Transcript pptx

Algorithms for Solar Active Region
Identification and Tracking
Michael Turmon
JPL/Caltech
Work with Todd Hoeksema, Xudong Sun (Stanford),
Harrison Jones, Elena Malanushenko (NSO),
Judit Pap (GSFC)
Capabilities Discussed Here
Identification
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Label active pixels in multivariate images, e.g.: (LOS B, Ic)
There exists a family of methods by many researchers
Largely a solved problem for active regions in photosphere
Bayesian approach maximizing posterior probability of labeling
• Has been released for HMI on jsoc.stanford.edu
Tracking
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Grouping of active pixels in labeling into ARs
Then, link identified ARs through a series of images
Single-link most likely tracker (optimization-based association)
Nearing release for HMI as hmi.Mharp_720s
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Motivation
Allow scientists in to understand great volumes of spatio-temporal data
in directly informative terms
Identification
Tracking
Object analysis
• Identification: Find objects in multispectral images
• Tracking: Link identified objects across a series of images
• Object Analysis: Model and classify object tracks
Move beyond looking at pixels to understanding phenomena
Identification
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Identification: Finding the Best Labeling
• Bayesian approach: maximize posterior probability having two terms
– Trade off fidelity to data (first term) vs. spatial coherence (second)
log Pr(class mask | obs. images) = constant +
log Pr(obs. images | class mask) + log Pr(class mask)
• Likelihood: Probability of a certain observed (field, intensity) given
activity type: e.g., quiet Sun, facula, sunspot
– Gaussian mixture model to parameterize each conditional density
• Prior: Enforces spatial smoothness of labeling to disambiguate cases
near the class boundary
– Nearby-neighbor smoothness via Markov random field (MRF) model
• Find mask via discrete optimization of posterior w.r.t. entire labeling
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Identification: Finding the Likelihood Term
Q
1: Experts identify classes
in sample images
Light
Intensity
F
Magnetic
Field
Labeling by inferred
statistical model
S
Key:
S(pot)
F(acula)
Q(uiet sun)
Q
Magnetogram
2: Learned mixture model
performs classification
automatically
Photogram
F
Q
N
S
S
Labeling
• Can not distinguish classes from just one observable
• Select mixture model using sample images labeled by scientists
– One mixture model per class
– To classify, compute each class’s probability under its mixture
– Move beyond ad hoc threshold rules to allow arbitrary class separators
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A Simple Likelihood (Data) Model
Active
Region
} ~10% darkening
Proxy Intensity
Quiet
Sun
LOS B/1000
• Chose ~50,000 pixels/class, fit two models (QS + AR)
– Only one (unipolar) AR shown in scatter plot above
• Used K = 7 Gaussian components for QS, K = 8 for AR
• Models are symmetric w.r.t. flips in sign of B
• These two classes overlap only a tiny bit around the stars
Identification: Partly-Labeled Data
• Hand labeling: time-consuming, asks too much
• Data from quiet Sun is easy to find; small amounts of other classes can
be obtained with care.
– E.g., scatter plot at left: 15K quiet examples + 607 sunspot + 340 facula
– Ensure atypical distribution of labeled data does not affect learned class
proportions.
• Developed methods using partly-classified data to bootstrap large
amounts of unlabeled data, in same clustering algorithm (EM)
• Yields ~20% classification accuracy improvement
Labeled Data
facula
Unlabeled Data
Previous Feature->Class Map
quiet
facula
sunspot
quiet
sunspot
New Feature->Class Map
Refinement: Symmetry in LOS B
• Data model should be invariant to the sign of LOS B
• Distributional constraint, for 2d observation y:
• For a normal mixture M, like our class-conditional
likelihoods, the constraint implies:
• Modify EM to respect this constraint: Average
sufficient statistics over the cyclic groups associated
with A.
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Symmetry in LOS B: Results
Constrained, K = 6
Best of 10 Runs
Flattened Ic
Samples from Quiet Sun
LOS B
Unconstrained, K = 6
Best of 10 Runs
Unconstrained, K = 6
Best of 10 Runs
Constraint
also adds
robustness
to model fits
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Refinement: Spatially-variant Measurement Noise
HMI LOS B Local RMS
LOS B Local RMS: Section
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Mask out
the ARs, take
RMS within
16x16 blocks
7.5
7.5 G
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6.5
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6.0 G
5.5
• Spatially-variant noise in LOS B and flattened intensity can be
modeled, especially for quiet Sun
• Generalize existing mixture setup for observed y at site s:
so the covariance is expressed in terms of, e.g., radial angle
• Plenty of QS pixels available to determine extra parameters in Aj
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Refinement: Customizing the Prior
• Account for spherical geometry with metric MRF prior
• Original prior penalizes all label-conflicts equally:
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• Modified prior penalizes differently across disk:
• Smaller penalties are assigned to farther-off conflicts:
where dist(s, s’) = great-circle distance between sites
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Spatially-varying Prior: Results
Left: KP LOS B.
