C

Solar Physics (2005) 228: 339–358

Springer 2005

2D FEATURE RECOGNITION AND 3D RECONSTRUCTION IN SOLAR EUV IMAGES MARKUS J. ASCHWANDEN Lockheed Martin Advanced Technology Center, Solar and Astrophysics Laboratory, Department L9-41, Building 252, 3251 Hanover St., Palo Alto, CA 94304, U.S.A.; (e-mail: [email protected])

(Received 1 February 2005; accepted 16 February 2005)

Abstract. EUV images show the solar corona in a typical temperature range of T
1 MK, which encompasses the most common coronal structures: loops, filaments, and other magnetic structures in active regions, the quiet Sun, and coronal holes. Quantitative analysis increasingly demands automated 2D feature recognition and 3D reconstruction, in order to localize, track, and monitor the evolution of such coronal structures. We discuss numerical tools that “fingerprint” curvi-linear 1D features (e.g., loops and filaments). We discuss existing finger-printing algorithms, such as the brightness-gradient method, the oriented-connectivity method, stereoscopic methods, time-differencing, and space–time feature recognition. We discuss improved 2D feature recognition and 3D reconstruction techniques that make use of additional a priori constraints, using guidance from magnetic field extrapolations, curvature radii constraints, and acceleration and velocity constraints in time-dependent image sequences. Applications of these algorithms aid the analysis of SOHO/EIT, TRACE, and STEREO/SECCHI data, such as disentangling, 3D reconstruction, and hydrodynamic modeling of coronal loops, postflare loops, filaments, prominences, and 3D reconstruction of the coronal magnetic field in general.

1. Introduction Large numbers of solar EUV images have been recorded by the Solar and Heliospheric Observatory/Extreme-ultraviolet Imaging Telescope (SOHO/EIT) and the Transition Region and Coronal Explorer (TRACE), and will be provided in future space missions, such as with the EUV Imaging Spectrometer (EIS) on the Solar-B mission, the EUV Imager (EUVI) on the two STEREO spacecrafts, or the Atmospheric Imaging Assembly (AIA) on the Solar Dynamics Observatory (SDO). Solar EUV images from those instruments display countless structures of the solar corona in the temperature range of ≈1–2 MK, such as the ubiquitous coronal loops, filaments, prominences, postflare loops, or nanoflares. Efficient analysis of such phenomena, in particular statistical studies, require automated algorithms in order to detect, disentangle, and infer 3D coordinates for further analysis and geometrical and physical modeling. Solar EUV images are dominated by curvi-linear features, for the following physical reason: it is the consequence of the low plasma-β parameter in the solar corona (i.e., the ratio of the thermal to the magnetic pressure), which forces every coronal plasma to be distributed along magnetic field lines, while cross-field diffusion is completely prohibited under coronal conditions.

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Unfortunately, the development of numerical algorithms for pattern recognition in solar EUV images lags far behind the rapid growth of solar EUV databases, which contain already many millions of images in different wavelengths. There is very little literature available on solar EUV feature recognition algorithms. In this paper we aim to characterize existing and planned EUV feature recognition algorithms (Section 2), which mostly deal with curvi-linear and space–time features. From the feature recognition algorithms discussed here, some exist in form of numerical codes, while others are outlined as concepts for future developments. The applications enable physical modeling, as it has been pioneered in recent years, and will guide the design of future software developments for solar EUV data analysis.

2. Solar EUV Feature Recognition Methods 2.1. BRIGHTNESS - GRADIENT

METHOD

Figure 1 (left) shows an EUV image recorded with TRACE at a wavelength of ˚ displaying an arcade of coronal loops at a temperature of T ≈ 1.5 MK. For 195 A, physical modeling of such coronal loops, a desirable first task consists of detecting such curvi-linear features with an automated algorithm.

