Finite-Dimensional Lie Algebras for Fast Diffeomorphic Image Registration

• Published in: Information Processing in Medical Imaging Vol. 24; pp. 249 - 260
• Main Authors: Zhang, Miaomiao, Fletcher, P. Thomas
• Format: Book Chapter Journal Article
• Language: English
• Published: Cham Springer International Publishing 2015
• Series: Lecture Notes in Computer Science
• Subjects: Aged; Aged, 80 and over; Algorithms; Brain - anatomy & histology; Deformable Image Registration; Female; Fourier Domain; Geodesic Path; Humans; Image Enhancement - methods; Image Interpretation, Computer-Assisted - methods; Image Registration; Information Storage and Retrieval - methods; Jacobi Field; Magnetic Resonance Imaging - methods; Male; Middle Aged; Numerical Analysis, Computer-Assisted; Pattern Recognition, Automated - methods; Reproducibility of Results; Sensitivity and Specificity; Subtraction Technique
• ISBN: 9783319199917; 3319199919
• ISSN: 0302-9743; 1011-2499; 1611-3349
• DOI: 10.1007/978-3-319-19992-4_19

This paper presents a fast geodesic shooting algorithm for diffeomorphic image registration. We first introduce a novel finite-dimensional Lie algebra structure on the space of bandlimited velocity fields. We then show that this space can effectively represent initial velocities for diffeomorphic image registration at much lower dimensions than typically used, with little to no loss in registration accuracy. We then leverage the fact that the geodesic evolution equations, as well as the adjoint Jacobi field equations needed for gradient descent methods, can be computed entirely in this finite-dimensional Lie algebra. The result is a geodesic shooting method for large deformation metric mapping (LDDMM) that is dramatically faster and less memory intensive than state-of-the-art methods. We demonstrate the effectiveness of our model to register 3D brain images and compare its registration accuracy, runtime, and memory consumption with leading LDDMM methods. We also show how our algorithm breaks through the prohibitive time and memory requirements of diffeomorphic atlas building.