1. 3D with EUVI images using optical flow First attempt on 30.4nm images Samuel Gissot Jean-François Hochedez SIDC/Royal Observatory of Belgium 5th SECCHI Consortium Meeting Orsay, France. March 05-08 2007.

2. 3D reconstruction method outline of the talk  Aim Prominence altitude Altitude gradients in supergranules?  Mutual registration of EUVI-A and B images Limb fitting (center and radius estimations) Roll angle, rotation transform and header parameters  Optical flow Apparent displacement estimation Error prediction  Stereoscopic reconstruction Formula Confidence level and limitations  Outlooks

3. 3D reconstruction method Global registration to (S/C-A, S/C-B, Sun) plane EUVI-AEUVI-B rotated EUVI-A rotated and scaled EUVI-B Input parameters: roll from ecliptic north (stereo science center website) HEE positions of S/C-A and S/C-B Optical flow computation Depth map construction as produced by secchi_prep.pro, no rotation, B-limb fitted on A-limb 0.5 deg adjustment of roll angle correction

4. Mutual registration of EUVI-A and B (δx,δy) Solar disc center in EUVI-A Solar disc center in EUVI-B Limb

5. Mutual registration of EUVI-A and B Ecliptic plane S/C-B S/C-A Sun Earth Normal direction to (S/C-A, S/C-B, Sun) plane Ecliptic north θ Expected shifts parallel to this line HEE latitude S/C-A HEE longitude S/C-B

6. Mutual registration of EUVI-A and B Ecliptic north Normal direction to (S/C-A, S/C-B, Sun) plane Center of Sun/EUVI-A scaling rotation to the (s/cA,s/cB,S) plane correction to roll angle applied to EUVI-B δθδθ θ

7. EUVI-A and B @304A, DATE: 20070128_000731 Mutual registration needed: EUVI-AEUVI-B Note limb fitted

8. Mutual registration of EUVI-A and B  Summary of parameters found: IDL> print,crx_im1,cry_im1,crx_im2,cry_im2 1054.85 953.178 1034.40 1002.37 IDL> print,rad_im1,rad_im2 627.406 616.642 ;;;; DATE: 20070128_000731 STEREO-B Earth STEREO-A Heliocentric distance (AU) 0.987015 0.984785 0.970853 Semidiameter (arcsec) 972.253 974.454 988.438 HCI longitude 51.783 51.906 52.306 HCI latitude -5.598 -5.720 -5.869 Carrington longitude 98.933 99.056 99.456 Carrington rotation number 2052.725 2052.725 2052.724 Heliographic (HEEQ) longitude -0.123 -0.000 0.400 Heliographic (HEEQ) latitude -5.598 -5.720 -5.869 Earth Ecliptic (HEE) longitude -0.132 -0.000 0.408 Earth Ecliptic (HEE) latitude 0.112 0.000 -0.118 Roll from ecliptic north 40.471 16.121 Roll from solar north 44.950 20.547 Separation angle with Earth 0.173 0.425 Separation angle A with B 0.587 IDL> print,header_304_a_norot.heex_obs 1.4523895e+11 IDL> print,header_304_a_norot.heey_obs 1.0245851e+09 IDL> print,header_304_a_norot.heez_obs -2.9908688e+08 IDL> print,header_304_a_norot.dsun_obs 1.4524287e+11 IDL> print,header_304_b_norot.heex_obs 1.4762296e+11 IDL> print,header_304_b_norot.heey_obs -3.4109876e+08 IDL> print,header_304_b_norot.heez_obs 2.8412190e+08 IDL> print,header_304_b_norot.dsun_obs 1.4762362e+11

9. Optical flow method  Gissot S., Hochedez (2007) A&A volume 464, issue 3: Multiscale optical flow probing of dynamics in solar EUV images. Algorithm, calibration and first results

10. 1 st Assumption : Brightness Constancy (BCA) Its linear approximation: At each pixel: 1 equation for 1 unknown in 1-D But, Still 1 equation for 2 unknowns in 2-D (images) Aperture issue Signal spatial dimension Image registration: I1I1 I2I2 I 2 -I 1 x δxδx

11. Following LUCAS KANADE (1981), we assume: Uniformity of the motion over a neighborhood Ω  Extra-equations (more than needed!) e.g. 9 equations if Ω = 3x3 pixels Over-determination  Least-square minimization 2 nd Assumption : Local Uniformity (LUA)

12. Brightness Variation (δI = BV)  Over-determined system  possible to add unknown(s)  We estimate δx, δy AND δI  Mathematically better Cope with time aliasing (lack of cadence) Model accounts for a larger fraction of I 2 - I 1 Neighborhood (scale) δx = θ = (δx, δy, δI) δIδI

13. Mutual registration of EUVI-A and B: difference image, δθ=0 degree (no additional correction)

14. Optical flow estimation, full image, low resolution (2) beta=0.5, δθ=0 deg

15. Mutual registration of EUVI-A and B: difference image, δθ=0.5 degree

16. Optical flow estimation, full image, low resolution (1) beta=0.5, δθ=0.5 deg

17. Mutual registration of EUVI-A and B: difference image, δθ=0.9 degree

18. Optical flow estimation, full image, low resolution (4) beta=0.5, δθ=0.9 deg

19. Depth reconstruction formula Sun center z EUVI-B EUVI-A δx B δx A δx=δxB-δxA z=1/tan(α)* δx α

20. Depth reconstruction

21. 0 160 0 320

22. Discussion (1/2)  Brightness change remains to be interpreted Transparency of SiXI emission  DEM “purification” will help Slight flatfields mis-match?  Error map on the optical flow remains to be exploited (method provides it)  Hope for best roll angles from headers

23. Discussion (2/2)  The flow could help to estimate δθ  Origin of δθ (roll angle correction) ? Misalignment between instruments and S/C pointing?  Static or not?  Correction method Bug in our method??

24. Conclusions  Calibration study: Refinement of roll angle between stereo A and B  First attempt of optical-flow application to 3D reconstruction: Initial global matching, optical-flow estimation and 3D interpretation  Under construction: www.sidc.be/velociraptor