Cross-Sim-NGF: FFT-Based Global Rigid Multimodal Alignment of Image Volumes using Normalized Gradient Fields

TL;DR

A global optimization method for rigid multimodal 3D image alignment, based on a novel efficient algorithm for computing similarity of normalized gradient fields (NGF) in the frequency domain, which exhibits excellent performance on all six possible modality combinations.

Abstract

Multimodal image alignment involves finding spatial correspondences between volumes varying in appearance and structure. Automated alignment methods are often based on local optimization that can be highly sensitive to their initialization. We propose a global optimization method for rigid multimodal 3D image alignment, based on a novel efficient algorithm for computing similarity of normalized gradient fields (NGF) in the frequency domain. We validate the method experimentally on a dataset comprised of 20 brain volumes acquired in four modalities (T1w, Flair, CT, [18F] FDG PET), synthetically displaced with known transformations. The proposed method exhibits excellent performance on all six possible modality combinations, and outperforms all four reference methods by a large margin. The method is fast; a 3.4Mvoxel global rigid alignment requires approximately 40 seconds of computation, and the proposed algorithm outperforms a direct algorithm for the same task by more than three orders of magnitude. Open-source implementation is provided.

Figures (3)

• Figure 1: Main idea of the proposed global alignment method. Input: Two image volumes of modalities [18F] FDG PET, and T1 weighted MR, as $A$ and $B$ respectively (displayed as slices). For a number of random 3D rotations $\mathbf{\theta}$, the similarity measure $s_{\text{ANGF}}$ between the masked normalized gradient fields is computed efficiently for all 3D displacements; finally, the sought transformation is found as the maximum of $s_{\text{ANGF}}$.
• Figure 2: Sample slices of 3D image pairs from the evaluation dataset generated from the CERMEP-IDB-MRXFDG dataset merida2021cermep. (a-d) the reference (transformed) images and (e-h) the floating images. Image (e) is to be registered to (a); (f) to (b), (g) to (c) and (h) to (d). The bottom row shows the ground-truth (GT) of each floating (Flo) image aligned to the corresponding reference (Ref) image.
• Figure 3: The success-rate of each considered method as a function of the acceptable displacement error $t$ (fraction of the 240 alignments where $d_E<t$); the results for all modality combinations are aggregated. Up and to the left is better.