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

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

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

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

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

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

EUVI-A and DATE: _ Mutual registration needed: EUVI-AEUVI-B Note limb fitted

Mutual registration of EUVI-A and B  Summary of parameters found: IDL> print,crx_im1,cry_im1,crx_im2,cry_im IDL> print,rad_im1,rad_im ;;;; DATE: _ STEREO-B Earth STEREO-A Heliocentric distance (AU) Semidiameter (arcsec) HCI longitude HCI latitude Carrington longitude Carrington rotation number Heliographic (HEEQ) longitude Heliographic (HEEQ) latitude Earth Ecliptic (HEE) longitude Earth Ecliptic (HEE) latitude Roll from ecliptic north Roll from solar north Separation angle with Earth Separation angle A with B IDL> print,header_304_a_norot.heex_obs e+11 IDL> print,header_304_a_norot.heey_obs e+09 IDL> print,header_304_a_norot.heez_obs e+08 IDL> print,header_304_a_norot.dsun_obs e+11 IDL> print,header_304_b_norot.heex_obs e+11 IDL> print,header_304_b_norot.heey_obs e+08 IDL> print,header_304_b_norot.heez_obs e+08 IDL> print,header_304_b_norot.dsun_obs e+11

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

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

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)

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

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

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

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

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

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

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

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

Depth reconstruction

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

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??

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: