Visualizing features and tracking their evolution

Visualizing Features and Tracking Their Evolution Ravi Samtaney, Deborah Silver, Norman Zabusky, and Jim Cao

Rutgers University

Scientists studying the dynamics of objects can use

these visualization techniques to extract

objects from 2D and 3D scalar

and vector fields and thereby reduce

“visual clutter.”

S cientific visualization aims to devise algorithms and methods that transform massive scientific data sets into pictures and other graphic representations that facilitate comprehension and interpretation. In many scientific domains,

analysis of these pictures has motivated further scientific investigation - laboratory experiments. numerical simulations. or remote observations.

If a particular region of activity is of interest, scientists attempt to identify and quantify it: What is it, what is its cause, how does it evolve, how long does it persist’? For example. scientists track a storm’s progress for weather prediction, the change in the ozone ”hole” for knowledge about the greenhouse effect, and the movement of air over an aircraft or automobile for better aerodynamic design.

Scientists want to study the essential dynamics of objects and their evolution: they want to describe them for controlled time periods. thus obtaining partial, and there- fore simpler. mathematical solutions to the original problem. Unfortunately, even this is a daunting task because the data generated is overwhelming. For example, a typical 3D numerical unsteady simulation (time dependent) in computational fluid dynamics (CFD) may involve hundreds of time steps and as many as 2563 or greater data points. Most scientists cannot routinely store this information locally or access it interactively for visualization and analysis. Performing visualization during computation can sometimes reduce the storage space and postprocessing time, but there still may be too much information to absorb, since many of these data sets are very “busy” (see Figure I . for example). Furthermore. most standard visualization procedures concentrate on rendering a data set. not on quantifying the numerous observed regions.

Because the scientist is primarily interested in higher level phenomena, a workable solution to the data problem is to focus on just those “features” -that is. to automatically extract and track them. This both reduces the amount of data and provides a crucial first step in understanding how these objects evolve.

In this article. we describe basic algorithms to extract coherent amorphous regions (features or objects) from two- and three-dimensional scalar and vector fields and then track them in a series of consecutive time steps. We use a combination of techniques from computer vision. image processing, computer graphics. and computational ge- ometry and apply them to data sets from computational fluid dynamics. We demonstrate how these techniques can reduce “visual clutter” and provide the first step to quantifying observable phenomena. These results can be generalized to other disci- plines with continuous time-dependent scalar (and vector) fields.

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Related work Feature-based tools are

typical in two-dimensional image processing and computer vision.’,* There has been some work in feature extraction in 3D,3-6 mostly related to medical imaging. Most of these methods use seed expansion to isolate one distinct region. Some of these techniques will be described later.

Tracking objects in a series of 2D images, that is, motion tracking and optical f low, is widely dealt with in computer vision.’ The major issue is to find a particular feature in a series of consecutive frames. Matching an object in one frame to one in another is called the correspondence problem. The objects are generally matched using a range of attributes such as pixel values, edges, moments, and ge- ometry.

Many such techniques are applicable’ in the scientific domain. Oceanography and meteorology have incorpo- rated tracking to process the remote sensing observations that are continually being generated. For example, in Arnaud, Desbois, and Maizi? cloud tracking is performed by calculating attributes of

/’ /

/’ I

Figure 1. Vorticity isosurface for 3D shock-interface interaction, shown in five time steps: Time = 200,220,240,260, and 280 in frames (1) through (S), respectively.

the clouds and searching for matches in the next data set. In fluid dynamics, tracking has been performed on a limited ba- sis for vortex tubes by first determining the core of a tube in one data set. A search window about the position of the core was then used to locate the core in the next data set.’

These and other scientific domains present additional challenges since scientific “objects” are three dimensional (not 3D projections)’ and tend to evolve and interact. A similar problem is posed by space tracking; that is. given a set of 2D contour slices representing a continuous 3D domain, we must determine the correspondence between the surfaces from one slice to the next. The characterization of possible scenarios and topologies is similar (see Shinagawa and Kunii’” for one example), although generally only edges are matched instead of entire regions.

Extracting regions of interest

Each domain has its own set of interesting objects or features. These are usu- ally defined as regions of the data set that satisfy certain constraints: for example. an area of low pressure may define an on- coming storm. Standard visualization programs highlight isovalued clusters, since the eye is naturally drawn to colored coherent areas. This is the simplest definition of a feature and is common to many areas of scientific research. In this definition, objects consist of a set of neighboring interior points above or below a certain threshold value and their boundaries. While many other types of features are of interest (for example. vector field lines and critical points“). in what follows we concentrate on thresholded clusters.

