Cross-Correlation and Rotation Estimation of Local ...

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Cross-Correlation and Rotation. Estimation of Local 3D. Vector Field Patches. Janis Fehr, Marco Reisert, Hans Burkhardt ...
Cross-Correlation and Rotation Estimation of Local 3D Vector Field Patches Janis Fehr, Marco Reisert, Hans Burkhardt

Overview / Motivation 3D Vector Fields -

3D flow fields (bio)-medical imaging ...

Objective:

Approach:

local descriptor for 3D vector fields → → →

rotation invariant or rotation variant (dep. on application) complete compute rotation offset between samples → registration



harmonic representation of local spherical 3D vector field patches



fast cross-correlation → rotation invariant descriptor → exact rotation offset estimation

2

Scalar Domain: Harmonic Expansion of Spherical Patches Local spherical patches

Spherical Harmonic Domain

Rotations in SH

Power-Spectrum: 3

Vectorial Harmonics (VH) functions f on spherical vector fields

Preserves all properties of the scalar Harmonics! 4

Features in VH Fast computation on discrete input

power-spectrum

Incomplete feature → loosing phase information → ambiguous → rotation information is lost

Toy application: key-point detection

5

Full correlation in VH correlation of signals on S²:

same correlation in VH: split into two rotations...

using...

Full correlation in VH

FT

Orthoview 3D correlation matrix

Problem: Trade-off between angular resolution and complexity !

Full correlation in VH Solution: Sinc-Interpolation in the angular space (zero padding)

Obtaining the rotation offset:

Example: Target patterns: fast correlation

Power spectrum

9

Experimental Results

Rotation Estimation: accuracy and speed

Conclusion:

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