Figure 1. Left: a TRACE image recorded on August 25, 1998, around 04:00 UT at a wavelength of 195 A˚ (Fe XI/FeX). The displayed image contains 256 × 256 pixels, with a pixel size of 0.5 arcsec. The dynamic range is reduced by displaying the square root of the flux. Note the fuzzy moss-structure underneath the coronal loop arcade, which complicates the detection of loops. Right: the left image is processed by an algorithm that counts the number of directions with a local maximum along four directions in each pixel, so the number ranges between 0 and 4. This image is then smoothed and contiguous loop structures are identified. Note also residuals of the jpeg-compression algorithm in noisy areas, outlining some edges of 8 × 8 blocks (courtesy of Louis Strous).

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The simplest algorithm to find bright curvi-linear features was pioneered by Strous (2000), consisting of the following steps: (1) for each pixel [i, j], a local 3×3-box with the fluxes Fi  j  (i  = i −1, i, i +1, j  = j −1, j, j +1) is inspected; (2) from the four pixel directions (horizontal, vertical, and two diagonals) the number Ni j of directions is counted that contain a local maximum, e.g., Fi > (Fi−1 +Fi+1 )/2 for the horizontal direction (i  = i − 1, i, i + 1); (3) a new image is constructed with the number of directions with local maxima, Ni j , which have values between 0 and 4 (shown in Figure 1 right); (4) the image Ni j is smoothed (by a 2D-boxcar with a length of 5 pixels) to reduce the data noise; and (5) adjacent pixels with a high value Ni j are combined to contiguous curvi-linear structures. This brightness-gradient algorithm is capable of identifying many partial segments of loop structures, but it does not connect these partial loop segments to complete loops, and also it picks up a number of noisy features that are not related to loops. 2.2. ORIENTED- CONNECTIVITY

METHOD

An advanced version of the brightness-gradient method of Strous (2000) has been developed by Lee, Newman, and Gary (2004), who improved the connection of loop segments by constraining the orientation with a magnetic field model, the so-called oriented-connectivity method. Lee, Newman, and Gary (2004) improve the Strous algorithm also by applying first a (7 × 7) median-filter (Figure 2b) to the original EUV image (Figure 2a) to eliminate data noise. The spatial variation of the background flux is also eliminated by unsharp masking (Figure 2c), i.e., a high-pass filter is applied by subtracting a smoothed 11×11 filter from the median-filtered image. This enhances the contrast of narrow structures, such as coronal loops. Unwanted background noise is further eliminated by two subsequent thresholding steps (Figure 2d), i.e., structures with fluxes below the median value in sub-regions (with size 31×31) are ignored. The final step combines adjacent bright pixels to continuous curvi-linear loop structures by searching for bright next-neighbor pixels in a limited angle range in direction of the projected local magnetic field. The result is shown in Figure 2e, which displays more or less complete bright-loop segments, essentially free of background noise. The code of Lee, Newman, and Gary (2004) provides a fairly robust “finger-printing” method for automated detection of curvilinear loops, although a few problems remain that probably never can be completely eliminated, such as misconnections in cases of crossing, nested, or faint loops. A simulation of an image containing dipolar magnetic loops is shown in Figure 3, along with the results of the oriented-connectivity method. Note the successes and limitations in identifying complete loops in crossing and nested regions. 2.3. MAGNETIC

FIELD EXTRAPOLATION CONSTRAINTS

A comparison of a theoretical magnetic field model with observed coronal loops is shown in Figure 4, using a potential-field extrapolation for the 3D magnetic field

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Figure 2. (a) Original TRACE image, (b) median-filtered image, (c) contrast-enhanced version of unsharp masked image, (d) curve features after thresholding, and (e) detected loops superimposed on original image (Lee, Newman, and Gary, 2004).

