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Applications of real analysis, differential calculus, and statistics for visualization (CSE788 WI11)


Regarding the math for real and differential calculus, it is recommended to refer to the following supplementary material:

Online supplementary material:

Isosurface analysis

  1. Marc Khoury, Rephael Wenger: On the Fractal Dimension of Isosurfaces. IEEE Trans. Vis. Comput. Graph. 16(6): 1198-1205 (2010).
  2. Carlos Eduardo Scheidegger, John M. Schreiner, Brian Duffy, Hamish Carr, Cláudio T. Silva: Revisiting Histograms and Isosurface Statistics. IEEE Trans. Vis. Comput. Graph. 14(6): 1659-1666 (2008).
  3. Hamish Carr, Brian Duffy, Brian Denby: On Histograms and Isosurface Statistics. IEEE Trans. Vis. Comput. Graph. 12(5): 1259-1266 (2006).
  4. Hamish Carr, Jack Snoeyink, Michiel van de Panne: Simplifying Flexible Isosurfaces Using Local Geometric Measures. IEEE Visualization 2004: 497-504.
  5. Chandrajit L. Bajaj, Valerio Pascucci, Daniel Schikore: The contour spectrum. IEEE Visualization 1997: 167-174.

Differential geometry

  1. Tino Weinkauf, Holger Theisel: Streak Lines as Tangent Curves of a Derived Vector Field. IEEE Trans. Vis. Comput. Graph. 16(6): 1225-1234 (2010).
  2. Ovidio Mallo, Ronald Peikert, Christian Sigg, Filip Sadlo: Illuminated Lines Revisited. IEEE Visualization 2005: 3
  3. Vivek Verma, David T. Kao, Alex Pang: A flow-guided streamline seeding strategy. IEEE Visualization 2000: 163-170.
  4. Detlev Stalling, Malte Zöckler, Hans-Christian Hege: Fast Display of Illuminated Field Lines. IEEE Trans. Vis. Comput. Graph. 3(2): 118-128 (1997).

Statistics

  1. Statistics for scientific data analysis: generate statistics (mean, variance, correlation, or higher order statistics) to augment data analysis.
    1. Chaoli Wang, Kwan-Liu Ma: A Statistical Approach to Volume Data Quality Assessment. IEEE Trans. Vis. Comput. Graph. 14(3): 590-602 (2008).
    2. Luke J. Gosink, John C. Anderson, Wes Bethel, Kenneth I. Joy: Variable Interactions in Query-Driven Visualization. IEEE Trans. Vis. Comput. Graph. 13(6): 1400-1407 (2007).
    3. Hiroshi Akiba, Nathaniel Fout, Kwan-Liu Ma: Simultaneous Classification of Time-Varying Volume Data Based on the Time Histogram. EuroVis 2006: 171-178.
    4. Shivaraj Tenginakai, Jinho Lee, Raghu Machiraju: Salient Iso-Surface Detection with Model-Independent Statistical Signatures. IEEE Visualization 2001.

  2. Classification/feature tracking: utilize statistics for material classification (transfer function design) and tracking (feature tracking).
    1. Yunhai Wang, Wei Chen, Guihua Shan, Tingxin Dong, Xuebin Chi: Volume exploration using ellipsoidal Gaussian transfer functions. PacificVis 2010: 25-32.
    2. Jesus Caban, Penny Rheingans: Texture-based Transfer Functions for Direct Volume Rendering. IEEE Trans. Vis. Comput. Graph. 14(6): 1364-1371 (2008).
    3. Jesus Caban, Alark Joshi, Penny Rheingans: Texture-based feature tracking for effective time-varying data visualization. IEEE Trans. Vis. Comput. Graph. 13(6): 1472-1479 (2007).
    4. Heike Jänicke, Alexander Wiebel, Gerik Scheuermann, Wolfgang Kollmann: Multifield Visualization Using Local Statistical Complexity. IEEE Trans. Vis. Comput. Graph. 13(6): 1384-1391 (2007).
    5. Joe Michael Kniss, Robert L. Van Uitert Jr., Abraham Stephens, Guo-Shi Li, Tolga Tasdizen, Charles D. Hansen: Statistically Quantitative Volume Visualization. IEEE Visualization 2005: 37.
    6. Joe Kniss, Gordon L. Kindlmann, Charles D. Hansen: Multidimensional Transfer Functions for Interactive Volume Rendering. IEEE Trans. Vis. Comput. Graph. 8(3): 270-285 (2002).

  3. Information theory: apply entropy or other information-theoretic measurement for data analysis and visualization.
    1. Lijie Xu, Teng-Yok Lee, Han-Wei Shen: An Information-Theoretic Framework for Flow Visualization. IEEE Trans. Vis. Comput. Graph. 16(6): 1216-1224 (2010).
    2. Chaoli Wang, Hongfeng Yu, Kwan-Liu Ma: Importance-Driven Time-Varying Data Visualization. IEEE Trans. Vis. Comput. Graph. 14(6): 1547-1554 (2008).
    3. Chaoli Wang, Han-Wei Shen: LOD Map - A Visual Interface for Navigating Multiresolution Volume Visualization. IEEE Trans. Vis. Comput. Graph. 12(5): 1029-1036 (2006).
    4. Udeepta Bordoloi, Han-Wei Shen: View Selection for Volume Rendering. IEEE Visualization 2005: 62.
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TRENCH_REAL_ANALYSIS.pdf
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Teng-Yok Lee,
Jan 4, 2011, 11:28 AM
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