3D Stereoscopic 3D Stereoscopic Reconstruction Reconstruction

of CMEs by Forward of CMEs by Forward ModelingModeling

5th Consortium STEREO-SECCHI 5th Consortium STEREO-SECCHI MeetingMeeting

OrsayOrsay, March 2007, March 2007

Y.BOURSIER Y.BOURSIER – P.LAMY – F.GOUDAIL - A.LLEBARIA– P.LAMY – F.GOUDAIL - A.LLEBARIA

OutlineOutlineI – IntroductionI – Introduction

II – CME models and their parametersII – CME models and their parameters

III – Method and algorithmIII – Method and algorithm

IV – ResultsIV – Results

V – ConclusionV – Conclusion

Classical stereoscopic techniques of Classical stereoscopic techniques of computer vision computer vision cannot achievecannot achieve a a reliable reconstruction of CMEs:reliable reconstruction of CMEs:

Problem 1: Problem 1: Morphology of CMEs Morphology of CMEs too complicated.too complicated.

A solutionA solution : strong assumption : strong assumption on the shape : forward on the shape : forward modeling.modeling.

Problem 2: Problem 2: Optically thin Optically thin medium.medium.

A solutionA solution : compare images with : compare images with simulated well known images.simulated well known images.

Problem 3: Problem 3: High frequency noise High frequency noise and largescale stable structures and largescale stable structures superimposed on CMEs.superimposed on CMEs.

A solutionA solution : find global : find global characteristic quantities not characteristic quantities not sensitive to photometric sensitive to photometric changes and not sensitive to changes and not sensitive to geometric details.geometric details.

STEREO – B COR2 STEREO – A COR2

Top 3D view

3D view

Purpose :Purpose :- Estimate the position and the direction of propagation of - Estimate the position and the direction of propagation of CMEs in space.CMEs in space.- Characterize the global morphology of CMEs.- Characterize the global morphology of CMEs.- Reconstruct CMEs in Space.- Reconstruct CMEs in Space.

Method : Method : - Build a library of simulated CMEs (forward modeling) - Build a library of simulated CMEs (forward modeling) sampling a large parameter space (position angles, sampling a large parameter space (position angles, shape, etc..)shape, etc..)- Compute global parameters and invariants.- Compute global parameters and invariants.- Compare these quantities with those calculated on the - Compare these quantities with those calculated on the observed images.observed images.- Identify by minimization the CME in the library that best - Identify by minimization the CME in the library that best fits the observation.fits the observation.- The selected CME model is supposed to best describe - The selected CME model is supposed to best describe the real CME.the real CME.

CME ModelsCME ModelsI – Spherical capI – Spherical cap

- Very basic model.- Very basic model.- Leading part of ice cream model of Schwenn - Leading part of ice cream model of Schwenn et al. (2005).et al. (2005).- Assume an hemispheric shape.- Assume an hemispheric shape.- Four parameters : 3 for position, and the cone - Four parameters : 3 for position, and the cone angle.angle.- Thickness dr is fixed to 0.1 Rsun.- Thickness dr is fixed to 0.1 Rsun.

y

α xC

Sun

O

dr

r

Lateral view

Front view

3D view

CME ModelsCME ModelsII – Fluxrope modelII – Fluxrope model

- More elaborated model (well suited to filament - More elaborated model (well suited to filament eruptions).eruptions).- Model already introduced by Thernisien et al. (2006).- Model already introduced by Thernisien et al. (2006).- Six parameters : 3 for position, 1 for orientation and 2 for - Six parameters : 3 for position, 1 for orientation and 2 for shape.shape.- Shape parameters : the cone angle and the radius r- Shape parameters : the cone angle and the radius rmax.max.