that is projected onto the 2D EUV image, after correction for time differences and solar differential rotation. It can be clearly seen in Figure 4 that the magnetic field lines are not exactly aligned with the observed EUV loops. This just means that a potential-field model is not the correct theoretical model, even if the photospheric boundary constraints are taken from an observed line-of-sight magnetogram. Perhaps a force-free magnetic field model would fit the observed data better, but there are free parameters that have to be varied, e.g., the α-value for a linear force-free model (with a constant α), or multiple α-values for a nonlinear force-free model (with different α-values for each loop). Moreover, even with optimum fitting of local α-values, we do not expect a perfect match, because the assumption of force-freeness is not fulfilled in the lower chromosphere (Metcalf et al., 1995). So, magnetic field modeling of observed EUV loops represents its own challenge and efforts are underway with systematic forward-fitting methods (e.g., Wiegelmann and Neukirch, 2002; Wiegelmann and Inhester, 2003; Wiegelmann, 2004). Given these imperfect 3D magnetic field models, our concern here is whether they still can be used as an a-priori constraint to detect and trace coronal loop structures in EUV images. Theoretically, the observed EUV loops have to match

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Figure 3. Simulated image of coronal loops, based on magnetic field extrapolations of three linked dipoles, filled with plasma over a finite loop cross-section (grey scale). The loop segments identified with the oriented-connectivity method are overlayed with thin lines (Lee, Newman, and Gary, 2004).

some 3D magnetic field model in all sections of the corona where the plasma-β parameter is smaller than unity, which is very likely in altitudes of 2 < h < 100 Mm (Gary, 2001). Inspecting the example given in Figure 4 we see that the field lines are closely aligned at the footpoints of the EUV loops (probably in heights of h ≈ 2 Mm), and deviate progressively more with altitude, say with a mismatch of ≈20 – 40◦ at an altitude of about one density scale height (λ ≈ 50 Mm for T = 1.0 MK). Nevertheless, following a potential field line from the footpoint upward, the direction of the observed EUV loop can be predicted with an uncertainty of 10 – 20◦ , if the deviation is continuously updated in the prediction. In practice, the field-line-aided directions should include a bunch of field lines surrounding the suspected footpoint, because the exact footpoint location is unknown due to the uncertain starting height of the EUV loops, although they could be estimated based on a hydrostatic model and the knowledge of the EUV filter response function R(T ). Although the oriented-connectivity code of Lee, Newman, and Gary (2004) has the capability to use a dipole magnetic field as a direction-guiding constraint, no literature exists about more general codes that allow for various choices of magnetic

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Figure 4. The thick black curves mark 30 coronal loops traced from a high-pass filtered SOHO/EIT image (August 30, 1996, 00:20:14 UT). The thin curves represent extrapolated magnetic field lines (using a potential-field model) based on a magnetogram recorded with SOHO/MDI (August 30, 1996, 20:48 UT), rotated to the same time as the EUV image. The magnetogram is shown with contour levels of B = −350, −250, . . . , +1150 G, in steps of 100 G (Aschwanden et al., 1999a).

field models to aid tracing of EUV loops. Progress in this problem, however, is expected in near future, once forward-fitting codes of nonlinear force-free field models become refined (e.g., Wiegelmann, 2004), and when vector-magnetograms from SOLIS and Solar-B will become available. 2.4. CURVATURE

RADIUS CONSTRAINTS

While the previously discussed methods involve a specific theoretical magnetic field model, which is always a matter of choice, and moreover the knowledge of footpoint locations is required, we might also consider more general principles that can guide oriented-connectivity methods in tracing EUV loops. The momentum or force MHD equation involves the Lorentz force FLor = j×B, which can be broken down into a magnetic pressure force and a magnetic tension

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force,




B2 j × B = −∇ 8π

 +

1 (B · ∇)B. 4π

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(1)

The effect of the loop curvature can be seen most clearly when we express the tension force in a coordinate system with unit vectors parallel (es ) and perpendicular (en ) to the magnetic field line (e.g., Priest, 1982, p. 102; Priest, 1994, p. 22),
 B d d B2 B dB B 2 des B2 1 (Bes ) = es + = es + en , (2) 4π ds 4π ds 4π ds ds 8π 4π rcurv where rcurv is the curvature radius of the loop. The first term on the right-hand side cancels with the component of −∇(B 2 /8π) parallel to the magnetic field line. So, from the parallel component of the magnetic field (B  es ) it follows that the Lorentz force is simply (j × B)curv =

