Visualizing features and tracking their evolution - Computer

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

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 therefore 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 geometry 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 disciplines with continuous time-dependent scalar (and vector) fields.

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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.” 20

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Related work

Connected thresholded regions can be extracted using Feature-based tools are 3D segmentation or regiontypical in two-dimensional imgrowing algorithms.6 If the reage processing and computer gion is to contain “high” valvision.’,*There has been some ues, local maxima may be work in feature extraction in used as seed nodes. The 3D 3D,3-6mostly related to medneighbors of the seeds are ical imaging. Most of these then recursively tested for inmethods use seed expansion clusion in the regions (see also to isolate one distinct region. Ma, Cohen, and Painter3). Some of these techniques will The region stops growing be described later. when it hits a node below the Tracking objects in a series chosen threshold value. The of 2D images, that is, motion data set will then be partitracking and optical f l o w , is tioned into “objects” and widely dealt with in computer background, and the set of vision.’ The major issue is to nodes that constitute the obfind a particular feature in a ject are stored in a data strucseries of consecutive frames. ture for efficient manipulaMatching an object in one tion. (For regular gridded data frame to one in another is sets. an octreeI2 is effective.) called the correspondence The w e r can choose seed problem. The objects are gennodes interactively, o r they erally matched using a range can be generated automatiof attributes such as pixel valcally by stepping through difues, edges, moments, and geferent threshold values from ometry. the maximum to the miniMany such techniques are mum. As the stepping proceapplicable’ in the scientific dure continues, new regions domain. Oceanography and are started by local maxima. meteorology have incorpo/’ / The shape and size of the re/’ rated tracking to process the gion can also be controlled by I remote sensing observations Figure 1. Vorticity isosurface for 3D shock-interface interacmultidimensional thresholdthat are continually being ing, topological parameters tion, shown in five time steps: Time = 200,220,240,260, and generated. For example, in known about the domain, or a 280 in frames (1) through (S), respectively. Arnaud, Desbois, and Maizi? gradient filter that defines the cloud tracking is performed “edges.”‘ by calculating attributes of Figure 1 shows a widely the clouds and searching for matches in used visualization method for displaying the next data set. In fluid dynamics, trackisosurfaces of a data set. The data set is a ing has been performed on a limited bascalar field with dimensions 256 x 64x 64 sis for vortex tubes by first determining derived from a vorticity vector field rethe core of a tube in one data set. A Each domain has its own set of inter- sulting from the perturbation of a Freonsearch window about the position of the esting objects or features. These are usu- air interface. In these five time steps from core was then used to locate the core in ally defined as regions of the data set that a sequence of 816. different regions are the next data set.’ satisfy certain constraints: for example. evident but are not clear or easily quanThese and other scientific domains an area of low pressure may define an on- tifiable. Once the individual regions are present additional challenges since sci- coming storm. Standard visualization isolated and stored, however, the atentific “objects” are three dimensional programs highlight isovalued clusters, tributes of each region can be calculated. (not 3D projections)’ and tend to evolve since the eye is naturally drawn to col- Since they are all separate regions, the and interact. A similar problem is posed ored coherent areas. This is the simplest boundaries are distinct and can be colby space tracking; that is. given a set of definition of a feature and is common to ored differently. (We discuss this model 2D contour slices representing a contin- many areas of scientific research. In this in greater detail below.) uous 3D domain, we must determine the definition, objects consist of a set of correspondence between the surfaces neighboring interior points above or beObject attributes. Attributes are usefrom one slice to the next. The charac- low a certain threshold value and their ful for quantifying the extracted regions terization of possible scenarios and boundaries. While many other types of (that is, a set of nodes satisfying certain topologies is similar (see Shinagawa and features are of interest (for example. vec- constraints) and for tracking. Some Kunii’” for one example), although gen- tor field lines and critical points“). in common attributes are defined below erally only edges are matched instead of what follows we concentrate on thresh- (all definitions assume regular data entire regions. olded clusters. sets).

Extracting regions of interest

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

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

Continuation

w h e r e x = ( 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

' /

,'

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?*-Bifurcation

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

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*Continuation. An object continues from time t, to t,,, with possible rotation. translation, or deformation; its size may remain the same, become larger, or begin to dissipate. *Creation. New objects appear above the threshold. *Dissipation. Objects disappear. *Bifi~rcation.An object separates into two or more substructures. * A m a l g a m a t i o n . Two or more objects merge.

I ~

Diss:pation

( k = 1.2, .... d )

M a x i m u m . An extracted region may have several local maxima. These can be detected with the seed-growing algorithm.h

I

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

V o l u m e . The number of nodes contained within the region is an approximation to the area or volume. Moment. The moments of inertia can be used to characterize the shape and orientation of the region. The second moments define an ellipse in 2D or an ellipsoid in 3D: I,,

=

w-'jr2u 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 consume 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 translated 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 o r 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 O A has bifurcated into the set then

Skl.