Right: Constant-b
labelings
(b ≡ 0, b ≡ 0.2)
b: N-S penalty
(left), all penalty
components
(middle, zoomed).
Rightmost:
labeling with
variable b
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HMI Identification Status
• Output Masks
– Available as hmi.Marmask_720s and hmi.Marmask_720s_nrt
– Full-disk 4Kx4K mask images in coordinates of observations
– Never re-map observed images to find the mask
• Further Calibration
– Calibration team is working on better removal of limbdarkening and time-dependent flat-field from intensity proxy.
– Current HMI region model does not really use the intensity
proxy because of limb artifacts.
• Enhancements
– A more detailed class breakdown is possible.
– E.g., umbra/penumbra were not reliably determined from MDI;
believe HMI should be better
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Tracking
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Components of “Tracking”
• Identification
(just discussed)
• Grouping
– Group separated features into AR
– Formal literature on this is not well-developed
– Use a simple template-based method
• Association
– Construct 1:1 map from previous AR set to next AR set.
• Chained together, you have a track.
– Criterion: maximize cumulative area of overlap
– Heuristics to “look harder” for new or dying ARs
• Naming
– Link a track to a name like NOAA AR#9077
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Active Region Tracking: Grouping into ARs
• Activity mask = a set of pixels
– Grouping into NOAA-like AR’s is not trivial
– Connected components insufficient
• Take a matched-filter type approach
– Convolve AR mask with a Gaussian kernel
– Threshold
– AR groups are within basins
50 Mm
• Devilish Details
– Gaussian in 3D pixel-pixel distance; stretched longitudinally;
FWHM ~50x25Mm (~40x20 MDI pixel) at disk center
– Convolution on sphere to treat the limb fairly
– AR masks sparse: fast convolution (HMI: 12s)
– More cleverness is possible, e.g. polarity
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Grouping and Spherical Geometry
• It is critical to take spherical geometry into account
when grouping.
• Convolution speed dictates tracker speed
50 Mm
Kernel
at
Limb
Kernel at
Disk Center
Example
AR Mag.
(for scale)
Example
AR Mask
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Active Region Tracking: Grouping Example
MDI Labeling
Identified Groups
2002 Sep. 02, 11:11 UTC
Convolved with Template
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Active Region Tracking: Association
• Associate ARs in before
and after images
Before
B
After
A
• Correlation-based tracker
– Standard latitude-dependent
motion model
– Use area of overlap of AR bitmaps on the sphere
– Overlap between a in A and b in B is D(a,b)
• Solve assignment problem to match A up to B:
with P a permutation matrix giving the B-to-A mapping
– Fast, exact solution by linear programming
– Slack variables account for new or dead ARs
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HMI Examples
Flipped N-S. Apologies!
Reduced: 1024x1024, 1/day
Feb. 2011 flaring AR: orange.
Yellow AR: merges.
Small ARs died after frame 1;
red AR died after frame 5.
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References
M. Turmon, H. Jones, J. Pap, O. Malanushenko, “Statistical feature recognition for
multidimensional solar imagery”, Solar Physics, 04/2010.
The mixture modeling work appeared in:
Mixtures-2001, “Recent Developments in Mixture Modelling,” Hamburg
Compstat-2004, Prague, as “Symmetric Normal Mixtures”
Earlier work:
J. Pap, H. Jones, M. Turmon & L. Floyd, “Study of the SOHO/VIRGO
Irradiance Variations using MDI and Kitt Peak images,” Proc. SOHO-11
Workshop, Davos, 2002.
H.P. Jones, M. Turmon, et al. “A comparison of feature classification methods
for modeling solar irradiance variation,” 34th COSPAR Scientific Assembly,
2002.
The research described here was carried out in part by the Jet Propulsion
Laboratory, California Institute of Technology, under contract with the National
Aeronautics and Space Administration. Copyright 2011. All rights reserved.
Government sponsorship acknowledged.
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