B2 1 en , 4π rcurv

(3)

which is perpendicular (i.e., normal en ) to the magnetic field line and is stronger the smaller the curvature radius rcurv is. Thus, the Lorentz force is directed towards the curvature center and tries to reduce the curvature, unless a magnetic pressure gradient or thermal pressure gradient is present across the loop that compensates this curvature force. If a coronal loop is deformed by external forces so that it has different curvature radii along its length, the segment with the smallest curvature radius experiences the largest Lorentz force and increases the local curvature radius until it matches the overall curvature radius of the loop. If the footpoints are fixed (line-tied), the loop will evolve into the lowest possible force state, which is characterized by a constant curvature radius along its length. If the field line is coplanar, a circular geometry will result, while in the non-planar case a twisted helical geometry with constant curvature radius results (neglecting other forces). Thus, the geometric constraint of a constant curvature radius is a natural outcome for a stationary solution. In practice, coronal loops may not always relax into this force-free or minimum-force state, because time-dependent currents, heat flows, and asymmetric cooling will continuously force the loop to adjust to a new equilibrium. Nevertheless, the constraint of a constant curvature radius in 3D field line coordinates can provide a powerful means to disentangle 2D loop projections. We give an example in Figure 5 (top), where a TRACE image is shown that exhibits a bundle of dipolar loops seen along a line-of-sight that is more or less aligned with the average loop plane. In Figure 5 (bottom) we show also the geometric projections of helical loops (with constant curvature radii but different numbers of twist), which can be used either as guidance constraints for oriented-connectivity methods in tracing EUV loops, or as parameterized models for forward-fitting of twisted loop geometries.

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Figure 5. TRACE 171 A˚ observations of a postflare loop system on September 14, 1999, 08:13:18 UT (top left) and 09:03:24 UT (top right). The flare started around 06:34 UT and occurred near the limb. The loop planes are oriented nearly along the line of sight. This perspective is most favorable to display the twist of non-coplanar loops. The system seems to be highly twisted during the first time interval (top left) and becomes more dipolar (coplanar) in the second configuration (top right). A series of theoretical loop geometries is shown with twist angles of 0, 0.3π, . . . , 3.0π, lying on a torus with a width-to-length ratio of 1:10. The projection angle is +4◦ between the line-of-sight and the loop planes (middle) and −4◦ (bottom). Note the similarity of the “sling-shot” loop geometries with observed loop systems (top), (Aschwanden, 2004; Section 6).

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Figure 6. A sigmoid loop structure observed with Yohkoh/SXT on December 24, 1992, 01:09 UT (left) and a model of a bipolar linear (constant-α) force-free magnetic field, computed for a positive αvalue, producing forward S-shapes (right; Pevtsov, Canfield, and McClymont, 1997). The theoretical field lines (right) can be used as guidance constraints for oriented-connectivity methods.

Another example is shown in Figure 6, where moderately twisted loop structures (with about one turn) have been observed with Yohkoh/SXT, called sigmoids, which can be modeled with force-free magnetic field models (Figure 6 right). The forcefree solutions of twisted field lines essentially correspond to helical geometries wound around curved torii with a constant curvature radius. Thus the constraint of a constant curvature radius represents a good guide to trace sigmoid-shaped loops with the oriented-connectivity method. An example with a highly-twisted helical fluxrope is shown in Figure 7 (top), ˚ (Gary and Moore, 2004). The heliobserved with TRACE in the CIV line at 1600 A cal geometry with constant curvature radius essentially corresponds to a force-free solution. Thus again, the constant curvature constraint can be used for directionguiding in tracing the fluxrope structure for oriented-connectivity methods. In practice, we envision an iterative algorithm where a parameterized geometric model is first forward-fitted to an observed structure, and then the best-fit model is used as guidance for oriented-connectivity tracing of the exact observed field line shape. So, in the first step, the orientation, the torus radius, and the number of twists is forward-fitted, which provides a good model for the second step of tracing the actual shape. Such numeric codes are not available yet, but we anticipate their development in the near future.