Connected thresholded regions can be extracted using 3D segmentation or region- growing algorithms.6 If the region is to contain “high” values, local maxima may be used as seed nodes. The 3D neighbors of the seeds are then recursively tested for in- clusion in the regions (see also Ma, Cohen, and Painter3). The region stops growing when it hits a node below the chosen threshold value. The data set will then be parti- tioned into “objects” and background, and the set of nodes that constitute the object are stored in a data structure for efficient manipula- tion. (For regular gridded data sets. an octreeI2 is effective.) The w e r can choose seed nodes interactively, o r they can be generated automatically by stepping through different threshold values from the maximum to the mini- mum. As the stepping procedure continues, new regions are started by local maxima. The shape and size of the region can also be controlled by multidimensional thresholding, topological parameters known about the domain, or a gradient filter that defines the “edges.”‘

Figure 1 shows a widely used visualization method for displaying isosurfaces of a data set. The data set is a scalar field with dimensions 256 x 64x 64 derived from a vorticity vector field re- sulting from the perturbation of a Freon- air interface. In these five time steps from a sequence of 816. different regions are evident but are not clear or easily quan- tifiable. Once the individual regions are isolated and stored, however, the attributes of each region can be calculated. Since they are all separate regions, the boundaries are distinct and can be colored differently. (We discuss this model in greater detail below.)

Object attributes. Attributes are useful for quantifying the extracted regions (that is, a set of nodes satisfying certain constraints) and for tracking. Some common attributes are defined below (all definitions assume regular data sets).

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Mass. The mass is the weighted sum of all the nodes contained within the extracted region,

wherex=(x , ,x ?..... xd) forthe dimension of the field. w ( x ) is the scalar value at the node x. and R = (xlw(x) > T,) for a particular threshold value T(,,.

Centroid. The weighted average of all the points in the isolated region is the centroid (the centroid is not always within the boundaries of the object), namely ., = wq. W(.).Xi dR

( k = 1.2, .... d )

Maximum. An extracted region may have several local maxima. These can be detected with the seed-growing algorithm.h

Volume . The number of nodes contained within the region is an approximation to the area or volume.

Continuation ' / \ I

,' ?*-Bifurcation )1

I

~ Diss:pation

I

I

~ Diss:pation

I

Figure 2. Tracking interactions: continuation (l), creation (2), dissipation (3), bifurcation (4), and amalgamation (5).

Moment. The moments of inertia can be used to characterize the shape and ori- entation of the region. The second moments define an ellipse in 2D or an ellip- soid in 3D:

I,, = w-'jr2 u<x) - -

(.q - . r , ) ( . r , -x , )&

(I, is a d x d matrix where I =l. 2. .... d and j = 1 ,2 ,..., d.)

Domain-specif ic variables. Each domain or data set will have different com- putable characteristics depending upon what other variables are available (average velocity or vorticity, circulation, tem- perature, pressure, and so forth).

Bounding surface. The extracted region's bounding surface is similar to the isosurface if the region was extracted by simple thresholding (except that each separate region is characterized by its own set of polygons). Bounding nodes can be tagged during region growing to speed up the computation.

While second-order moments are a good approximation to bloblike regions, they do not accurately capture tube or sheetlike structures. Higher order moments may provide a better approximation. as well as an error measure for the second moments. Skeletons (spines) are also useful to abstract regions and characterize vortex cores.y

Tracking features Tracking can be performed in either a

preprocessing or postprocessing mode. In postprocessing mode. regions are first extracted from all the data sets and then correlated. In preprocessing mode, the regions extracted from one data set are used to search for the regions in the next data set (see Villasenor and Vincent' for an example).

In what follows. we concentrate on the postprocessing method. Since objects may move or change significantly. some simple qualifications must be stated to limit the range and number of possible scenarios. The most basic assumption is that the time between successive data sets

(At = t,+, - t ,) is small. (The sampling frequency is large enough to capture object interactions.)

Interactions. During any experiment. objects evolve. The evolutionary events can be characterized as follows:

*Continuation. An object continues from time t, to t,,, with possible rota- tion. translation, or de- formation; its size may remain the same, become larger, or begin to dissipate.

*Creation. New objects appear above the threshold.

*Dissipation. Objects dis- appear.

*Bif i~rcat ion. An object separates into two or more substructures.

*Amalgamat ion . Two or more objects merge.

