Introducing a novel sub-millimeter lung CT image registration error quantitation tool

Abstract

Background: Lung computed tomography (CT) scan image registration is being used for lung function analysis such as ventilation. Given the high sensitivity of functional analyses to image registration errors, an image registration error scoring tool that can measure submillimeter image registration errors is needed.

Purpose: To propose an image registration error scoring tool, termed λ, whose spatial sensitivity can be used to quantify image registration errors in steep image gradient regions under realistic noise conditions.

Methods: λ compares two images, termed reference and evaluated. The HU and distance scales of both images are normalized by user-selected scaling criteria. For each voxel in the reference image, the 4D Euclidian distances between the reference voxel and the nearby evaluated voxels are calculated, and the minimum of these distances is $\lambda$ . We tested $\lambda$ in simulated individual blood vessels comprised of 1, 3, and 5 mm diameter cylinders in 1 × 1 × 1 mm³ voxel images, which were blurred to simulate CT scanner intrinsic resolution and volume averaging. We placed the simulated vessels in a homogeneous background simulating parenchymal tissue density and injected 20, 40, and 60 HU standard deviation Gaussian noise. We used isotropic Gaussian filters with 0.5, 1.0, and 1.5 mm standard deviation kernels to smooth the simulated images. We assessed $\lambda$ using reference-evaluated vessel shifts of -1.0 to 1.0 mm in 0.05 mm steps via rigid translational and rotational deformations. We examined whether $\lambda$ tracked the translation vector via its internal spatial component. We restricted $\lambda$ to voxels using the angle, termed $\theta$ , between the $\lambda$ vector and the normalized spatial-distance axes, terming the results the restricted- $\lambda$ , ${\lambda }_R$ , where $\theta$ was hypothesized to be a proxy for image gradient. We determined whether $\theta$ was coincident with the image gradient by examining if the voxels with $\left|\theta \right|\le {30}^{\circ }$ tracked the evaluated vessels. We used the 95^th percentile of ${\lambda }_R$ , ${\lambda }_R^{95}$ , to determine spatial sensitivity, which we took as a conservative estimate of registration error, by fitting ${\lambda }_R^{95}$ to a modified absolute-value function for each tested rigid translation, noise level, smoothing kernel, and vessel radius combination. We demonstrated the use of $\lambda$ on a clinical example consisting of a set of 25 deformably registered free-breathing thoracic CT scans. We visually compared the $\lambda$ and ${\lambda }_R$ results against the HU differences between each clinical image pair.

Results: We found θ to be coincident with the image gradient. We found that $\lambda$ 's spatial component tracked the vessel shifts. We determined the spatial sensitivity limit of ${\lambda }_R^{95}$ to be < 0.2 mm. The noise level and smoothing kernel influenced ${\lambda }_R^{95}$ sensitivity, worsening with increasing noise, and improving with increasing smoothing. For the clinical images, we observed $\lambda$ to qualitatively match the absolute difference of intensity in the image pairs and ${\lambda }_R$ to restrict itself to high gradient regions or regions of visually apparent errors.

Conclusion: ${\lambda }_R^{95}$ detected sub-millimeter positioning errors between simulated vessels in the presence of typical CT noise. The noise magnitude and choice of noise smoothing kernel were inversely related to ${\lambda }_R^{95}$ sensitivity, implying that study-specific tuning of the pre-smoothing kernel may be required. The demonstrated ability in geometric tests of ${\lambda }_R^{95}$ to detect subvoxel DIR errors warrants further evaluation and testing.

Keywords: digital phantom; image registration; registration metric; validation.