2.5. MULTIPLE

TEMPERATURE FILTERS

Regardless what temperature range a coronal loop structure has, the same structure will be detectable in filters from different instruments with similar temperature response functions, or in multiple filters of the same instrument if they have an overlapping temperature response. Thus, feature recognition in one filter can be used as a proxy for retrieving the same structure in another filter. This sounds

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Figure 7. A multiple-turn fluxrope has been observed with TRACE 1600 A˚ (C IV) during the X3 (GOES-class) flare on July 15, 2002, 20:04 UT (top; Gary and Moore, 2004), which can be modeled with a helical geometry with multiple turns and constant curvature radius (bottom).

trivial, but the practical application of multiple temperature filter analysis of coronal loops entails many challenges that are often underestimated, such as differences in image coalignment, sensitivity, spatial resolution, cospatiality, background subtraction, time variability, confusion with adjacent and background structures, multi-thread structures, and unknown temperature differential emission measure distributions. In Figure 8 we show EUV images of the same loop structure, some of them ˚ T ≈ 1.0 MK; recorded at almost identical temperatures, e.g., with TRACE (171 A; ˚ Figure 8, top left) and with SOHO/CDS (Mg IX, 368.07 A; T ≈ 0.9 MK; Figure 8, middle right). While the overall semi-circular geometry of the entire loop bundle can be perceived in all CDS images (Figure 8, middle and bottom rows), fine structure containing at least 10 loop strands at each temperature can be resolved in the TRACE images (Figure 8, top row). Thus the geometry of the loop strands seen in TRACE images can be used as a good constraint to disentangle unresolved features seen in the CDS image. If a loop strand is clearly discernible in one particular filter of an instrument, it can often be used as guidance for oriented-connectivity methods to trace the corresponding loop features in images at other wavelengths, other temperature ranges, and from other instruments, since the underlying magnetic field structure is often common. However, a mistake that is often made is that loop tracings seen in different temperature filters are assumed to be manifestations of the same physical loop structure, which often can be disproved by accurate cospatiality tests. Recent analysis of TRACE triple-filter data provides evidence that coronal

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Figure 8. Multiple-temperature filter images of the same loop system, recorded with TRACE in 171 A˚ (Fe IX/Fe X; T ≈ 1.0 MK; top left) and 195 A˚ (Fe XII; T ≈ 1.5 MK; top middle), and with SOHO/CDS in 525.80 A˚ (O III; T ≈ 0.09 MK; middle left), 629.73 A˚ (O V; T ≈ 0.2 MK; middle), 368.07 A˚ (Mg IX; T ≈ 0.9 MK; middle right), 624.94 A˚ (Mg X; T ≈ 1.1 MK; bottom left), and 335.41 A˚ (Fe XVI; T ≈ 2.1 MK; bottom right). Note that the geometry of loop features is similar in different filters and temperatures, although no detailed match exists (courtesy of Amy Winebarger).

loops almost always consist of multiple loop strands with different temperatures (Chae et al., 2002; Aschwanden, 2004), and thus each temperature filter is selective to a different subset of loop strands. Nevertheless, even with loop strands that are not exactly cospatial in different temperature filters, their orientations are sufficiently similar inside a loop bundle so that structures traced in one filter can be used as a proxy for oriented-connectivity methods in a different filter. Multi-filter algorithms for EUV feature recognition are not available yet, but are expected to be developed in near future.