These actions are illustrated in Figure 2 and are discussed below.

Continuation. A feature that remains the same from one time step to another is said to continue. T o determine whether a particular object in one data set continues as an object in a subsequent data set. the correspondence criteria need to be fully defined. In what follows, we present a basic notion of correspondence for our scientific domain that is general enough to be applicable in many other domains.

Our definitions are based upon the in- tuitive notions of scientists who have studied the evolution of these amorphous regions in the past. For example, in Fig- ure 2 we immediately notice that 0:. (object 1 at time t = a ) continues as Oq, and 02 + 0:. (Boldface a refers to a set 0 of N objects extracted at time t = i, whereas OA refers to a particular object A at time t = i.)

Definition 1: Object Oh+' corresponds to O,i if (Ob+;'IoverIap(OA, OF, ) > overlap(01, OFi) for all oi,:g E Okl)

that is, the nodes of object OK+' have maximum overlap (location and value) with those of object 0,i. A second condition is

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sometimes necessary: overiap(OA. O/;\) > To,,,, where To,,, is a threshold on the size of the intersection.

The above condition requires storing the objects in their entirety. Since the set of nodes that define the objects may con- sume a great deal of storage (even if only two time steps are processed at once), it is sometimes more convenient to save only the computed attributes, such as distance volume, and circulation, and use those to determine correspondence. We can choose either the closest attribute - attribute(Oh+') that is most similar to attribute(0j) from all the other objects in OA -or those attributes whose relative difference is below a set threshold or threshold percentage. For moving regions where the velocity information is available, objects can be rotated or trans- lated before comparing.

Bifurcation and umalgamrrtion. An object that splits into two or more substructures in the next time step is said to bifurcate. Conversely, amalgamation occurs if two or more objects merge.

Definition 2: If a group of Nobjects ( N > l), Skladded are equivalent to 0j. then OA has bifurcated at time i + 1 into the regions of s$'.

The equivalence criteria are defined above. The mass, volume. and circulation can be added and compared to the original object. The weighted centroids of the bifurcated regions can be compared to the original object. If OA has bifurcated into the set Skl. then

C attribute(S;Sr ) - attribute( 0,; ) < Tattrihute

Amalgamation is the inverse property, namely,

Definition 3: If a group of objects SA added are equivalent to 02l. then the regions of SA have merged into object OA+l.

In Figure 2,O; has bifurcated into the two objects 0: and O?. Similarly, 0: and 0: merge to become 0,".

Creation and dissipation. Creation occurs when an object cannot be correlated with any object in the previous time step. An object dissipates when there is no object in a subsequent time step that can be matched to it.

Figure 3. Directed acyclic graph (DAG) history of the evolution of observed regions from Figure 1.

Definition 4: If an object is not a continuation of an object at time t, and has not been classified as part of a merge or bifurcation. then 0,!,+lis a new object (creation).

Definition 5: If an object 0:, cannot be correlated with any object at and has not been classified as part of an amalgamation or bifurcation. then 0 L has dissipated.

In Figure 2. 0: dissipates in the next time step, and 0: appears for the first time. Dissipation (creation) occurs when regions fall below (above) the chosen threshold value.

Tracking. The method described below performs a basic (simple and fast) matching and relies upon centroid. mass. volume. and circulation (in 2D). Toler- ances are used to determine the "good- ness" of the match. (Similar methods are listed in Ballard and Brown' and in Ar- naud. Desbois, and MaizLx)

Extract the objects from each data set. numbering each object and maintaining a list of attributes. Starting with the first and second data set, compare every data set with the subsequent one. For each object (centroid) in data set i, calculate which centroids from data set i+l are closest to it and test whether the volume, mass, and so forth are within the prescribed tol- erances ( Tk,ttr,hutc). If a match is found, tag those objects and remove them from the list. After all the objects that continue have been removed. test combinations of two or more from for bifurcation and amalgamation. We determine bifurcation and amalgamation by the difference between the average weighted centroids, total volume. total mass. and circulation

of the combinations with the original.

Becauxe the number of combinations are exponentially large, certain observations can be used to limit the testing. For example. if the regions of interest are generally "large." the number of objects can be significantly reduced. Further- more, interactions only occur within neighborhoods. For example, in Figure 2a. object 4 is unlikely to merge with object 1 in the next time step. For objects at time t, and r,+\. the closest object or near- est neighbor to 0,; is that which mini- mizes dist(Oi, 0;'). The next neighbor- hood level is defined as those objects in r,,' that are closer to Oi in a particular direction than any other objects. This can be determined by constructing a Voronoi diagram of the centroids or using win- dows and distance measures for an approximation.