Top view

Lateral view

3D view

y

α xC

Sun

O rmax

r max

CME ModelsCME ModelsIII – Cloud-like modelIII – Cloud-like model

- Extension of the fluxrope model.- Extension of the fluxrope model.- Well suited to filaments eruptions with magnetic reconnections.- Well suited to filaments eruptions with magnetic reconnections.- Six parameters : 3 for position, 1 for orientation and 2 for shape.- Six parameters : 3 for position, 1 for orientation and 2 for shape.- Shape parameters : the cone angle and the radius r- Shape parameters : the cone angle and the radius rmax.max.

y

α xC

Sun

O rmax

maxr

Top view

Lateral view

3D view

CMEs parametersCMEs parameters

x

y

z

Sun

O

C

r

x

y

z

Sun

O

C

r

Spherical capSpherical cap : 4 parameters : 4 parameters3 for position :3 for position :

Longitude PhiLongitude PhiLatitude ThetaLatitude ThetaRadial distance rRadial distance r

1 for shape :1 for shape :Angle of the cone AlphaAngle of the cone Alpha

Fluxrope and cloud-likeFluxrope and cloud-like : 6 : 6 parametersparameters3 for position :3 for position :

Longitude PhiLongitude PhiLatitude ThetaLatitude ThetaRadial distance rRadial distance r

2 for shape :2 for shape :Angle between feet AlphaAngle between feet AlphaCoefficient k linked to rCoefficient k linked to rmax max

with thewith theassumption assumption rrmaxmax=k*r=k*r

1 for orientation :1 for orientation :Angle PsiAngle Psi

System coordinates are compatible with the WCS. (see Thompson et al. 2006)

Library of imagesLibrary of imagesThree-dimensionnal electron density of the CME Three-dimensionnal electron density of the CME computed from its analytic expression.computed from its analytic expression.

Then compressed by octree to significantly reduce the Then compressed by octree to significantly reduce the computation time (see Saez et al. 2005)computation time (see Saez et al. 2005)

Images generated by a raytracing algorithm Images generated by a raytracing algorithm incorporating Thomson scatteringincorporating Thomson scattering..

STEREO – B COR2 STEREO – A COR2

Library of imagesLibrary of imagesSpace of parameters sampled for each model and Space of parameters sampled for each model and domain reduced for symmetry reasons :domain reduced for symmetry reasons :

LatitudeLatitude : from 0° to 80° with a step of 10°. : from 0° to 80° with a step of 10°.

Spherical capSpherical cap : : 63006300 images. images.LongitudeLongitude : from 0° to 90° with a step of 10°. : from 0° to 90° with a step of 10°.

Radial distance rRadial distance r : from 2 Rsun to 8 Rsun with a step of 1 Rsun. : from 2 Rsun to 8 Rsun with a step of 1 Rsun.

Cone angle alphaCone angle alpha : from 10° to 100° with a step of 10°. : from 10° to 100° with a step of 10°.

FluxropeFluxrope and and Cloud-likeCloud-like : : 2700027000 images for each model images for each modelLongitudeLongitude : from 40° to 90° with a step of 10°. : from 40° to 90° with a step of 10°.

Radial distanceRadial distance : from 2 Rsun to 8 Rsun with a step of 2 Rsun. : from 2 Rsun to 8 Rsun with a step of 2 Rsun.

AngleAngle Alpha Alpha : from 10° to 90° with a step of 20°.: from 10° to 90° with a step of 20°.

CoefficientCoefficient kk : from 0.2 to 1.0 with a step of 0.2. : from 0.2 to 1.0 with a step of 0.2.

Orientation PsiOrientation Psi : from 0° to 80° with a step of 20°. : from 0° to 80° with a step of 20°.

Couples of stereoscopic images can be simulated with a Couples of stereoscopic images can be simulated with a separation angle between satellites ranging from 10° to separation angle between satellites ranging from 10° to 50° with a step of 10°.50° with a step of 10°.

Geometric characterizationGeometric characterizationA pixel of brigthness maxima on edge on A pixel of brigthness maxima on edge on

one image one image = =

a line-of-sight (los) tangent to the surface.a line-of-sight (los) tangent to the surface.

