ResultsMethod details
Bayesian Maximal Paths for Coronary Artery Segmentation from 3D CT Angiograms
David Lesage, Elsa D. Angelini, Isabelle Bloch, and Gareth Funka-Lea
Abstract:We propose a recursive Bayesian model for the delineation
of coronary arteries from 3D CT angiograms (cardiac CTA) and discuss
the use of discrete minimal path techniques as an efficient optimization
scheme for the propagation of model realizations on a discrete graph.
Design issues such as the definition of a suitable accumulative metric are
analyzed in the context of our probabilistic formulation.
Our approach jointly optimizes the vascular centerline and associated
radius on a 4D space+scale graph. It employs a simple heuristic scheme
to dynamically limit scale-space exploration for increased computational
performance. It incorporates prior knowledge on radius variations and
derives the local data likelihood from a multiscale, oriented gradient
flux-based feature. From minimal cost path techniques, it inherits practical
properties such as computational efficiency and workflow versatility.
We quantitatively evaluated a two-point interactive implementation on
a large and varied cardiac CTA database. Additionally, results from the
Rotterdam Coronary Artery Algorithm Evaluation Framework are provided
for comparison with existing techniques. The scores obtained are
excellent (97.5% average overlap with ground truth delineated by experts)
and demonstrate the high potential of the method in terms of
robustness to anomalies and poor image quality.
Summary
|
|
OV |
76.0% |
100.0% |
97.5% |
39.7 |
100.0 |
81.5 |
1 |
17 |
3.99 |
OF |
6.1% |
100.0% |
78.8% |
3.0 |
100.0 |
70.8 |
1 |
26 |
5.76 |
OT |
76.0% |
100.0% |
97.7% |
39.7 |
100.0 |
81.5 |
1 |
18 |
4.36 |
AI |
0.20 mm |
0.49 mm |
0.29 mm |
22.4 |
58.4 |
37.0 |
6 |
20 |
11.62 |
Total |
|
|
|
|
|
|
1 |
26 |
8.16 |
All results
|
|
8 |
0 |
92.3 |
46.7 |
7 |
80.8 |
41.4 |
9 |
98.0 |
49.0 |
7 |
0.24 |
37.4 |
12 |
9.8 |
8 |
1 |
100.0 |
100.0 |
1 |
100.0 |
100.0 |
1 |
100.0 |
100.0 |
1 |
0.30 |
38.1 |
11 |
6.0 |
8 |
2 |
78.7 |
59.8 |
7 |
66.9 |
74.4 |
3 |
78.9 |
58.8 |
7 |
0.49 |
58.4 |
9 |
7.3 |
8 |
3 |
100.0 |
100.0 |
1 |
100.0 |
100.0 |
1 |
100.0 |
100.0 |
1 |
0.33 |
37.1 |
15 |
8.0 |
9 |
0 |
100.0 |
100.0 |
1 |
100.0 |
100.0 |
1 |
100.0 |
100.0 |
1 |
0.23 |
31.0 |
12 |
6.5 |
9 |
1 |
99.4 |
74.7 |
7 |
98.9 |
89.8 |
8 |
99.4 |
49.8 |
8 |
0.24 |
39.8 |
11 |
9.3 |
9 |
2 |
100.0 |
100.0 |
1 |
100.0 |
100.0 |
1 |
100.0 |
100.0 |
1 |
0.30 |
31.3 |
13 |
7.0 |
9 |
3 |
95.6 |
49.0 |
13 |
95.8 |
84.5 |
2 |
100.0 |
100.0 |
1 |
0.23 |
36.9 |
12 |
8.7 |
10 |
0 |
99.1 |
54.3 |
9 |
98.7 |
49.3 |
14 |
100.0 |
100.0 |
1 |
0.22 |
32.5 |
10 |
9.0 |
10 |
1 |
100.0 |
100.0 |
1 |
100.0 |
100.0 |
1 |
100.0 |
100.0 |
1 |
0.30 |
29.8 |
17 |
9.0 |
10 |
2 |
97.8 |
87.8 |
1 |
86.7 |
47.5 |
3 |
97.9 |
77.0 |
3 |
0.33 |
39.1 |
12 |
7.2 |
10 |
3 |
100.0 |
100.0 |
1 |
100.0 |
100.0 |
1 |
100.0 |
100.0 |
1 |
0.32 |
34.6 |
8 |
4.5 |
11 |
0 |
100.0 |
100.0 |
1 |
100.0 |
100.0 |
1 |
100.0 |
100.0 |