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2.6. STEREOSCOPIC

METHODS

Stereoscopic images, i.e., two images of the same coronal loop region from two different aspect angles, provide additional information that can be used to constrain the geometric location of a loop structure in a second image based on the projected position in a first image, especially for small differences in the aspect angle. There are two ways to obtain stereoscopic solar EUV images, either using the solar rotation to vary the aspect angle (e.g., Aschwanden and Bastian, 1994a,b), or to use multiple spacecraft (Davila, 1994), as they will become available from the STEREO mission to be launched in 2006. The first method of solar-rotation stereoscopy requires stationary structures, or at least a stationary magnetic field, in which case the method of dynamic stereoscopy can be applied (Aschwanden et al., 1999b). The advantage of stereoscopic data for feature recognition is the fact that a particular geometric structure with known 3D geometry can be projected to arbitrary directions, and this way its appearance can be predicted for different aspect angles. In practice, however, general 3D density models cannot be obtained easily, but can be inferred iteratively, after a number of stereoscopic projection and fitting steps. The simplest structures to reconstruct are 1D features, such as coronal loops, which can be parameterized with a 1D geometry x(s), and in principle can be reconstructed unambiguously in 3D from two projections via triangulation methods. Such triangulation methods are also called “feature tie-pointing” and have been developed particularly for applications to stereoscopic solar EUV images (Liewer et al., 2000; Hall et al., 2004). Automated feature tracking between two images taken at different times can be aided by taking advantage of directionality constraints and the well-known solar rotation during the considered time interval. An example is given in Figure 9, where a coplanar loop is rotated to different times with a variable loop inclination angle, which can be retrieved by matching the directionality in the second images. Thus, stereoscopic datasets not only enable automated feature tracking, but allow also for 3D reconstruction of linear features. 2.7. TIME

DIFFERENCING METHODS

Time differencing schemes, which make use of the difference of two subsequent images in time, I (x, y) = I (x, y, t = t2 ) − I (x, y, t = t1 ) (also called “runningdifference images”), are most suitable to render dynamic phenomena, which show up as non-zero fluxes in difference images, while stationary structures cancel out. Thus, time differencing methods are used to display brightening flare loops, oscillating loops, propagating waves, moving CME shock fronts, soft X-ray jets, etc. The method is most effective to bring out a dynamic phenomenon with weak flux on top of stationary structures with strong flux, because the small dynamic range of the non-stationary structures can be enhanced to 100%. Nevertheless, there are also drawbacks of this method that can cause substantial confusion in the interpretation. There are two important distinctions: (1) either a structure is just varying its

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Figure 9. The principle of dynamic stereoscopy is illustrated here with an example of two adjacent loops, where a thicker loop is bright at time t1 , while a thinner loop is brightest at time t2 . From the loop positions (xi , yi ) measured at an intermediate reference time t (i.e., t1 < t < t2 ; middle panel in middle row), projections are calculated for the previous and following days for different inclination angles θ of the loop plane (left and right panel in middle row). By extracting stripes parallel to the calculated projections θ = 10◦ , 20◦ , 30◦ (panels in bottom part), it can be seen that both loops appear only co-aligned with the stripe axis for the correct projection angle θ = 20◦ , regardless of the footpoint displacement x between the two loops. The coalignment criterion can, therefore, be used to constrain the correct inclination angle θ, even for dynamically changing loops (Aschwanden et al., 1999a).

brightness but stays co-spatial, which shows up in the difference with the same positive (for brightening) or negative sign (for darkening); (2) or a structure is moving, which causes a positive difference at the new position and a negative difference at the old position, sometimes leading to a confusing display, especially when the old and new positions overlap spatially. So, a bright feature in a difference image can mean two things, either a structure brightened, or moved to a new position, or both. The ambiguity in the interpretation can often be overcome by simple modeling and simulations of difference images.

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Figure 10. LASCO C2 images of the CME of April 30, 1997, processed by average-differencing (top row) and edge-enhancing (bottom row). The leading edge is marked +, the trailing edge X, the sides *, and the centroid O. Helical lines (marked with arrows) are seen below the rim that possibly trace the magnetic field (Wood et al., 1999).

An application of time differencing is shown in Figure 10, showing an expanding CME with a fluxrope structure seen at the solar limb (Wood et al., 1999). A sequence of simple difference images is shown in the top row of Figure 10, while additional edge-enhancing (high-pass filtering) is shown in the bottom row of Figure 10. Note that this technique is very suitable to reveal the twisted helical structure of the fluxrope, which would be unrecognizable in the original images. Other efficient applications of time differencing can be seen in the detection of oscillating loops in TRACE images (Aschwanden et al., 1999b, 2002; Wang and Solanki, 2004), propagating acoustic waves (DeForest and Gurman, 1998; De Moortel, Hood, and Arber, 2000), or propagating EIT waves (Wang, 2000; Thompson et al., 1998). If the propagation is directional, a sequence of time difference image slices perpendicular to the propagation direction is a most efficient technique to display the spatiotemporal dynamics.

2.8. SPACE –TIME

FEATURE DETECTION METHODS

For statistics of events that overlap in time, a spatiotemporal feature recognition method is required, which traces features not only in the 2D space of an image,

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but also in the time dimension, so it represents a feature detection in a 3D space– time data cube. Such 3D space–time data cubes are now abundantly produced as movies from EUV telescopes such as EIT or TRACE. One of the most popular applications of such automated 3D space–time feature detection codes are designed to obtain statistics of nanoflares. Independently, three such codes have been developed for automated detection of EUV nanoflares (Krucker and Benz, 1998; Parnell and Jupp, 2000; Aschwanden et al., 2000), which all work similarly: (1) automated detection of time-variable pixels (or macropixels) with significant fluctuations above the noise level; (2) spatial combination of adjacent time-variable pixels to clusters (flare areas); and (3) temporal combination of spatially-coherent structures in the time domain. The automated detection of time-variable pixels requires a number of preparatory steps, such as image coalignment, correction for solar rotation, correction for pointing jitter of the spacecraft, difference imaging, elimination of hot CCD pixels, elimination of non-solar spikes (e.g., hits of the CCD camera by cosmic-ray and auroral high-energy particles), evaluation of the Poisson counting noise, and detection above threshold levels. An example of such a pattern recognition code is shown in Figure 11. One of the goals of such automated nanoflare detection codes is to evaluate the frequency distribution of volume- and time-integrated event energies. There are a number of systematic effects that affect the outcome of the resulting frequency distributions, such as (1) the event definition and discrimination, (2) the sampling completeness, (3) the observing cadence and exposure time, (4) the rules of the pattern recognition algorithms, (5) the geometric and physical model of the energy content, (6) the modeling of the line-of-sight integration, (7) the extrapolation to undetected energy ranges, (8) the wavelength bias and associated filter response function, (9) the fitting procedure of the frequency distribution, and (10) the error estimates of the power-law slopes. An important criterion is the completeness of the temperature coverage, which generally requires coordinated multi-wavelength observations. Another important consideration is the volume modeling of the detected 2D projections of EUV features, which turned out to be fractal for most EUV features (flares, nanoflares) rather than space-filling (Figure 12).

2.9. ACCELERATION

AND VELOCITY CONSTRAINTS

For spatiotemporal feature detection algorithms, an additional constraint can be exploited: the time-continuity of propagation parameters, such as the distance, velocity, or acceleration. An example is shown in Figure 13 for the tracing of a CME feature in a sequence of EUV and white-light images. The height–time position h(t), the velocity profile v(t), and the acceleration profile a(t) could be fitted with continuous functions, that are related to each other by the well-known

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Figure 11. The spatial clustering of the pattern recognition code is illustrated for the 12 largest events on February 17, 1999, 02:15-03:00 UT. The contours outline local EUV intensity maps around the detected structures. The crosses mark the positions of macropixels with significant variability (Nσ > 3). The spatiotemporal pattern algorithm starts at the pixel with the largest variability, which is located at the center of each field of view, and clusters nearest neighbors if they fulfill the time coincidence criterion (tpeak ± 1t). Those macropixels that fulfill the time coincidence criterion define an event, marked with diamonds, and encircled with an ellipse. Each macropixel that is part of an event, is excluded in subsequent events. Note that the events 0, 1, 3, 11 belong to the same active region, where the four zones have peaks at different times and thus make-up four different events. The units of the axis are in 0.5 arcsec pixels (Aschwanden et al., 2000).

