This Article 
   
 Share 
   
 Bibliographic References 
   
 Add to: 
 
Digg
Furl
Spurl
Blink
Simpy
Google
Del.icio.us
Y!MyWeb
 
 Search 
   
Discontinuities in Continuous Scatter Plots
November/December 2010 (vol. 16 no. 6)
pp. 1291-1300
Dirk J. Lehmann, University of Magdeburg
Holger Theisel, University of Magdeburg
The concept of continuous scatterplot (CSP) is a modern visualization technique. The idea is to define a scalar density value based on the map between an n-dimensional spatial domain and an m-dimensional data domain, which describe the CSP space. Usually the data domain is two-dimensional to visually convey the underlying, density coded, data. In this paper we investigate kinds of map-based discontinuities, especially for the practical cases n = m = 2 and n = 3 | m = 2, and we depict relations between them and attributes of the resulting CSP itself. Additionally, we show that discontinuities build critical line structures, and we introduce algorithms to detect them. Further, we introduce a discontinuity-based visualization approach—called contribution map (CM)—which establishes a relationship between the CSP's data domain and the number of connected components in the spatial domain. We show that CMs enhance the CSP-based linking & brushing interaction. Finally, we apply our approaches to a number of synthetic as well as real data sets.

[1] S. Bachthaler, S. Frey, and D. Weiskopf, Poster: CUDA-Accelerated Continuous 2D Scatterplots. IEEE Visualization Conference 2009, 2009.
[2] S. Bachthaler and D. Weiskopf, Continuous scatterplots. IEEE Transactions on Visualization and Computer Graphics, 14 (6): 1428–1435, 2008.
[3] S. Bachthaler and D. Weiskopf, Efficient and Adaptive Rendering of 2-D Continuous Scatterplots. Comput. Graph. Forum 28 (3): 743–750 (2009), 2009.
[4] R. Becker and W. Cleveland, Brushing scatterplots. Technometrics, 29 (2): 127–142, 1987.
[5] J. F. Canny, A computational approach to edge detection. Pattern Analysis and Machine Intelligence, 29: 679–698, 1986.
[6] H. Carr, B. Duffy, and D. Brian, On histograms and isosurface statistics. IEEE Transactions on Visualization and Computer Graphics, 12: 1259–1266, 2006.
[7] J. C. Carr, R. K. Beatson, J. B. Cherrie, T. J. Mitchell, W. R. Fright, B. C. McCallum, and T. R. Evans, Reconstruction and representation of 3d objects with radial basis functions. SIGGRAPH `01: Proceedings of the 28th annual conference on Computer graphics and interactive techniques, pages 67–76, 2001.
[8] H. Edelsbrunner, D. Morozov, and A. K. Patel, The stability of the apparent contour of an orientable 2-manifold. Workshop Top. Methods in Data Anal. Visual. (to appear), pages 183–192, 2009.
[9] J. Heinrich and D. Weiskopf, Continuous Parallel Coordinates. IEEE Transactions on Visualization and Computer Graphics (Proceedings Visualization/Information Visualization 2009), 15 (6), 2009.
[10] R. Peikert and M. Roth, The Parallel Vectors Operator - A Vector Field Visualization Primitive. In Proceedings of the 10th IEEE Visualization Conference (VIS `99), pages 263–270, Washington, DC, USA, 1999. IEEE Computer Society.
[11] D. Shepard, A two-dimensional interpolation function for irregularly-spaced data. ACM `68: Proceedings of the 1968 23rd ACM national conference, pages 517–524, 1968.
[12] H. Theisel, J. Sahner, T. Weinkauf, and H.-P. Hege, H.-C. Seidel, Extraction of parallel vector surfaces in 3d time-dependent vector fields and appliction to vortex core line tracking. Proc. IEEE Visualization, pages 631–638, 2005.
[13] H. Theisel and H.-P. Seidel, Feature flow fields. Data Visualzation 2003, pages 141–148, 2003.
[14] B. Tversky, J. B. Morrison, and M. Betrancourt, Animation: Can it facilitate? International Journal of Human Computer Studies, pages 747–262, 2002.
[15] T. Weinkauf, H. Theisel, A. V. Gelder, and A. Pang, Stable feature flow fields. IEEE Transactions on Visualization and Computer Graphics, 2010.
[16] T. Weinkauf, H. Theisel, H.-C. Hege, and H.-P. Seidel, Boundary switch connectors for topological visualization of complex 3d vector fields. Vis-Sym2004, pages 183–192, 2004.

Index Terms:
Discontinuity, Scatterplot, Topology, Data Visualization
Citation:
Dirk J. Lehmann, Holger Theisel, "Discontinuities in Continuous Scatter Plots," IEEE Transactions on Visualization and Computer Graphics, vol. 16, no. 6, pp. 1291-1300, Nov.-Dec. 2010, doi:10.1109/TVCG.2010.146
Usage of this product signifies your acceptance of the Terms of Use.