camarri, Angelo Iollo, Marcelo Buffoni, and Maria Vittoria Salvetti. 2005. Simulation of the three-dimensional flow around a square cylinder between parallel walls at moderate Reynolds numbers. In XVII Congresso di Meccanica Teorica ed Applicata. Firenze University Press, Florence, Italy, 1–12.
[10]
Hamish Carr, Zhao Geng, Julien Tierny, Amit Chattopadhyay, and Aaron Knoll. 2015. Fiber surfaces: Generalizing isosurfaces to bivariate data. Computer Graphics Forum 34, 3 (2015), 241–250.
[11]
Zhiqin Chen and Hao Zhang. 2021. Neural marching cubes. ACM Trans. Graph. 40, 6, Article 251 (2021), 15 pages.
[12]
Albert Chern, Felix Kn?ppel, Ulrich Pinkall, and Peter Schr?der. 2017. Inside fluids: clebsch maps for visualization and processing. ACM Trans. Graph. 36, 4, Article 142 (jul 2017), 11 pages.
[13]
Albert Chern, Felix Kn?ppel, Ulrich Pinkall, Peter Schr?der, and Steffen Wei?mann. 2016. Schr?dinger’s smoke. ACM Trans. Graph. 35, 4, Article 77 (2016), 13 pages.
[14]
Martin Dameris. 2015. Stratosphere/Troposphere Exchange and Structure | Tropopause. In Encyclopedia of Atmospheric Sciences (Second Edition) (second edition ed.), Gerald R. North, John Pyle, and Fuqing Zhang (Eds.). Academic Press, Oxford, 269–272.
[15]
David Eberly. 1996. Ridges in image and data analysis. Kluwer Academic Publishers, Dordrecht.
[16]
Mohammad Farazmand and George Haller. 2012. Computing Lagrangian coherent structures from their variational theory. Chaos: An Interdisciplinary Journal of Nonlinear Science 22, 1 (2012), 013128.
[17]
Lucas I. Finn and Bruce M. Boghosian. 2006. A global variational approach to vortex core identification. Physica A: Statistical Mechanics and its Applications 362, 1 (2006), 11–16. Discrete Simulation of Fluid Dynamics.
[18]
Bengt Fornberg. 1988. Generation of finite difference formulas on arbitrarily spaced grids. Mathematics of computation 51, 184 (1988), 699–706.
[19]
Raphael Fuchs, Ronald Peikert, Helwig Hauser, Filip Sadlo, and Philipp Muigg. 2008. Parallel vectors criteria for unsteady flow vortices. IEEE Transactions on Visualization and Computer Graphics 14, 3 (2008), 615–626.
[20]
Izrail Moiseevitch Gelfand and S. V. Fomin. 1963. Calculus of variations. Prentice-Hall Inc., Englewood Cliffs, N. J.
[21]
Anna Johanna Pia G?lcher, Maxim Dionys Ballmer, and Paul James Tackley. 2021. Coupled dynamics and evolution of primordial and recycled heterogeneity in Earth’s lower mantle. Solid Earth 12, 9 (2021), 2087–2107.
[22]
Tobias G?nther, Markus Gross, and Holger Theisel. 2017. Generic Objective Vortices for Flow Visualization. ACM Transactions on Graphics (Proc. SIGGRAPH) 36, 4 (2017), 1–11.
[23]
Tobias G?nther and Holger Theisel. 2017. Backward Finite-Time Lyapunov Exponents in Inertial Flows. IEEE Transactions on Visualization and Computer Graphics (Proc. IEEE SciVis 2016) 23, 1 (2017), 970–979.
[24]
Tobias G?nther and Holger Theisel. 2018. The State of the Art in Vortex Extraction. Computer Graphics Forum 37, 6 (2018), 149–173.
[25]
Hanqi Guo and Tom Peterka. 2021. Exact Analytical Parallel Vectors. In 2021 IEEE Visualization Conference (VIS). IEEE, New Orleans, LA, USA, 101–105.
[26]
Markus Hadwiger, Matej Mlejnek, Thomas Theu?l, and Peter Rautek. 2019. Time-Dependent Flow seen through Approximate Observer Killing Fields. IEEE Transactions on Visualization and Computer Graphics 25, 1 (Jan 2019), 1257–1266.