Visualizing object histories. After the tracking procedure. we know the history of each object. Different representations can be used to display this information. For example, the histories of objects in Figure 2 can be characterized as follows:

a, b: l ( a ) + I(h). 2(a) + 2(b) + 3(b).

b, E: 2(h) + 2(c). 3 (h ) + l(c), 4(b) + 3 ( a ) + 4(a) + 4(b);

3(c) + 4(c).

In Figure 3, the information is repre- sented as a directed acyclic graph (DAG). A legend of the object names and their attributes is needed for com- plete understanding of these representations (the file used by the tracking program stores the object legends). Alternately, for 2D. a plot of the X-centroid position with respect to time can also highlight evolution (and position). as seen in Figure 6 (on p. 24).

Objects can also be colored by their histories, either by assigning their de-

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I Figure 4. Schematic of the shock-interface problem.

scendants the same color or by shading descendants as a percentage of their par- ents’ color (for example, by volume). Both the D A G and the X-centroid plot can be color coded with the objects.

Implementation. The current implementation of the program is divided into two parts, a feature extractor and a feature tracker. The feature extractor performs thresholding and segmentation (it works with the simulation or as a module in AVS from Advanced Visual Systems. A set of rules can be supplied to further enhance the segmentatiom6 The output from this program is a file specifying each object and the attributes describing the object. The bounding surface can be used to view the regions.

The feature tracker reads in the set of objects and attributes from each data set and then performs the correspondence in two or three dimensions. Distance is used as the primary matching parameter. The output is either a text file containing the history, a DAG, or a set of color- coded polygonal objects.

Example simulations

We demonstrate feature extraction and tracking in both a 2D and a 3D simulation of a shock-interface interaction in CFD.

One of the fundamental interactions in compressible hydrodynamics is between a shock wave and a density inho- mogeneity. The physical situation, shown in Figure 4, can be characterized by a shock wave propagating through a fluid of density pl, striking a contact interface and passing into a region of density pr. The governing equations are the compressible Euler equations.

The physical processes can be divided

Figure 5.2D shock- interface air-Freon vorticity plot at time = ( a) 160,

(d) 1,280. The darker regions on the color map indicate higher negative vorticity.

(b) 480, (C) 800,

Figure 6. Feature tracking for the 2D shock interface: plot of the CVS centroid ( X value) versus time.

100 (b)

n 300 400 500

100 (c)

0 300 400 UXI I ‘9”

Perturbed Air-R22 Interface. M = 1.5. a = 60”. ma, = 0.0225.

550

into two phases: ( 1 ) a rapid vorticity de- position phase (vorticity is defined as o = V x I L , where I I is the velocity field) and (2) a vorticity evolution phase during which the interface is characterized

by the presence of coherent vortex structures (CVSs), which are the “features” or “objects” of interest to the fluid dynamicist. Quantification of CVS properties (such as circulation. area,

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Figure 7. Feature tracking, 3D air- Freon shock- interface. Evolv- ing regions are tracked and given the same color. Time = (1) 200, (2) 220, (3) 240, (4) 260, ( 5 ) 280.

Figure 8. DAG history for the 3D shock-interface simulation.

and centroid) and their interactions with each other is essential for a physical understanding and development of reduced models of the ensuing turbu- lent mixing phase.

2D example. In the 2D shock-interface simulation. the interface is aidFreon inclined at 60 degrees to the vertical with an incident shock Mach number. M = 1.5. The data sets are 800 x 160 with uniform

unity grid spacing. The quantity being studied is the vorticity field. Vorticity is a vector quantity; however, in the following two examples, we use the magnitude of the vorticity field.

In Figure 5, four of the 3,200 images are shown at times to = 160, tb = 480, t, = 800, and t d = 1,280. As the shock traverses the interface, vorticity is deposited on the interface and appears as the dark region in to. Four CVSs are then formed and sub- sequently amalgamate. The amalgamation of c v s s (1) and (2) is observed in td.

The entire physical process is characterized by the generation of a vortex layer followed by splitting, filamentation, and finally amalgamation. The four dom- inant CVSs are tracked with the threshold value, To = 0.0225. We do not track the filamentary structures that lie above the threshold because we want to focus on the CVS cores.

