MUSTER: Longitudinal Deformable Registration by Composition of Consecutive Deformations

TL;DR

MUSTER introduces a multi-session approach to longitudinal image registration by composing consecutive non-linear deformations to recover accurate voxelwise changes across time. It replaces conventional pairwise similarity with a scale-invariant, likelihood-based SiLNCC, coupled with Gaussian and Jacobian-based regularization and a simultaneous rigid alignment, all implemented efficiently on GPUs via a Log-Euclidean parameterization. Through synthetic multi-site data and ADNI MRI scans, MUSTER demonstrates improved deformation recovery for small-scale changes and yields clinically meaningful associations between tissue changes and cognitive decline, comparable to state-of-the-art segmentation methods. The framework is versatile, computationally efficient, and adaptable to various similarity metrics, making it suitable for large-scale longitudinal neuroimaging studies and clinical workflows.

Abstract

Longitudinal imaging allows for the study of structural changes over time. One approach to detecting such changes is by non-linear image registration. This study introduces Multi-Session Temporal Registration (MUSTER), a novel method that facilitates longitudinal analysis of changes in extended series of medical images. MUSTER improves upon conventional pairwise registration by incorporating more than two imaging sessions to recover longitudinal deformations. Longitudinal analysis at a voxel-level is challenging due to effects of a changing image contrast as well as instrumental and environmental sources of bias between sessions. We show that local normalized cross-correlation as an image similarity metric leads to biased results and propose a robust alternative. We test the performance of MUSTER on a synthetic multi-site, multi-session neuroimaging dataset and show that, in various scenarios, using MUSTER significantly enhances the estimated deformations relative to pairwise registration. Additionally, we apply MUSTER on a sample of older adults from the Alzheimer's Disease Neuroimaging Initiative (ADNI) study. The results show that MUSTER can effectively identify patterns of neuro-degeneration from T1-weighted images and that these changes correlate with changes in cognition, matching the performance of state of the art segmentation methods. By leveraging GPU acceleration, MUSTER efficiently handles large datasets, making it feasible also in situations with limited computational resources.

Figures (15)

• Figure 1: a: MUSTER does deformable registration between all images of a time series. Here a series of T1-weighted brain scans from ADNI is displayed. The arrows indicates the deformations relating the images of the time series. For simplicity most of the deformations are not shown. b: The deformation fields that deform the images to the first image $I_1$ are visualized as colormaps. The color hue shows the deformation direction orthogonal to the image plane, and the color intensity shows the magnitude of the deformation. c: The determinant of the spatial Jacobian of the deformation field. Dark regions show contraction, and bright regions show expansion of the tissue.
• Figure 2: Illustration of the deformation fields on 1-dimentional images. The rectangles represent voxels, the $\times$ represents the centers of voxels and the arrows are deformations. $\bm \Phi_{ji}^i$ is the deformation that "pulls" $\bm I_j$ to $\bm I_i$ and $\bm \Phi_{ij}^j \approx (\bm \Phi_{ji}^i)^{-1}$ is the deformation that "pulls" $\bm I_i$ to $\bm I_j$. $\bm \Phi_{kj}^i$ is the deformation of the voxels from $\bm I_i$ in the interval between $\bm I_k$ and $\bm I_j$. a illustrates the meaning of the sub- and superscripts. b shows how two consecutive deformations can be combined to construct a combined deformation.
• Figure 3: Overview of the deformations relating the images of a image series. $\phi_{ij}$ denotes the flow field between the consecutive images $\bm I_i$ and $\bm I_j$. $\bm \phi_{ij}^j$ denotes deformation on a grid between $\bm I_i$ and $\bm I_j$. All deformations between all images can be constructed by composing the consecutive deformations.
• Figure 4: $E\left[\text{LNCC}_R\right]$ plotted as a function of CNR.
• Figure 5: a: Local normalized cross-correlation as a function of contrast to noise ratio and alignment of two 1 dimensional images estimated using a Monte Carlo simulation. See Appendix \ref{['se:cross_cor_exp']} for implementation details. The x-axis represent the CNR ratio and the y axis is the offset between the step functions. The offset and contrast to noise ratio is illustrated with a small plot for each axis. b: Scale invariant local normalized cross-correlation plotted for the Monte Carlo simulation as in a.