[27]
George Haller. 2011. A variational theory of hyperbolic Lagrangian Coherent Structures. Physica D: Nonlinear Phenomena 240, 7 (2011), 574–598.
[28]
Nili Harnik, Chaim I Garfinkel, and Orli Lachmy. 2016. The influence of jet stream regime on extreme weather events. Dynamics and Predictability of Large-Scale, High-Impact Weather and Climate Events 2 (2016), 79–94.
[29]
James L. Helman and Lambertus Hesselink. 1989. Representation and Display of Vector Field Topology in Fluid Flow Data Sets. Computer 22, 8 (1989), 27–36.
[30]
James L. Helman and Lambertus Hesselink. 1991. Visualizing Vector Field Topology in Fluid Flows. IEEE Computer Graphics and Applications 11 (May 1991), 36–46.
[31]
Hans Hersbach, Bill Bell, Paul Berrisford, Shoji Hirahara, Andr?s Hor?nyi, Joaqu?n Mu?oz-Sabater, Julien Nicolas, Carole Peubey, Raluca Radu, Dinand Schepers, Adrian Simmons, Cornel Soci, Saleh Abdalla, Xavier Abellan, Gianpaolo Balsamo, Peter Bechtold, Gionata Biavati, Jean Bidlot, Massimo Bonavita, Giovanna De Chiara, Per Dahlgren, Dick Dee, Michail Diamantakis, Rossana Dragani, Johannes Flemming, Richard Forbes, Manuel Fuentes, Alan Geer, Leo Haimberger, Sean Healy, Robin J. Hogan, El?as H?lm, Marta Janiskov?, Sarah Keeley, Patrick Laloyaux, Philippe Lopez, Cristina Lupu, Gabor Radnoti, Patricia de Rosnay, Iryna Rozum, Freja Vamborg, Sebastien Villaume, and Jean-No?l Th?paut. 2020. The ERA5 global reanalysis. Quarterly Journal of the Royal Meteorological Society 146, 730 (2020), 1999–2049.
[32]
Lutz Hofmann and Filip Sadlo. 2019. The Dependent Vectors Operator. Computer Graphics Forum 38, 3 (2019), 261–272.
[33]
Lutz Hofmann and Filip Sadlo. 2020. Extraction of Distinguished Hyperbolic Trajectories for 2D Time-Dependent Vector Field Topology. Computer Graphics Forum 39, 3 (2020), 303–316.
[34]
Jeffrey P. M. Hultquist. 1992. Constructing Stream Surfaces in Steady 3D Vector Fields. In Proc. Visualization (Boston, Massachusetts). IEEE, Boston, MA, USA, 171–178.
[35]
Tao Ju, Minxin Cheng, Xu Wang, and Ye Duan. 2014. A robust parity test for extracting parallel vectors in 3D. IEEE Transactions on Visualization and Computer Graphics 20, 12 (2014), 2526–2534.
[36]
Michael Kern, Tim Hewson, Filip Sadlo, R?diger Westermann, and Marc Rautenhaus. 2018. Robust Detection and Visualization of Jet-Stream Core Lines in Atmospheric Flow. IEEE Transactions on Visualization and Computer Graphics 24, 1 (2018), 893–902.
[37]
Gordon L. Kindlmann, Charisee Chiw, Tri Huynh, Attila Gyulassy, John Reppy, and Peer-Timo Bremer. 2018. Rendering and Extracting Extremal Features in 3D Fields. Computer Graphics Forum 37, 3 (2018), 525–536.
[38]
Diederik P. Kingma and Jimmy Ba. 2017. Adam: A Method for Stochastic Optimization. arXiv:1412.6980 [cs.LG]
[39]
Patrick Koch, Heini Wernli, and Huw C. Davies. 2006. An event-based jet-stream climatology and typology. International Journal of Climatology 26, 3 (2006), 283–301.
[40]
Tony Lindeberg. 1998. Edge Detection and Ridge Detection With Automatic Scale Selection. International Journal of Computer Vision 30 (09 1998), 117–154.
