Topology preserving compression of 2D vector fields

We present an algorithm for compressing 2D vector fields that preserves topology. Our approach is to simplify the given data set using constrained clustering. We employ different types of global and local error metrics including the earth mover's distance metric to measure the degradation in topology as well as weighted magnitude and angular errors. As a result, we obtain precise error bounds in the compressed vector fields. Experiments with both analytic and simulated data sets are presented. Results indicate that one can obtain significant compression with low errors without losing topology information.

[1]  Lambertus Hesselink,et al.  Feature comparisons of vector fields using earth mover's distance , 1998 .

[2]  Hans Hagen,et al.  C1-interpolation for vector field topology visualization , 1999, Proceedings Visualization '99 (Cat. No.99CB37067).

[3]  Alexandru Telea,et al.  Simplified representation of vector fields , 1999, Proceedings Visualization '99 (Cat. No.99CB37067).

[4]  Lambertus Hesselink,et al.  Feature comparisons of 3-D vector fields using earth mover's distance , 1999, Proceedings Visualization '99 (Cat. No.99CB37067).

[5]  Robert van Liere,et al.  Collapsing flow topology using area metrics , 1999, Proceedings Visualization '99 (Cat. No.99CB37067).

[6]  David Kenwright.  Automatic detection of open and closed separation and attachment lines , 1998 .

[7]  Bernd Hamann,et al.  Construction of vector field hierarchies , 1999, Proceedings Visualization '99 (Cat. No.99CB37067).

[8]  Lambertus Hesselink,et al.  Visualizing vector field topology in fluid flows , 1991, IEEE Computer Graphics and Applications.

[9]  Arthur Veldman,et al.  Spectro-Consistent Discretization of Navier-Stokes: a Challenge to RANS and LES , 1998 .

[10]  Al Globus,et al.  A tool for visualizing the topology of three-dimensional vector fields , 1991, Proceeding Visualization '91.

[11]  Chandrajit L. Bajaj,et al.  Topology preserving data simplification with error bounds , 1998, Comput. Graph..

[12]  Hans Hagen,et al.  Visualization of higher order singularities in vector fields , 1997 .

[13]  Valerio Pascucci,et al.  Visualization of scalar topology for structural enhancement , 1998 .

[14]  Jane Wilhelms,et al.  Multi-dimensional trees for controlled volume rendering and compression , 1994, VVS '94.