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 MeetingOrsay, France. March 05-08 2007.

3D reconstruction methodoutline 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-A EUVI-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

SunEarth

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

δθ

θ

EUVI-A and B @304A, DATE: 20070128_000731Mutual registration needed:

EUVI-A EUVI-BNote limb fitted

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

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

1st 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

Sig

nal

spatial dimension

Image registration:

I1 I2I2-I1

2I

x

δx

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

2nd 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 I2 - I1

Neighborhood (scale)

δx = θ = (δx, δy, δI)

δI

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

δxB δxA

δx=δxB-δxA

z=1/tan(α)* δx

α

Depth reconstruction

0

160

0 320

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:

www.sidc.be/velociraptor