[41]
William E. Lorensen and Harvey E. Cline. 1987. Marching Cubes: A High Resolution 3D Surface Construction Algorithm. SIGGRAPH Comput. Graph. 21, 4 (Aug 1987), 163–169.
[42]
Gustavo M. Machado, Sebastian Boblest, Thomas Ertl, and Filip Sadlo. 2016. Space-Time Bifurcation Lines for Extraction of 2D Lagrangian Coherent Structures. Computer Graphics Forum (Proc. EuroVis) 35, 3 (2016), 91–100.
[43]
Gustavo Mello Machado, Filip Sadlo, and Thomas Ertl. 2013. Local Extraction of Bifurcation Lines. In Vision, Modeling and Visualization. The Eurographics Association, Lugano, Switzerland, 17–24.
[44]
Gloria L. Manney and Michaela I. Hegglin. 2018. Seasonal and Regional Variations of Long-Term Changes in Upper-Tropospheric Jets from Reanalyses. Journal of Climate 31, 1 (2018), 423 — 448.
[45]
Tony McLoughlin, Robert S Laramee, Ronald Peikert, Frits H Post, and Min Chen. 2010. Over Two Decades of Integration-Based, Geometric Flow Visualization. Computer Graphics Forum 29, 6 (2010), 1807–1829.
[46]
John W. Nielsen-Gammon. 2001. A Visualization of the Global Dynamic Tropopause. Bulletin of the American Meteorological Society 82, 6 (2001), 1151 — 1168. <1151:AVOTGD>2.3.CO;2
[47]
David Oettinger, Daniel Blazevski, and George Haller. 2016. Global variational approach to elliptic transport barriers in three dimensions. Chaos: An Interdisciplinary Journal of Nonlinear Science 26, 3 (2016), 033114.
[48]
David Oettinger and George Haller. 2016. An autonomous dynamical system captures all LCSs in three-dimensional unsteady flows. Chaos: An Interdisciplinary Journal of Nonlinear Science 26, 10 (2016), 103111.
[49]
Timo Oster, Christian R?ssl, and Holger Theisel. 2018a. Core Lines in 3D Second-Order Tensor Fields. Computer Graphics Forum 37, 3 (2018), 327–337.
[50]
Timo Oster, Christian R?ssl, and Holger Theisel. 2018b. The Parallel Eigenvectors Operator. In Vision, Modeling and Visualization, Fabian Beck, Carsten Dachsbacher, and Filip Sadlo (Eds.). The Eurographics Association, Eindhoven, The Netherlands, 39–46.
[51]
Christian Pagot, D Osmari, Filip Sadlo, Daniel Weiskopf, Thomas Ertl, and Jo?o Comba. 2011. Efficient parallel vectors feature extraction from higher-order data. Computer Graphics Forum 30, 3 (2011), 751–760.
[52]
Ronald Peikert and Martin Roth. 1999. The “Parallel Vectors” Operator – A Vector Field Visualization Primitive. In Proc. IEEE Visualization. IEEE, San Francisco, CA, USA, 263–270.
[53]
Ronald Peikert and Filip Sadlo. 2008. Height ridge computation and filtering for visualization. In 2008 IEEE Pacific Visualization Symposium. IEEE, IEEE, Kyoto, japan, 119–126.
[54]
Anthony E Perry and Min S Chong. 1987. A description of eddying motions and flow patterns using critical-point concepts. Annual Review of Fluid Mechanics 19, 1 (1987), 125–155.
[55]
Ulrich Pinkall and Konrad Polthier. 1993. Computing discrete minimal surfaces and their conjugates. Experimental mathematics 2, 1 (1993), 15–36.
[56]
Frits H. Post, Benjamin Vrolijk, Helwig Hauser, Robert S. Laramee, and Helmut Doleisch. 2003. The State of the Art in Flow Visualisation: Feature Extraction and Tracking. Computer Graphics Forum 22, 4 (2003), 775–792.
[57]
Wolfgang Quapp and Benjamin Schmidt. 2011. An empirical, variational method of approach to unsymmetric valley-ridge inflection points. Theoretical Chemistry Accounts 128 (2011), 47–61.
[58]
Peter Rautek, Matej Mlejnek, Johanna Beyer, Jakob Troidl, Hanspeter Pfister, Thomas Theu?l, and Markus Hadwiger. 2020. Objective observer-relative flow visualization in curved spaces for unsteady 2D geophysical flows. IEEE Transactions on Visualization and Computer Graphics 27, 2 (2020), 283–293.
[59]
Peter Rautek, Xingdi Zhang, Bernhard Woschizka, Thomas Theu?l, and Markus Hadwiger. 2024. Vortex Lens: Interactive Vortex Core Line Extraction using Observed Line Integral Convolution. IEEE Transactions on Visualization and Computer Graphics (Proceedings IEEE VIS 2023) 30, 1 (2024), 55–65.
[60]
Martin Reuter, Silvia Biasotti, Daniela Giorgi, Giuseppe Patan?, and Michela Spagnuolo. 2009. Discrete Laplace-Beltrami operators for shape analysis and segmentation. Computers & Graphics 33, 3 (2009), 381–390.
[61]
Martin Roth. 2000. Automatic extraction of vortex core lines and other line-type features for scientific visualization. Vol. 9. ETH Zurich, Zurich, Switzerland.
[62]
Martin Roth and Ronald Peikert. 1998. A higher-order method for finding vortex core lines. In Proc. IEEE Visualization. IEEE, Research Triangle Park, NC, USA, 143–150.
[63]
Jan Sahner, Tino Weinkauf, Nathalie Teuber, and Hans-Christian Hege. 2007. Vortex and Strain Skeletons in Eulerian and Lagrangian Frames. IEEE Transactions on Visualization and Computer Graphics 13, 5 (2007), 980–990.
[64]
William Schroeder, Rob Maynard, and Berk Geveci. 2015. Flying edges: A high-performance scalable isocontouring algorithm. In IEEE Symposium on Large Data Analysis and Visualization (LDAV). IEEE, 33–40.
[65]
David Sujudi and Robert Haimes. 1995. Identification of Swirling Flow in 3D Vector Fields. Technical Report. Departement of Aeronautics and Astronautics, MIT. AIAA Paper 95-1715.
[66]
Holger Theisel, Markus Hadwiger, Peter Rautek, Thomas Theu?l, and Tobias G?nther. 2021. Vortex criteria can be objectivized by unsteadiness minimization. Physics of Fluids 33, 10 (2021), 107115.
[67]
Holger Theisel, Jan Sahner, Tino Weinkauf, Hans-Christian Hege, and Hans-Peter Seidel. 2005. Extraction of parallel vector surfaces in 3D time-dependent fields and application to vortex core line tracking. In Proc. IEEE Visualization. IEEE, Minneapolis, MN, USA, 631–638.
[68]
Holger Theisel and Hans-Peter Seidel. 2003. Feature Flow Fields. In Proc. Symposium on Data Visualisation. The Eurographics Association, Grenoble, France, 141–148.
[69]
Allen Van Gelder and Alex Pang. 2009. Using PVsolve to Analyze and Locate Positions of Parallel Vectors. IEEE Transactions on Visualization and Computer Graphics 15, 4 (2009), 682–695.
[70]
Tino Weinkauf, Jan Sahner, Holger Theisel, and Hans-Christian Hege. 2007. Cores of Swirling Particle Motion in Unsteady Flows. IEEE Transactions on Visualization and Computer Graphics (Proc. Visualization) 13, 6 (2007), 1759–1766.
[71]
Tino Weinkauf, Holger Theisel, Allen Van Gelder, and Alex Pang. 2010. Stable feature flow fields. IEEE Transactions on Visualization and Computer Graphics 17, 6 (2010), 770–780.
[72]
Steffen Wei?mann, Ulrich Pinkall, and Peter Schr?der. 2014. Smoke rings from smoke. ACM Trans. Graph. 33, 4, Article 140 (2014), 8 pages.
[73]
Xingdi Zhang, Markus Hadwiger, Thomas Theu?l, and Peter Rautek. 2021. Interactive exploration of physically-observable objective vortices in unsteady 2D flow. IEEE Transactions on Visualization and Computer Graphics 28, 1 (2021), 281–290.