Mean-shifted surface curvature algorithm for automatic bone shape segmentation in orthopedic surgery planning: a sensitivity analysis

Figures & data

Table I.  Parameters and ranges for the sensitivity analysis.

Curvature	kc	1-ring MS kc	2-ring MS kc
Surface resolution (No. of faces)	3000	10,000	20,000
Kernel function	Epanechnikov		Biweight
b	Range: 10^2 to 10^−8		Step: 10^−1

Table II.  Features of the validation data.

CT image size	512 × 512 pixels
Voxel size	0.74 × 0.74 × 1.0 mm
Demographic data	9 males, 2 females Mean age: 77 years (61–95)
Surfaces	Femur	Pelvic bone
Left	10	10
Right	10	10
No. of triangles (mean ± std)	74337 ± 13241	81563 ± 12776

Figure 1. (a) and (b) The three curvatures (from left to right: mean, Gaussian, and non-linear k_c) mapped on the pelvic bone mesh with 3k faces (a) and 20k faces (b). (c) and (d) Corresponding curvature values. For clarity, the ordinate range was set from −2 to +2.

Figure 2. The three mapped curvatures (mean, Gaussian, and non-linear k_c) for the femur mesh (3k and 2k faces).

Figure 3. Histograms of the three curvature distributions (pelvic bone) computed for the 3k (a), 10k (b), and 20k (c) surface resolutions.

Figure 4. Curvature k_c, mean-shifted curvature with 1-ring neighborhood, and mean-shifted curvature with 2-ring neighborhood for 3k faces (a), 10k faces (b), and 20k faces (c).

Figure 5. Curvature k_c, mean-shifted curvature with 1-ring neighborhood, and mean-shifted curvature with 2-ring neighborhood for 3k faces (a), 10k faces (b), and 20k faces (c).

Table III.  Number of clusters for ridge (R) and pit (P) regions as a function of the b value, the kernel function, and the surface resolution obtained after computing the 1-ring MS curvature, automatic curvature thresholding, and vertex clustering.

Kernel	Epanechnikov						Biweight
Surface resolution	3k		10k		20k		3k		10k		20k
b value	R	P	R	P	R	P	R	P	R	P	R	P
100	7	3	32	14	87	42	7	3	32	14	90	38
10	7	3	32	14	87	42	7	3	32	14	90	38
1	7	3	32	14	87	42	19	3	32	13	90	38
1.00E−01	7	3	32	14	87	42	23	3	122	52	107	41
1.00E−02	7	3	32	14	87	42	23	6	121	52	107	41
1.00E−03	7	3	32	14	87	42	23	6	121	52	107	41
1.00E−04	7	3	32	14	87	42	23	6	121	52	107	41
1.00E−05	7	3	32	14	87	42	23	6	121	52	107	41
1.00E−06	7	3	32	14	87	42	23	6	121	52	107	41
1.00E−07	7	3	32	14	87	42	23	4	121	52	107	41
1.00E−08	7	3	32	14	87	42	23	6	121	52	107	41

Table IV.  Median and range values (25th and 75th percentiles) for the ridge and pit cluster distributions, obtained from the pelvic bone processing, computed across the 20 bone models. For clarity, floating point numbers are rounded to the nearest integer.

		3k			10k			20k
		kc	1-ring MS kc	2-ring MS kc	kc	1-ring MS kc	2-ring MS kc	kc	1-ring MS kc	2-ring MS kc
Ridge	Median	37	15	6	74	25	13	204	82	34
	Range	34–40	13–17	10–13	71–81	19–27	10–15	199–212	79–90	22–39
Pit	Median	11	5	3	29	15	8	87	41	24
	Range	8–12	4–5	3–4	26–32	11–18	7–11	78–89	36–47	22–27

Table V.  Median and range values (25th and 75th percentiles) for the ridge and pit cluster distributions, obtained from the femur processing, computed across the 20 bone models. For clarity, floating point numbers are rounded to the nearest integer.

		3k			10k			20k
		kc	1-ring MS kc	2-ring MS kc	kc	1-ring MS kc	2-ring MS kc	kc	1-ring MS kc	2-ring MS kc
Ridge	Median	44	14	7	130	43	21	260	87	45
	Range	41–47	12–15	7–9	125–141	38–49	15–25	247–271	74–94	39–52
Pit	Median	7	5	4	20	18	14	48	41	31
	Range	5–8	4–6	3–4	19–23	16–20	13–15	44–50	37–43	25–36

Figure 6. Color-coded regions clustered for 3k-face surface of the hemi-pelvic bone. The upper and lower images display the anterior and posterior views, respectively.

Figure 7. Color-coded regions clustered for 3k-face surface of the femur. The upper and lower images display the anterior and posterior views, respectively.