Ultrasound Specific Similarity Measures for Three-Dimensional Mosaicing Christian Wachinger, Nassir Navab Computer Aided Medical Procedures (CAMP), Technische Universität München, Germany
USSM for 3D Mosaicing - Wachinger, Navab 2
Problem Statement Proposed 3D mosaicing techniques by (Gee, 2003) and (Poon, 2006) use a sequence of pairwise registrations Partial Overlap: Accumulation errors: Misalignment High demands on the overlap invariance of similarity measures USSM for 3D Mosaicing - Wachinger, Navab 3
Registration Strategies – Similarity Plots Simultaneous Pairwise moving image 2 along the cranio-caudal axis USSM for 3D Mosaicing - Wachinger, Navab 4
Similarity Measures • Maximum likelihood estimation to model registration mathematically u, v : images • Bivariate log-likelihood function ε : noise f : intensity mapping log L ( T, ε , f ) = log P ( u | v, T, ε , f ) • Multivariate log-likelihood function X T = { T 1 , . . . , T n } log L ( T , ε , f ) = log P ( u j | u i , T i , f i , ε i ) i 6 = j • Assuming additive Gaussian noise and variation of intensity mapping leads to SSD, NCC, CR, and MI (Viola 1995, Roche 2000) USSM for 3D Mosaicing - Wachinger, Navab 5
Speckle • Ultrasound images are degraded by artifacts caused by coherent wave interference USSM for 3D Mosaicing - Wachinger, Navab 6
Ultrasound Specific Similarity Measures P ( u | v, T, ε , f ) • Ultrasound specific likelihood terms • Strintzis and Kokkinidis ‘97 - US motion estimation – SK 1 : multiplicative Rayleigh noise µ ¶ − π · y 2 P ( y ) = π · y · exp u ( x ) = v ( T ( x )) · ε 2 4 – SK 2 : signal dependent Gaussian noise µ ¶ p − y 2 1 u ( x ) = v ( T ( x )) + v ( T ( x )) · ε P ( y ) = √ 2 πσ exp 2 · σ 2 USSM for 3D Mosaicing - Wachinger, Navab 7
Ultrasound Specific Similarity Measures • Cohen and Dinstein ‘02 – CD 1 : division of Rayleigh noises u ( x ) · ε 1 = v ( T ( x )) · ε 2 ε = ε 1 2 · y u ( x ) = v ( T ( x )) · ε , ⇔ P ( y ) = ( y 2 + 1) 2 ε 2 – CD 2 : logarithm of division of Rayleigh noises log u ( x ) = log v ( T ( x )) + log ε USSM for 3D Mosaicing - Wachinger, Navab 8
Multivariate Ultrasound Specific Similarity Measures CD 1 : SK 1 : ⎡ ! 2 ⎤ õ i k ¶ 2 ∙ π µ i k ¶¸ X X ⎣ log j 2 i 2 ⎦ k k E k +1 E k − log j 2 j 2 i k j k 4 k k i 6 = j i 6 = j CD 2 : SK 2 : ∙ ¸ h i X X log j k + ( i k − j k ) 2 j k − log( e 2(˜ i k − ˜ ˜ i k − ˜ j k ) +1) E k E k j k i 6 = j i 6 = j ˜ i k = log u i ( T i ( x k )) i k = u i ( T i ( x k )) ˜ j k = u j ( T j ( x k )) j k = log u j ( T j ( x k )) USSM for 3D Mosaicing - Wachinger, Navab 9
CD 1 SK 1 SSD SK 2 CD 2 USSM for 3D Mosaicing - Wachinger, Navab 10
Conclusion • Good results for CD 2 are conform with those from Boukerroui et al. and Revell et al. • Need to adapt the mosaicing framework to ultrasound images • First step are ultrasound specific similarity measures • Not much difference between using high- and low-resolution images • Conduct further experiments to evaluate the performance of multivariate similarity measures • We thank Siemens Corporate Research for generously providing ultrasound images. USSM for 3D Mosaicing - Wachinger, Navab 11
Thank you for your attention! USSM for 3D Mosaicing - Wachinger, Navab 12
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