Summary of Work for Joint Research Interchanges with DARWIN Integrated Product Team 1998

The intent of Stanford University's SciVis group is to develop technologies that enabled comparative analysis and visualization techniques for simulated and experimental flow fields. These techniques would then be made available under the Joint Research Interchange for potential injection into the DARWIN Workspace Environment (DWE). In the past, we have focused on techniques that exploited feature based comparisons such as shock and vortex extractions. Our current research effort focuses on finding a quantitative comparison of general vector fields based on topological features. Since the method relies on topological information, grid matching and vector alignment is not needed in the comparison. This is often a problem with many data comparison techniques. In addition, since only topology based information is stored and compared for each field, there is a significant compression of information that enables large databases to be quickly searched. This report will briefly (1) describe current technologies in the area of comparison techniques, (2) will describe the theory of our new method and finally (3) summarize a few of the results

Summary of Work for Joint Research Interchanges with DARWIN Integrated Product Team

The intent of Stanford University's SciVis group is to develop technologies that enabled comparative analysis and visualization techniques for simulated and experimental flow fields. These techniques would then be made available un- der the Joint Research Interchange for potential injection into the DARWIN Workspace Environment (DWE). In the past, we have focused on techniques that exploited feature based comparisons such as shock and vortex extractions. Our current research effort focuses on finding a quantitative comparison of general vector fields based on topological features. Since the method relies on topological information, grid matching an@ vector alignment is not needed in the comparison. This is often a problem with many data comparison techniques. In addition, since only topology based information is stored and compared for each field, there is a significant compression of information that enables large databases to be quickly searched. This report will briefly (1) describe current technologies in the area of comparison techniques, (2) will describe the theory of our new method and finally (3) summarize a few of the results

Critical Point Identification In 3D Velocity Fields

Classification of flow fields involving strong vortices such as those from bluff body wakes and animal locomotion can provide important insight to their hydrodynamic behavior. Previous work has successfully classified 2D flow fields based on critical points of the velocity field and the structure of an associated weighted graph using the critical points as vertices. The present work focuses on extension of this approach to 3D flows. To this end, we have used the Gauss-Bonnet theorem to find critical points and their indices in the 3D velocity vector field, which functions similarly to the Poincare-Bendixon theorem in 2D flow fields. The approach utilizes an initial search for critical points based on local flow field direction, and the Gauss-Bonnet theorem is used to refine the location of critical points by dividing the volume integral form of the Gauss-Bonnet theorem into smaller regions. The developed method is cable of locating critical points at sub-grid level precision, which is a key factor for locating critical points and determining their associated eigenvalues on coarse grids. To verify this approach, we have applied this method on sample flow fields generated from potential flow theory and numerical methods

Lower bounds for embedding the Earth Mover Distance metric into normed spaces

Thesis (M. Eng.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2005.Includes bibliographical references (p. 71-73).This thesis presents a lower bounds for embedding the Earth Mover Distance (EMID) metric into normed spaces. The EMID is a metric over two distributions where one is a mass of earth spread out in space and the other is a collection of holes in that same space. The EMD between these two distributions is defined as the least amount of work needed to fill the holes with earth. The EMD metric is used in a number of applications, for example in similarity searching and for image retrieval. We present a simple construction of point sets in the ENID metric space over two dimensions that cannot be embedded from the ED metric exactly into normed spaces, namely l1 and the square of l2. An embedding is a mapping f : X --> V with X a set of points in a metric space and ' Va set of points in some normed vector space. When the Manhattan distance is used as the underlying metric for the EMD, it can be shown that this example is isometric to K2,4 which has distortion equal to 1.25 when it is embedded into I and( 1.1180 when embedded into the square of 12. Other constructions of points sets in the EMID metric space over three and higher dimensisions are also discussed..by Javed K.K. Samuel.M.Eng