The history of the objects can be repre- sented by plotting the x centroid of each CVS as a function of time (Figure 6) or as a DAG. The choice of the threshold value is, in general, domain dependent. In this case, the threshold is chosen based on the theoretical total vorticity on the interface. One of the important quantities in the domain is the total negative circulation (r-), that is, the sum of all the negative vorticity. It was observed that more than 75 per- cent of r- was concentrated within the tracked CVSs for t c 500.

3D example. A 3D M = 2.0 shock interaction with an airFreon interface is shown in Figures 1 and 7. The planar interface is inclined at 45 degrees to the plane of the shock. Each data set is of dimension 256 x 64 x 64 and contains vorticity magnitudes.

Due to a physical phenomenon called vortex stretching, which is absent in 2D, the topologies of the CVS are more complex in this case. In Figure 1, isosurfaces ( T u = 0.15) of five of the 816 data sets are presented at tl = 200, t2 = 220, t3 = 240, t4 = 260, t5 = 280. Only the large-scale regions are of interest here, so small regions were disregarded. The extracted regions were tracked in consecutive data sets, and the color-coded history is shown in Figure 7. (The overall history of the five data sets is shown in the D A G in Figure 8.)

At tl in Figure 7, seven coherent vor- tices (colored differently) are observed in the flow field. The most complex vortex structure, labeled 0, is in the shape of a half vortex ring with two tails. The evolution of this structure is important in fluid dynamics. At t2, CVS 0; has split

July 1994 25


Figure 9. The hairpin-like coherent vortex structure (CVS) is isolated and its evolution is tracked over time.

into three parts: the two tails, 0; and 0;. and the ring portion, 0;. Note that the three objects in the middle of the domain have dissipated. As time progresses, both 0: and O’, bifurcate once more, and the tip portion (0: and 0: )amalgamates after t3.

A movie of all the data sets was made. with each region color coded. In Figure 9. 0: is tracked and rendered by itself. Some of the object properties for the first and last frame are given as text in the figure.

W e have demonstrated how some basic segmentation and tracking algorithms can en-

hance visualization and analysis of large time-dependent data sequences. We are currently improving the algorithm and testing more-complex computer vision and other methods to determine the best techniques for large 3D scientific data sets.

Domain-dependent identification parameters may be appropriate in certain instances. Centroids can be misleading, as in the case of a torus and an object in the center, where both will have the same centroid. The correspondence problem could be mitigated by using template matching, voxel-to-voxel-based compar- isons if all the information can be stored. opt imiza t ion techniques (parameter space matching), and learning algorithms to find the best match over a number of parameters.

When At is small, fewer discontinuities in the history plots result. As At in- creases, objects move farther and their volume changes more rapidly. making i t harder t o correlate them. While small time steps are desirable. this option is not always available (especially if the feature extractor is not implemented with the

simulation). In this case, the various tol- erances, Tatlrlhule. must increase. A common error that occurs when the threshold is too low is that regions will be tagged as continuing when they have ac- tually bifurcated into two regions, one large. almost the size of the original, and one small region. The small region is then regarded as a “new” object (this can be avoided by retesting “new” regions). We are performing more experiments to determine the algorithm’s sensitivity to At.

While the D A G representation and other plots are useful. they must be correlated with the extracted object information. An interactive interface would help in highlighting the objects visually. For example, if a node on the D A G were chosen, the object (and the history) cor- responding to that node would be rendered. Defining features is also an important area of study. Each domain has its own set of interesting features, with parameters t o define the feature and tracking criteria. Once the features are defined, they can be classified6 and stored for later use. One can envision a sophisticated database for scientific applications where events found in one simulation can be searched for in others and then rendered automatically.

The ultimate goal of visualization is to help us understand and analyze data. With the advent of faster parallel com- puters. more sophisticated sensing de- vices. and higher bandwidth communica- tion channels. information is being produced in ever greater amounts. This information must be presented to the scientist in a form suitable for cogent as- similation. There is an urgent need for better tools to automatically search for and compare space-time features.

Acknowledgments This work was performed with the help of

the members of the Laboratory for Visiomet- rics and Modeling at Rutgers University. The simulations were done on the Cray-90 at the Pittsburgh Supercomputer Center and on the CM5 at the National Center for Supercomput- ing Applications. We acknowledge the support of the NASA Ames Research Center (NAG 2-829), the US Department of Energy (DE- FG02-93ER25179.A000). ARPA (HPCD), and the CAIP Center, Rutgers University. The above work was partly based upon Ravi Sam- taney’s doctoral dissertation (Rutgers Univer- sity, 1993). We thank David Epstein for his as- sistance in making the figures.

