TABLE 1.
Sequential list of all the steps performed within the proposed optimal method, along with inputs, outputs and parameters of each step and the dimension (2D or 3D) in which the step is performed. (Ox) denotes an output from a previous step where x is the step number
| No | Step | Input | Output | Parameters | Dimension |
|---|---|---|---|---|---|
| 1 | Bias removal | Original unmasked image | De-biased image (O1) | / | 2D |
| 2 | Sinc interpolation to obtain isotropic voxels | De-biased image (O1) Liver mask |
Interpolated de-biased image (O2’) Interpolated liver mask (O2’’) |
/ | 3D |
| 3 | Masking | Interpolated de-biased image (O2’) Interpolated liver mask (O2’’) |
Interpolated masked de-biased image (O3) | / | 2D |
| 4 | Frangi filtering | Interpolated masked de-biased image (O3) | Interpolated vesselness filtered image (O4) | Gaussian kernel σ=[1,12] with a step of 0.5 α=0.3 β=0.7 c= half of Frobenius norm |
3D |
| 5 | Interpolation to original voxel size | Interpolated vesselness filtered image (O4) | Vesselness filtered image (O5) | / | 3D |
| 6 | Masking | Vesselness filtered image (O5) Liver mask |
Masked vesselness filtered image (O6) | / | 2D |
| 7 | Thresholding with a low threshold | Masked vesselness filtered image (O6) | Basic vessel model (O7) | Threshold = 0.05 * max(vesselness) | 3D |
| 8 | Removal of small objects | Basic vessel model (O7) | Basic vessel model with objects with diameter > 3 mm (O8) | Size of small object = number of pixel of a circle with 3 mm diameter | 2D |
| 9 | Connected component analysis | Basic vessel model with objects with diameter > 3 mm (O8) | Basic objects (O9) | / | 2D |
| 10 | Dilation | Basic object (O9) | ROI of object (O10) | Structuring element: disc with radius = 5 | 2D, per object |
| 11 | Masking | De-biased image (O1) Liver mask |
Masked de-biased image (O11) | / | 2D |
| 12 | Local thresholding | ROI of object (O10) Masked de-biased image (O11) |
Locally thresholded image (O12) | Threshold determined for each ROI through variance minimization | 2D, per object |
| 13 | Region growing | Locally thresholded image (O12) Masked de-biased image (O11) |
Region grown image (O13) | Threshold = median of locally thresholded image, per slice 27-neighborhood | 2D/3D |
| 14 | Erosion | Liver mask | Eroded mask (O14) | Structuring element: disc with radius = 6 | 2D |
| 15 | Masking | Region grown image (O13) Eroded mask (O14) |
Segmented image (O15) | / | 2D |
| 16 | Removal of small objects | Segmented image (O15) | Segmented image with objects with diameter > 3 mm (O16) | Size of small object = number of pixel of a circle with 3 mm diameter | 2D |