Bone enhancement filtering: Application to sinus bone segmentation and simulation of pituitary surgery

Figures & data

Figure 1. Anatomy of pituitary gland area (adapted from reference [1]) (left); and a schematic demonstrating endoscopic pituitary surgery (adapted from reference [2]) (right).

Figure 2. Sagittal slice of a CT dataset in the region of interest for pituitary gland surgery (see Figure 1). In the image, black corresponds to air, gray to soft tissue, and white to bone. Note the low intensity values and holes in the bone structure at right. This is an important bone the neurosurgeon needs to break in order to reach the pituitary gland.

Table I.  Local structure classification based on the Hessian matrix, assuming | λ₁ | ≤ | λ₂ | ≤ | λ₃ | [7], [8].

Eigenvalue conditions	Local structure	Examples
λ1 ≈ λ2 ≈ 0, λ3 > >0	sheet-like	bone, skin
λ1 ≈ 0, λ2 ≈ λ3 > >0	tube-like	vessels, nerves
λ1 ≈ λ2 ≈ λ3 > >0	blob-like	nodule
lambda1 ≈ λ2 ≈ λ3 ≈ 0	noise-like	background, noise

Figure 3. Distribution surface illustration: an ellipsoid with one short semi-minor axis corresponding to the detected scale of the sheet-like structure and two equal semi-major axes that we choose to be twice the semi-minor axis. The eigenvectors of the Hessian matrix corresponding to non-zero eigenvalues are shown in red. They are locally perpendicular to the sheet-like structure.

Table II.  Theoretical properties of the ratios defined to construct the sheetness measure.

Ratios	Sheet	Tube	Blob	Noise
Rsheet = | λ2 |/| λ3 |	0	1	1	undefined
Rblob = | (2 | λ3 | − | λ2 | − | λ1 |) |/| λ3 |	2	1	0	undefined
	λ3	√2λ3	√3λ3	0

Figure 4. Experiment on synthetic objects. Slices of the input volumes, the sheetness measure, the speed term, and a surface rendering of the segmentation.

Table III.  The agreement level between the ground truth boundary and and that obtained by the geometric flow.

Object	Average distance error (voxels)	Maximum error (voxels)	Ratio (%)
plate	0.22	1.00	95
rib	0.25	1.12	95
spiral	0.26	1.22	91

Figure 5. Comparison between different segmentation methods. Our method connects most of the thin bone structure and reconstructs more bone than the approach in reference [1] and thresholding.

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