MIND Demons for MR-to-CT deformable image registration in image-guided spine surgery

Abstract

Purpose Localization of target anatomy and critical structures defined in preoperative MR images can be achieved by means of multi-modality deformable registration to intraoperative CT. We propose a symmetric diffeomorphic deformable registration algorithm incorporating a modality independent neighborhood descriptor (MIND) and a robust Huber metric for MR-to-CT registration. Method The method, called MIND Demons, solves for the deformation field between two images by optimizing an energy functional that incorporates both the forward and inverse deformations, smoothness on the velocity fields and the diffeomorphisms, a modality-insensitive similarity function suitable to multi-modality images, and constraints on geodesics in Lagrangian coordinates. Direct optimization (without relying on an exponential map of stationary velocity fields used in conventional diffeomorphic Demons) is carried out using a Gauss-Newton method for fast convergence. Registration performance and sensitivity to registration parameters were analyzed in simulation, in phantom experiments, and clinical studies emulating application in image-guided spine surgery, and results were compared to conventional mutual information (MI) free-form deformation (FFD), local MI (LMI) FFD, and normalized MI (NMI) Demons. Result The method yielded sub-voxel invertibility (0.006 mm) and nonsingular spatial Jacobians with capability to preserve local orientation and topology. It demonstrated improved registration accuracy in comparison to the reference methods, with mean target registration error (TRE) of 1.5 mm compared to 10.9, 2.3, and 4.6 mm for MI FFD, LMI FFD, and NMI Demons methods, respectively. Validation in clinical studies demonstrated realistic deformation with sub-voxel TRE in cases of cervical, thoracic, and lumbar spine. Conclusions A modality-independent deformable registration method has been developed to estimate a viscoelastic diffeomorphic map between preoperative MR and intraoperative CT. The method yields registration accuracy suitable to application in image-guided spine surgery across a broad range of anatomical sites and modes of deformation.

Inter-scanner variation independent descriptors for constrained diffeomorphic demons registration of retina OCT

“…The patch distance HscriptNp is computed using a Huber metric 13 H to improve robustness against noise and speckle as HscriptNp(I,bold-italicrj,bold-italicrk)=1|scriptNp|∑z∈scriptNpH(I(bold-italicrj+z),I(bold-italicrk+z)), where z denotes an offset from the center of scriptNp. Equal weighting is applied in (2) through mean filtering instead of Gaussian weighting 14,15 to improve computational efficiency. As such, a patch is cuboid instead of an ellipsoid obtianed from Gaussian filtering.…”

“…As such, a patch is cuboid instead of an ellipsoid obtianed from Gaussian filtering. 14,15 An asymmetric stencil scriptNs depicted in Fig. 1(a) is additionally designed to accentuate structures present along the A-scan direction and minimize sensitivity to poor through-plane resolution.…”

“…The geodesics of ϕ i are energy minimizing paths with the geodesic shortest length (GSL) measured in terms of the minimizing energy as ρ(bold-italicϕi(0.5),bold-italicϕi)=infbold-italicvi∫00.5false‖bold-italicvifalse(0.5−(−1)iτfalse)false‖V2dτ, with a boundary ϕ i ( x , 0.5) = x , ϕ 0 ( x , 0) = y , and ϕ 1 ( x , 1) = z for a point x , y , and z in the domains of a virtual image I 0.5 , I 0 , and I 1 , respectively. This section briefly summarizes the symmetric diffeomorphic Demons optimization approach used in MIND Demons 3,14 (see prior work 3,14 for detail) and describes extensions added to MIND Demons to enable robust cross-scanner, inter-subject diffeomorphic deformable registration of OCT volumetric images.…”

SPIE Medical Imaging 50th anniversary: historical review of the Image-Guided Procedures, Robotic Interventions, and Modeling conference

“…Among the top 50 most downloaded proceedings ( Table 3 ) is (a) work by Garg et al 8 on brain shift. Also among such highlights are methods for rigid and nonrigid registration in spine surgery, including (b) work by Reaungamornrat et al 9 on a Demons registration method based on diffeomorphic transforms with the MIND metric, which won both the Young Scientist Award and the Robert F. Wagner All-Conference Student Paper Award ( Table 5 ).…”

Performance evaluation of MIND demons deformable registration of MR and CT images in spinal interventions

“…A variant of the MIND Demons algorithm using an asymmetric energy formulation (instead of the symmetric one in equation (7)) was introduced in (Reaungamornrat et al 2016b). The asymmetric form offers the potential advantage of speed per iteration (bypassing recalculation of m I 1 ) and estimates a deformation ψ yielding m I 0 ◦ ψ ≈ m I 1 via the energy minimization: $$E_A=\underset{\mathrm{bold-italic\xi },\mathrm{bold-italic\psi }}{\text{inf}}\frac{1}{2}true\{{\alpha }_S^2\underset{\mathrm{bold-italicx}\in \mathrm{normal\Omega }}{\int }S{false({\mathit{m}}_{I_0◦\mathrm{bold-italic\xi }},{\mathit{m}}_{I_1},\mathrm{bold-italicx}false)}^{2}d\mathrm{bold-italicx}+{\alpha }_P^2{false\Vert \nabla \mathrm{bold-italic\psi }false\Vert }_2^2+{\alpha }_U^2{false\Vert Lfalse(\mathrm{bold-italic\psi }-\mathrm{bold-italic\xi }false)false\Vert }_2^{2}true\}$$ where ξ denotes an intermediate deformation using the Demons alternating optimization (Section 2.3).…”