We define manually n pixels and We define manually n pixels and we search the surface tangent to n los.we search the surface tangent to n los.

Spherical cap : surface of order 2.Spherical cap : surface of order 2.- Exact reconstruction by minimization is - Exact reconstruction by minimization is

possible (downhill simplex method).possible (downhill simplex method).- Set of 4 parameters is estimated.- Set of 4 parameters is estimated.

Fluxrope and cloud-like : surface of Fluxrope and cloud-like : surface of order 4.order 4.

- Two many parameters.- Two many parameters.- Need more information.- Need more information.- Local approximation by a spherical cap.- Local approximation by a spherical cap.- Use the distance “d” between Sun - Use the distance “d” between Sun

center andcenter and leading edge of the approximated leading edge of the approximated

spherical cap.spherical cap.

STEREO – B COR2 STEREO – A COR2

Top 3D view

3D view LOS

LOS

Characteristic quantitiesCharacteristic quantitiesMaximum of geometric criteria and minimum of Maximum of geometric criteria and minimum of photometric criteria :photometric criteria :

- Angular witdh AW.- Angular witdh AW.- Gravity center G (geometric moments of order 1).- Gravity center G (geometric moments of order 1).- Area of ellipse of inertia E (geometric moments of order - Area of ellipse of inertia E (geometric moments of order

2).2).- - 3 geometric invariants by translation, rotation, homotethy 3 geometric invariants by translation, rotation, homotethy

computed from geometric moments of order 3.computed from geometric moments of order 3.

G

AW

E

AW

GE

Fluxrope : Cloud : 50,4.0,90,6,0,90 kRsunr 50,4.0,40,6,30,60 kRsunr

Reconstruction of fluxrope and Reconstruction of fluxrope and cloud-likecloud-like

1 – Work on couple of images :1 – Work on couple of images :

Reconstruct G in space : Reconstruct G in space : Estimate of longitude and Estimate of longitude and latitudelatitude..

Local approximation of edge by a sphere and measure of Local approximation of edge by a sphere and measure of : comparison with the library (Elimination of non relevant : comparison with the library (Elimination of non relevant cases – tolerance 15%).cases – tolerance 15%).

2 – Work independently on images :2 – Work independently on images :

Compare the characteristic quantities and with Compare the characteristic quantities and with those of the library (Elimination of non relevant cases – those of the library (Elimination of non relevant cases – tolerance 15%).tolerance 15%).

Correlate the vector of 3 invariants with those of the Correlate the vector of 3 invariants with those of the library (Elimination of correlations <0.95).library (Elimination of correlations <0.95).

3 – Fusion of results of each image :3 – Fusion of results of each image :

Set of 4 remaining parameters present for both Set of 4 remaining parameters present for both views are conserved.views are conserved.

d

WA ˆ E

Tests and results : spherical capTests and results : spherical cap

24.0ˆ

36.0ˆ

45.1ˆ

65.1ˆ

Rsunrr 45.0ˆ Rsunrr 2.1ˆ 6.1ˆ 9.6ˆ

- Tests on Tests on 61006100 couplescouples of stereoscopic images with separation angle of stereoscopic images with separation angle from 10° to 50°. from 10° to 50°. - 6 ‘edge’ pixels were automatically selected on each image : 12 tangent 6 ‘edge’ pixels were automatically selected on each image : 12 tangent lines-of-sight.lines-of-sight.- Longitude and latitude (then direction of propagation) are well recovered.Longitude and latitude (then direction of propagation) are well recovered.- Estimate of distance r and cone angle alpha efficient but sensitive to Estimate of distance r and cone angle alpha efficient but sensitive to occultations near Sun and next to 15 Rsun : occultations near Sun and next to 15 Rsun :

LongitudeLatitude

Tests and results : cloud-likeTests and results : cloud-like

2.0ˆ

83.0ˆ

25.0ˆ

7.3ˆ

Tests on 5062 couples of simulated COR2 images with with separation angle from 10° to 50°.separation angle from 10° to 50°.