References 1. D. Ballard and C. Brown. Computer Vision,

Prentice Hall, Englcwood Cliffs, N.J., 1982.

2. B. Jahne, Digital Image Processing, Springer Verlag. 1991.

3. K. Ma. M. Cohen, and J. Painter, “Volume Seeds: A Volume Exploration Tech- nique,” J . Visualization and Computer An- imation. Vol. 4. No. 2, 1991, pp. 135-140.

4. J. Miller et al.. “Geometrically Deformed Models: A Method for Extracting Closed Geometric Models from Volumes,” Com- puter Graphic.\. Vol. 25, No. 4, July 1991,

5 .

6.

7.

8.

9.

10

pp. 217-226

J. Udupa. “3D Visualization of Images.” Tech. Report MIPG196, Medical Image Processing Group, Univ. of Pennsylvania, Philadelphia, Pa., June 1993.

D. Silver and N. Zabusky. “Quantifying Visualizations for Reduced Modeling in Nonlinear Science: Extracting Structures from Data Sets,” J . Visual Comm. and Zm- age Representation, Vol. 4, No. 1. Mar. 1993, pp. 46-61.

I. Carlbom. I . Chakravarty, and W. Hsu. “Integrating Computer Graphics, Com- puter Vision, and Image Processing in Sci- entific Applications,” Computer Graphics, Vol. 26, No. 1. Jan. 1992, pp. 8-16,

Y. Amaud, M. Desbois, and J. Maizi, “Au- tomatic Tracking and Characterization of African Convective Systems on Meteosat Pictures,” Am. Meteorological Soc., May 1992, pp. 443-453.

J. Villasenor and A. Vincent, “An Algo- rithm for Space Recognition and Time Tracking o f Vorticity Tubes in Turbu- lence.“ Conipitter Vision Graphics and Im- age Processing: Image Understanding. Vol. 55. No. 1, Jan. 1992. pp. 27-35.

Y . Shinagawa and T. Kunii, “Constructing a Reeb Graph Automatically from Cross Sections,” I E E E Computer Graphics and Applicarions. Vol. 11, No. 6, Nov. 1991, pp. 4s-s 1

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11. J. Hclman and L. Hcsselink. "Reprcsen- tation and Display of Vector Field Topol- ogy in Fluid Flow Data Sets." Compirtrr. Vol. 22. No. 8. Aug. 1989. pp. 27-36.

12. J. Wilhelms and A. Van Gelder. "Octrees for Faster Isosurfacc Generation." A C M Trans. Graphics, Vol. 11. No. 3. July 1992. pp. 201-227.

Raytheon. the Max Planck Institute for Physics and Astrophysics. the Princeton Plasma Research Laboratorv. and Bell Labo- ratories.

He holds a BEE degree from thc College of theCityofNewYork(1951),an MSfromMIT (1953). and a PhD from the California Insti- tute of Technology (1 059).

Jim Cao is pursuing his PhD degree in the De- partment of Computer Science, Rutgers Uni- versity. His research interests include paral- lelidistributed computing and scientific visualization. He received a BS degree from the East China Institute and an MS from Zhe- jiang University. both in computer science, in 1984 and 1987.

Redder\ can contact the au x s dt the Laboratory for Visiometrics dnd Modeling, CAIP Cen- ter. Rutgers Universit\ PO Box 1390. Piscataway. NJ. 08855-1390. e-mail (samtaney, silver, nzabuskv jcao}@vizlab rutgers edu Ravi Samtaney is a postdoctoral research fel-

low in the Department of Mechanical and Aerospace Engineering at Rutgers University. His research interests are theoretical and computational fluid dynamics, high-speed compressible flows, vortex dynamics, parallel computing, and scientific visualization.

He obtained his BS degree in mechanical engineering at the Indian Institute of Tech- nology. Bombay, in 1986 and his MS and PhD degrees in mechanical and aerospace engineering at Rutgers University in 1988 and 1993.

Deborah Silver is an assistant prolessor in thc Department of Electrical and Computer En- gineering at Rutgers IJnivcrsity. Her research interests include scientific visualization. computer graphics. geometric modeling. and parallel computing.

She received her BS in computer scicnce from Columbia University in 1Y84 and her MS and PhD degrees in computer science from Princeton University in 1986 and 1988.

Norman Zabusky is the State of New Jersey Professor of Computational Fluid Dynamics in the Department of Mechanical and Aerospace Engineering at Rutgers University. Before joining Rutgers in 1988. he worked at

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