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.

is not a Definition 4: If an object 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). Tolerances are used to determine the "goodness" of the match. (Similar methods are listed in Ballard and Brown' and in Arnaud. 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 tolerances ( 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 t w o o r 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. Furthermore, 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 nearest neighbor to 0,; is that which minimizes dist(Oi, 0;').The next neighborhood 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 windows 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). 3 ( a ) + 4(a) + 4(b); b, E: 2 ( h ) + 2(c). 3 ( h ) + l(c), 4(b) + 3 ( c ) + 4(c). In Figure 3, the information is represented as a directed acyclic graph ( D A G ) . A legend of the object names and their attributes is needed for complete 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-interfaceproblem.

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scendants the same color or by shading descendants as a percentage of their parents’ 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 D A G , or a set of colorcoded polygonal objects.

100 (b)

300

400

500

300

400

UXI

100 (c)

0

Figure 5.2D shockinterface air-Freon vorticity plot at time = ( a) 160, (b) 480, (C)800, (d) 1,280. The darker regions on the color map indicate higher negative vorticity.

I ‘9”

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

550

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

into two phases: ( 1 ) a rapid vorticity deposition 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 airFreon shockinterface. Evolving 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 turbulent 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 subsequently 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 dominant CVSs are tracked with the threshold value, To = 0.0225. We d o 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 represented 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 percent 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 vortices (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

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Acknowledgments

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

This work was performed with the help of the members of the Laboratory for Visiometrics 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 Supercomputing Applications. We acknowledge the support of the NASA Ames Research Center (NAG 2-829), the US Department of Energy (DEFG02-93ER25179.A000). ARPA (HPCD), and the CAIP Center, Rutgers University. The above work was partly based upon Ravi Samtaney’s doctoral dissertation (Rutgers University, 1993).We thank David Epstein for his assistance in making the figures.

References 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 enhance 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 3 D 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 comparisons if all the information can be stored. o p t i m i z a t i o n 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 increases, objects move farther and their volume changes more rapidly. making it 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 tolerances, 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 actually 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) corresponding to that node would be rendered. Defining features is also a n 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 computers. more sophisticated sensing devices. and higher bandwidth communication channels. information is being produced in ever greater amounts. This information must be presented to the scientist in a form suitable for cogent assimilation. There is an urgent need for better tools to automatically search for and compare space-time features.

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 Technique,” J . Visualization and Computer Animation. 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,” Computer Graphic.\. Vol. 25, No. 4, July 1991, pp. 217-226 5 . J. Udupa. “3D Visualization of Images.” Tech. Report MIPG196, Medical Image Processing Group, Univ. of Pennsylvania,

Philadelphia, Pa., June 1993. 6. D. Silver and N. Zabusky. “Quantifying Visualizations for Reduced Modeling in Nonlinear Science: Extracting Structures from Data Sets,” J. Visual Comm. and Zmage Representation, Vol. 4, No. 1. Mar. 1993,pp. 46-61. 7. I. Carlbom. I. Chakravarty, and W. Hsu. “Integrating Computer Graphics, Computer Vision, and Image Processing in Scientific Applications,” Computer Graphics, Vol. 26, No. 1. Jan. 1992,pp. 8-16, 8. 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. 9. J. Villasenor and A. Vincent, “An Algorithm for Space Recognition and Time Tracking o f Vorticity Tubes in Turbulence.“ Conipitter Vision Graphics and Image Processing: Image Understanding. Vol. 55. No. 1, Jan. 1992. pp. 27-35. 10 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 Topology 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 Laboratories. He holds a BEE degree from thc College of theCityofNewYork(1951),an MSfromMIT (1953). and a PhD from the California Institute of Technology (1059). Jim Cao is pursuing his PhD degree in the De-

partment of Computer Science, Rutgers University. His research interests include parallelidistributed computing and scientific visualization. He received a BS degree from the East China Institute and an MS from Zhejiang University. both in computer science, in 1984 and 1987.

Ravi Samtaney is a postdoctoral research fellow 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 Technology. Bombay, in 1986 and his MS and PhD degrees in mechanical and aerospace engineering at Rutgers University in 1988 and 1993.

Redder\ can contact the au x s d t the Laboratory for Visiometrics dnd Modeling, CAIP Center. Rutgers Universit\ PO Box 1390. Piscataway. NJ. 08855-1390. e-mail (samtaney, silver, nzabuskv jcao}@vizlabrutgers edu

Building a Secure National Information Infrastructure

17th National

Deborah Silver is an assistant prolessor in thc

Department of Electrical and Computer Engineering 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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