- Local approximation by a spherical cap constrained with - Local approximation by a spherical cap constrained with 12 lines-of-sight.12 lines-of-sight.

- Excellent estimate of longitude and latitude by - Excellent estimate of longitude and latitude by reconstruction of G.reconstruction of G.

Longitude

Latitude

Tests and results : cloud-Tests and results : cloud-likelikeThe algorithm returns a list of possible set of parameters for the observed

CME.When the correct set of parameters is proposed in the list, the test is considered as successful.When no set is proposed or when the correct set is not present in the final list, the algorithm fails. Probability of success :

96.2 %Probability of failure : 3.8 %

No value returned : 3.7 %

False values returned : 0.1%

When success :

Probability of 1 set : 46 %Probability of 1 or 2 sets : 66 %Probability of less than 5 sets : 91.5 %

Histogram of number of set of 4 parameters

returned when success

ConclusionConclusion- Tests on fluxrope in progress.- Tests on fluxrope in progress.- Refining the sampling of space of parameters in progress.- Refining the sampling of space of parameters in progress.

- Quantitative and qualitative results have revealed that :- Quantitative and qualitative results have revealed that :- Position parameters and then direction of propagation Position parameters and then direction of propagation are very well recovered.are very well recovered.- Global morphology of CME is well characterized.Global morphology of CME is well characterized.- 3D velocity will be easily calculated from position and 3D velocity will be easily calculated from position and shape parameters.shape parameters.

- Method purely geometric based on parametric models of - Method purely geometric based on parametric models of CMEs. CMEs. - Need minimum manual interaction (the user must locate - Need minimum manual interaction (the user must locate the CME front with few points).the CME front with few points).- Algorithm can be turned into a fully automatic process if - Algorithm can be turned into a fully automatic process if CME is properly isolated from other structures on images.CME is properly isolated from other structures on images.

- New models can be easily added. Suggestions ??- New models can be easily added. Suggestions ??- Algorithm can use additional points of view (LASCO/C2-- Algorithm can use additional points of view (LASCO/C2-C3).C3).

Reconstruction of fluxrope and Reconstruction of fluxrope and cloud-likecloud-like

1 - Local approximation of leading edge by a spherical cap : 1 - Local approximation of leading edge by a spherical cap : measure of distance between center of Sun and leading edge.measure of distance between center of Sun and leading edge.

Analytic expression of d=f(r,alpha,k) : comparison of all d in Analytic expression of d=f(r,alpha,k) : comparison of all d in the library with and elimination of non relevant cases (tolerance of the library with and elimination of non relevant cases (tolerance of +/- 15 % on ). +/- 15 % on ).

First estimate of longitude and latitude.First estimate of longitude and latitude.

2 - Computation of G on STEREO-A and STEREO-B images, then 2 - Computation of G on STEREO-A and STEREO-B images, then reconstruction in Space.reconstruction in Space.

Second estimate of longitude and latitudeSecond estimate of longitude and latitude..

3 - 3 - On each imageOn each image : :a - Measure of angular width and of the area of ellipse of a - Measure of angular width and of the area of ellipse of

inertia .inertia .Comparison with AW and E in library and Comparison with AW and E in library and

elimination of non relevant set of parameters (tolerance of elimination of non relevant set of parameters (tolerance of +/- 15 %).+/- 15 %).b - Correlation with a vector with 3 discriminant geometric b - Correlation with a vector with 3 discriminant geometric invariants.invariants.

Elimination of correlations <0.95.Elimination of correlations <0.95.

4 - 4 - Fusion of resultsFusion of results obtained on each image : obtained on each image : set of parameters set of parameters present for both views are conserved.present for both views are conserved.

d

dd

WA ˆ E