Using the Local Phase of the Magnitude of the Local Structure Tensor for Image Registration

1. Using the Local Phase of the Magnitude of the Local Structure Tensor for Image Registration Anders Eklund, Daniel Forsberg, Mats Andersson, Hans Knutsson Linköping University

2. Agenda • Phasebased image registration • The localstructuretensor • Extending the phaseidea-combininglocalphase and tensormagnitude • Results on synthetic data • Results on real data

3. Phasebased image registration • Image registration is normallydone by using the image intensity, for example by maximizing the correlation or the mutual information between the images • Easytocreate test images for whichintensitybasedalgorithmsfail…

4. Phasebased image registration • A better approach is touse the localphase, insteadof the image intensity • The localphase is bettersuited for the assumptionsmade in the opticalflowalgorithm(no intensitydifferencebetween images, the image is locallysmooth) • The localphasecan for example be estimated by usingquadrature filters

5. Quadrature filters Frequencydomain Spatial domain Real part Imaginary part

6. Phasebased image registration • The complexvalued filter response q is a bandpass filtered version of the analytical signal • Lines areevenfunctions, relatedtocosine • Edgesareoddfunctions, relatedtosine • The quotientof the real and the imaginaryfilter responses gives information about the neighbourhood (edge or line, bright line, dark line, etc)

7. Localphase Dark tobrightedge Bright line Dark line Bright to dark edge

8. Phasebasedregistration • Phasebasedregistrationworkswellfor images with different intensity • Thereare, however, images for whicheven the phasebased approach fails • Example, the shapesof the objectsareconsistentbetween the images, buta dark tobrightedge in one image is a brightdo dark edge in the other image

9. Twonice test images Altered image Reference image The image intensity as well as the localphase has changed Whatis constantbetweenthese images? The shapeof the objects!

10. Real images? • Arethere images in the real world for which the shapesareconstant, but the intensity and the localphasechanges?

11. Quantitative MRISame subject, same slice, different MR settings Slice 2 Slice 1 Slice 3 Slice 4

12. Extending the phaseidea • Wewant a similaritymeasurethat is invariant bothto image intensity and to the localphase, i.e. thatonlyconsiders the shapeof the objects • The localphase is invariant to the image intensity, but is different for dark tobrightedges and brightto dark edges

13. Localphase Altered image Reference image

14. The localstructuretensor • The localstructuretensorrepresents the localstructure as a 2 x 2 matrix (for 2D)in each pixel • The localstructuretensorcan, for example, be estimated by usingquadrature filters

15. Tensormagnitude • The magnitudeof the localstructuretensor is invariant to the localphase(the orientationof a line and an edgein the same direction is the same) • The tensormagnitude is not invariant tothe image intensity • The tensormagnitude is highwherethereis a welldefinedorientation

16. Tensormagnitude Altered image Reference image

17. Localphaseoftensormagnitude • Combine the localphase and the tensormagnitudetoachieveinvariancebothtoimage intensity and tolocalphase • Applyquadrature filters to the original image and calculate the tensormagnitude in each pixel • Apply the quadrature filters again, nowto the tensormagnitude

18. Localphaseoftensormagnitude Altered image Reference image

19. Evaluationofsimilaritymeasure • Howgood is our new similaritymeasure? • Mutual information of the image intensity (blue) • Mutual information of the localphase (green) • Mutual information oflocalphaseoftensormagnitude (pink) • One image wasrotatedbetween -30 and 30 degrees • Normalizedvaluestohave a maximum of 1

20. Reference and altered test image

21. MRI slices 1 and 3

22. Evaluationofregistrationperformance • Tested the new similaritymeasurebothwithrigid and non-rigid registration • No bigincrease in processingtime,possibletouseexistingalgorithms • Calculate the tensormagnitudeof the reference image and the source image • Send the tensormagnitude images to the registrationalgorithm • Apply the founddisplacementfieldtothe original images

23. Rigid registration • For rigid registrationof the MRI slices the localphaseof the image intensityworks as wellas the localphaseof the tensormagnitude • If the fat border is removed (constant for all four slices), only the localphaseof the tensormagnitudeworks

24. Non-rigid registration • Non-rigid registration is hardersince it is not possibletouse global information • For the non-rigid registrationthe Morphonwasused, whichis a phasebased non-rigidregistrationalgorithm

25. Shifted test imagesintensitydifference

26. Registrationresults Localphaseoftensormagnitude Localphaseof image intensity

27. MRI slices 1 and 3absolute intensitydifference Original Shifted

28. Registrationresults Localphaseoftensormagnitude Localphaseof image intensity

29. Summary • A new similaritymeasure for image registrationhas beenpresented • The ideaofphasebasedregistrationwasextendedby using the localphaseof the tensormagnitude, insteadof the localphaseof the image intensty • Promisingresults for synthetic and real data havebeenpresented

30. Thankyou for your attention!