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Figure 12. Measurement of the fractal area of the Bastille-Day flare, observed by TRACE 171 A˚ on July 04, 2000, 10:59:32 UT. The Haussdorff dimension is evaluated with a box-counting algorithm for pixels above a threshold of 20% of the peak flux value. Note that the Haussdorff dimension is invariant (D = 1.5–1.6) when the image is rebinned with different macro-pixel sizes (64, 32, 16, 8, 4, 2, 1), as indicated with a mesh grid. The full-resolution image is shown in the top left frame (Aschwanden, 2004).

Newton’s laws of motion,  t a(t) dt, v(t) = v0 + t0

h(t) = h 0 + v0 (t − t0 ) +

(4)  t

t

a(t) dt dt. t0

(5)

t0

For the acceleration profile a(t), either an exponentially increasing or decreasing function is often a good approximation. For the CME observations shown in Figure 13, a combination function of an exponentially increasing and decreasing acceleration was found to fit the data. Thus, once one of the time-dependent parameters [h(t), v(t), a(t)] has been parameterized, either analytically or by an empirical polynomial or spline fit, the position h(t) of a feature can then be interpolated to

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Figure 13. Height–time h(t) (top), velocity v(t) (second frame), and acceleration a(t) profiles (third frame), and GOES-10 soft X-ray flux profiles (bottom) for a CME observed with TRACE, UVCS, and LASCO during the April 21, 2002, X1.5 GOES-class flare, shown during the interval of 00:47−03:20 UT. The solid lines represent the best fits with an analytical function.

arbitrary times to aid automated feature detection. Extrapolation outside the observed height range might still provide a good first guess in most of the cases, although the accuracy becomes less certain for larger distances.

3. Conclusions Automated feature detection in solar EUV images became a rapidly growing industry, where a number of innovative and powerful algorithms have been developed.

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However, given the enormous size of already existing and anticipated future databases, in particular stereoscopic data, and given the complex and fractal geometry of the observed phenomena (coronal loops, filaments, prominences, nanoflares, flares, postflare loop systems, and CMEs), we find ourselves still in the infancy of intelligent pattern recognition algorithms. Automated 2D feature recognition codes have been developed to fingerprint coronal loops, e.g., with brightness-gradient and oriented-connectivity methods, but current methods render only partial loop segments and incomplete magnetic field lines. A more complete characterization of the coronal magnetic field is expected from combining magnetic field extrapolation codes with EUV feature detection algorithms. Twisted magnetic structures (e.g., filaments, fluxropes, or sigmoids) represent a special topological challenge to disentangle, but we expect that future pattern recognition codes will make use of curvature radius constraints in the 3D geometric space to disentangle the 2D projections. Even relatively simple curvi-linear structures (e.g., coronal loops, flare loops) show often interleaved and intertwined geometries which can only be disentangled with multiple temperature filter observations. Almost no existing EUV feature recognition code takes advantage of multi-wavelength observations, although we expect that only efficient exploitation of multi-filter data will enable us to reveal the multi-strand or multi-thread structure of loops in the quiet corona, active regions, and flares. Currently we see the development of simple (single-image) 2D feature detection into higher dimensional space, such as stereoscopic (multiple aspect angles), evolutionary (multiple images in time), and broad-band temperature (images from multiple filters) methods, where each additional dimension introduces more complexity. Stereoscopic methods could only be applied to solar-rotation datasets so far, while multi-spacecraft data will become available in near future. Evolutionary methods dealt mostly with running-difference enhancing and detection of spatiotemporal clusters of time-variable pixels, but more sophisticated applications that take advantage of continuity in temperature, velocity, and acceleration are expected. Of course, there is a lot of overlap between feature detection methods and geometric/physical modeling of features, so we expect that most efficient feature detection methods will be aided by forward-fitting of suitably parameterized models in future codes. Acknowledgements We acknowledge inspiring and helpful discussions that contributed to this work, with Allen Gary, David Alexander, Paulett Liewer, Eric DeJong, Jake Lee, Arnold Benz, S¨am Krucker, and Clare Parnell. Also I thank the referee, Thomas Wiegelmann, for helpful comments to improve this paper. Part of the work was supported by the NASA TRACE (NAS5-38099) and NASA STEREO/SECCHI contracts (N00173-02-C-2035, administrated by NRL).

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