![](media/image1.jpeg){width="1.4791666666666667in"
height="0.4791666666666667in"} **Advanced Scientific Computing
Research**

**Computer Science**

**FY 2006 Accomplishment**

**Feature Identification and Tracking**

## Chandrika Kamath

##  Lawrence Livermore National Laboratory

*Scientific Data Management Center*

Summary

***In many scientific problems, there is a need to identify structures
or features of interest, extracting characteristics of these features,
and tracking the features over time. This capability is especially
important when the dataset is very large or complex. Instead of visually
analyzing the data, scientists want to either focus-in on the areas of
interest, or summarize the dataset by identifying the location of the
structures of interest and their characteristics. If there is a time
component to these data, we can also extract the dynamics of the
structures over time. In FY2005, we implemented two classes of
techniques to classify orbits in a Poincaré plot. Orbits with specific
class labels can then be processed further to extract characteristics of
interest which, in turn, can be used in designing experiments and
comparing experiments to simulations. In addition, we also implemented
algorithms for tracking features over time. These techniques are
currently being applied in the context of experimental and simulation
datasets from Princeton Plasma Physics Laboratory (PPPL), and will be
applied to data from other Office of Science applications in the
future.***

Identifying and tracking structures or features of interest in data is
difficult when the dataset is massive. It can be especially challenging
when the features are complex, not very well-defined, and evolve over
time. This problem of feature identification and tracking arises in many
application domains, ranging from combustion to turbulence.

We are working with scientists at PPPL to analyze the orbits in a
Poincaré plot. These arise in fusion devices such as the National
Compact Stellarator Experiment (NCSX) at PPPL. These devices allow
physicists to perform experiments which determine the best shape for the
hot reacting plasma and the magnetic fields necessary to hold it in
place. Computational simulations of these devices enable the design of
experiments, which, in turn, are used to validate the simulations. One
of the tasks in the analysis of the simulations and the experiments is
the classification of orbits in Poincaré plot and the extraction of
features for specific orbits.

![](media/image3.png){width="0.9152777777777777in"
height="0.6125in"}![](media/image4.png){width="0.9152777777777777in"
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**Figure 1: A quasi-periodic orbit, an island chain, and a separatrix
orbit, illustrating the differences in shape in orbits.**

A Poincaré plot is created by particles moving around the toroidal
device. A single particle traces a three dimensional trajectory over
time. The intersections of this trajectory with a plane perpendicular to
the magnetic axis form an orbit. Based on the shape of an orbit, it is
assigned a class label (Figure 1.) It can be difficult to identify the
shape when there are few points describing an orbit or an orbit of one
type appears like another. For example, two island orbits can appear as
a separatrix if their tips are close to each other. Or, a separatrix
which is not very wide can appear as a quasi-periodic orbit. To address
these issues, we implemented an approach which first converted the orbit
data to polar coordinates, and then fit the points using piecewise
polynomials. The number of polynomials and the number of gaps in the
data can then be used to assign a class label to the orbit. In another
algorithm, we explored the use of graph-based techniques to extract
characteristics of the orbit. We found that by using machine learning
techniques such as decision trees, we could obtain more accurate
classification than an earlier approach using simple rules.

Once an orbit has been assigned a class label, we are interested is
extracting features such as the number of islands, the width of the
islands, and the width of the separatrix. These features will be used to
characterize each orbit and a plot composed of many orbits.

The task of tracking objects of interest occurs in many problems, such
as tracking flame fronts in combustion, tracking blobs in plasma, and
tracking particles in a particle simulation. Each problem has its unique
characteristics which imply that we need a suite of tracking algorithms
so we can select the most suitable algorithm for a dataset.

![](media/image6.png){width="1.3333333333333333in"
height="1.3333333333333333in"}
![](media/image7.png){width="1.3333333333333333in"
height="1.3333333333333333in"}

**Figure 2. A noisy image from NSTX (left) and its denoised version
(right). It is unclear if the vertical line to the left of the blob is
considered signal or noise.**

For example, consider the problem of tracking blobs in the National
Spherical Torus Experiment (NSTX) at PPPL. The images taken by the high
speed camera are noisy (Figure 2, left panel). While traditional image
analysis techniques can reduce some of this noise (Figure 2, right
panel), it is not clear if the vertical streak to the left of the bright
blob is part of the signal or the noise. Such noise does not appear in
simulation data. Also, some tracking algorithms require that the data
satisfy certain assumptions. For example, optical flow methods require
that the intensity of the image change slowly at each pixel in the
image. Such techniques would be inapplicable if the intensity changed
drastically across frames, which occurs frequently in NSTX images.

![](media/image8.png){width="1.167361111111111in"
height="1.167361111111111in"}
![](media/image9.png){width="1.1597222222222223in"
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**Figure 3. Two consecutive frames from NSTX indicating a large change
in the intensity at the center of the images.**

In the coming year, we will continue our work in the analyses of
Poincaré plots, enhancing and deploying our software at PPPL. We will
continue to enhance our suite of tracking algorithms and apply them to
problems such as NSTX images, plasma physics simulations, and
combustion.

Details of our analyses and publications are at
http://www.llnl.gov/casc/sapphire.

**For further information on this subject contact:**

Chandrika Kamath

Lawrence Livermore National Laboratory

kamath2@llnl.gov

## (925)-423-3768