Introduction

With the advancement of ultra-high field MRI, Time-of-Flight angiography with voxel sizes$$$\leq$$$300µm has become available. To analyze these high resolution data quantitatively, automatic vessel segmentation is required as manual segmentation becomes unfeasible for such large datasets and high resolutions. However, automatic small vessel segmentation is challenging, since the vessel-to-background ratios decrease with decreasing vessel diameter.
Here a novel Openly available sMall vEsseL sEgmenTaTion pipelinE (OMELETTE) is presented. The goal of OMELETTE is to provide high quality small vessel segmentations while being easy to use. OMELETTE's performance is compared with a Frangi-based benchmark for 20 publicly available, high resolution ToF angiograms acquired at 7T¹.

Methods

OMELETTE utilizes Jerman's filter² to enhance vessels and then performs a novel thresholding approach to generate a binary vessel segmentation. All source code was developed in Python3 and takes advantage of the scikit-image package. The proposed pipeline and further documentation is publicly available at: https://gitlab.com/hmattern/omelette/

Similar to the well-known Frangi filter³, the Jerman filter² computes the vesselness of an image by analyzing the eigenvalues of the hessian matrix computed for each voxel at multiple scales. In contrast to Frangi's approach, the Jerman's vessel response function (used to generate the actual enhancement) is based on the volume ratio of the Hessian matrix eigenvalues, commonly used for diffusion tensor analysis². To improve the enhancement for vessels with low vessel-to-background ratios, a regularization is utilized (controlled by $$$\tau$$$=0.5..1.0). Therefore, Jerman's filter requires a single parameter, while Frangi's filter has three free parameters ($$$ \alpha, \beta, \gamma$$$).

Commonly the enhancement is converted into a segmentation by applying an empirical threshold which trades of the detection of small vessels and falsely segmented noise. To overcome this lengthy trail-and-error tuning, thresholds in OMELETTE are selected automatically with a 3-class Otsu histogram analysis (returning a low and high threshold). Voxels above the high threshold can be considered vessels with high confidence, while voxels below the low threshold are considered background. To leverage this information and differentiate background and vessels in between the thresholds, hysteresis thresholding is used⁴. Hysteresis thresholding is a bi-threshold procedure in which voxels above the higher threshold are segmented directly. Voxels above the lower threshold are only segmented if they are connected to voxels above the high threshold. This enforces vessel continuity and reduces segmentation of noise.
To improve small vessel segmentation further, OMELETTE provides a novel iterative thresholding approach with soft-enhancement (inspired by compressed sensing's soft-thresholding). As shown in Fig. 1, the segmentation results are propagated back to the filter enhancement. If a voxel was classified as a vessel, its enhancement is increased by the enhancement factor $$$\kappa$$$. Thus, the enhancement $$$E$$$ in the next iteration $$$i+1$$$ is $$$ E(i+1) = E(i) + E(i)*\kappa*S(i)$$$ with $$$S$$$ as the binary segmentation. This process is repeated $$$N$$$ times and intensities above 1.0 are clipped.

To evaluate the segmentation performance, the publicly available 7T ToF angiograms of the studyforrest dataset¹ have been used. Prior to segmentation, the 300µm isotropic data of all 20 subjects were bias field-corrected with N4 (provided by ANTs)⁵. The commonly used Frangi filter³ and segmentation with a single empirically selected threshold was used as the benchmark pipeline. The following parameters were used: $$$\tau$$$=0.5, $$$\kappa$$$=0.05, 50 iterations (OMELETTE); $$$\alpha$$$=0.5, $$$\beta$$$=0.5 ,$$$\gamma$$$=0.05, threshold=0.05 (benchmark); scales=1.0:0.5:2.5 (both pipelines). For quantitative comparison of sensitivity, specificity, and dice coefficient, ilastik's semi-automatic pixel classification⁶ was used to generate reference segmentations.

Results

Segmentation performance of OMELETTE and the Frangi-based benchmark was compared quantitatively (see Fig. 2). With respect to the semi-manually segmented reference, the specificity of both pipelines was on par. For the sensitivity and dice coefficient OMELETTE returned 53.2% and 5.4% higher scores than the benchmark, respectively.
For qualitative comparison of the segmentation performance, axial, whole brain Maximum Intensity Projections (MIPs) and coronal MIPs over the basal ganglia are shown in Fig. 3 and 4, respectively. In line with the quantitative evaluation, OMELETTE provided better segmentation performance than the benchmark. Further, OMELETTE outperformed the reference segmentation. Hence, even with semi-automatic approaches, small vessel segmentation in high resolution 3D data is challenging.

Discussion

With the combination of Jerman's filter and a novel thresholding approach, OMELETTE outperformed the benchmark quantitatively and qualitatively. Further, the qualitative comparisons showed an advantage of OMELETTE compared to the reference. Although, the reference cannot be considered a ground truth, which represents a bias in the analysis, the quantitative results are still sensible. Previous studies showed that Jerman's filter outperform Frangi's filter for enhancing vessels with low contrast². Further, the qualitative results show the superior performance of the proposed pipeline.
Besides the improved segmentation performance and being openly available (source code, data, and auxiliary tools), OMELETTE is easy to use as the enhancement filter requires tuning of single parameter and thresholds are selected automatically.
In the future, OMELETTE will be compared to further segmentation pipeline^7,8 and results for the DRIVE challenge⁹ (retina vessel segmentation with available ground truth) will be reported.

Conclusion

OMELETTE is a novel, easy to use, publicly available vessel segmentation pipeline which outperforms the Frangi-based benchmark.

Acknowledgements

This work was funded by the DFG-MA 9235/1-1.