1 |
0.31 |
40.0 |
6 |
3.5 |
11 |
1 |
91.9 |
48.4 |
5 |
11.9 |
49.2 |
11 |
91.9 |
48.4 |
5 |
0.35 |
46.9 |
8 |
7.5 |
11 |
2 |
95.7 |
48.6 |
13 |
86.7 |
45.6 |
17 |
95.7 |
48.5 |
14 |
0.27 |
38.5 |
12 |
13.3 |
11 |
3 |
93.1 |
47.9 |
6 |
16.7 |
18.2 |
7 |
93.0 |
47.9 |
6 |
0.31 |
37.0 |
12 |
9.2 |
12 |
0 |
100.0 |
100.0 |
1 |
100.0 |
100.0 |
1 |
100.0 |
100.0 |
1 |
0.26 |
31.0 |
11 |
6.0 |
12 |
1 |
96.9 |
71.1 |
7 |
7.9 |
5.4 |
14 |
96.9 |
49.7 |
8 |
0.32 |
33.8 |
12 |
10.8 |
12 |
2 |
100.0 |
100.0 |
1 |
100.0 |
100.0 |
1 |
100.0 |
100.0 |
1 |
0.29 |
38.0 |
12 |
6.5 |
12 |
3 |
94.7 |
47.7 |
5 |
11.6 |
5.8 |
11 |
94.4 |
47.2 |
7 |
0.40 |
34.7 |
11 |
9.3 |
13 |
0 |
99.1 |
49.6 |
7 |
95.9 |
47.9 |
9 |
100.0 |
100.0 |
1 |
0.25 |
39.2 |
11 |
8.3 |
13 |
1 |
100.0 |
100.0 |
1 |
100.0 |
100.0 |
1 |
100.0 |
100.0 |
1 |
0.27 |
34.2 |
17 |
9.0 |
13 |
2 |
96.1 |
49.7 |
8 |
89.3 |
47.9 |
10 |
96.1 |
49.0 |
10 |
0.25 |
42.2 |
10 |
9.7 |
13 |
3 |
100.0 |
100.0 |
1 |
100.0 |
100.0 |
1 |
100.0 |
100.0 |
1 |
0.28 |
36.7 |
14 |
7.5 |
14 |
0 |
95.8 |
48.4 |
13 |
35.5 |
30.3 |
18 |
95.8 |
48.4 |
16 |
0.27 |
48.6 |
8 |
11.8 |
14 |
1 |
100.0 |
100.0 |
1 |
100.0 |
100.0 |
1 |
100.0 |
100.0 |
1 |
0.37 |
32.2 |
18 |
9.5 |
14 |
2 |
100.0 |
100.0 |
1 |
100.0 |
100.0 |
1 |
100.0 |
100.0 |
1 |
0.33 |
37.7 |
15 |
8.0 |
14 |
3 |
99.0 |
78.9 |
8 |
36.7 |
18.4 |
16 |
99.0 |
49.5 |
12 |
0.42 |
30.9 |
19 |
15.5 |
15 |
0 |
100.0 |
100.0 |
1 |
100.0 |
100.0 |
1 |
100.0 |
100.0 |
1 |
0.26 |
44.7 |
10 |
5.5 |
15 |
1 |
100.0 |
100.0 |
1 |
100.0 |
100.0 |
1 |
100.0 |
100.0 |
1 |
0.24 |
37.6 |
10 |
5.5 |
15 |
2 |
99.8 |
97.7 |
4 |
63.1 |
35.1 |
11 |
99.7 |
96.1 |
6 |
0.28 |
37.5 |
11 |
9.0 |
15 |
3 |
100.0 |
100.0 |
1 |
100.0 |
100.0 |
1 |
100.0 |
100.0 |
1 |
0.29 |
32.4 |
15 |
8.0 |
16 |
0 |
100.0 |
100.0 |
1 |
100.0 |
100.0 |
1 |
100.0 |
100.0 |
1 |
0.23 |
39.4 |
9 |
5.0 |
16 |
1 |
100.0 |
100.0 |
1 |
100.0 |
100.0 |
1 |
100.0 |
100.0 |
1 |
0.28 |
35.9 |
12 |
6.5 |
16 |
2 |
100.0 |
100.0 |
1 |
100.0 |
100.0 |
1 |
100.0 |
100.0 |
1 |
0.25 |
31.0 |
11 |
6.0 |
16 |
3 |
99.7 |
77.6 |
2 |
100.0 |
100.0 |
1 |
100.0 |
100.0 |
1 |
0.29 |
39.4 |
7 |
4.2 |
17 |
0 |
97.3 |
51.4 |
7 |
55.9 |
31.3 |
12 |
97.3 |
51.4 |
7 |
0.37 |
42.1 |
16 |
12.3 |
17 |
1 |
90.2 |
47.3 |
10 |
11.7 |
6.0 |
20 |
90.2 |
45.8 |
11 |
0.42 |
38.3 |
14 |
13.8 |
17 |
2 |
99.2 |
78.0 |
8 |
89.6 |
46.1 |
20 |
99.2 |
77.3 |
12 |
0.37 |
36.7 |
12 |
12.7 |
17 |
3 |
83.1 |
42.5 |
15 |
14.8 |
7.4 |
21 |
83.0 |
42.2 |
18 |
0.47 |
35.8 |
20 |
19.0 |
18 |
0 |
98.9 |
50.0 |
10 |
95.0 |
48.5 |
15 |
98.9 |
50.0 |
10 |
0.26 |
36.4 |
14 |
12.8 |
18 |
1 |
100.0 |
100.0 |
1 |
100.0 |
100.0 |
1 |
100.0 |
100.0 |
1 |
0.27 |
35.2 |
16 |
8.5 |
18 |
2 |
80.6 |
41.7 |
17 |
25.0 |
13.3 |
2 |
80.6 |
41.7 |
17 |
0.24 |
43.1 |
7 |
9.5 |
18 |
3 |
100.0 |
100.0 |
1 |
100.0 |
100.0 |
1 |
100.0 |
100.0 |
1 |
0.27 |
35.3 |
14 |
7.5 |
19 |
0 |
100.0 |
100.0 |
1 |
100.0 |
100.0 |
1 |
100.0 |
100.0 |
1 |
0.29 |
41.2 |
11 |
6.0 |
19 |
1 |
100.0 |
100.0 |
1 |
100.0 |
100.0 |
1 |
100.0 |
100.0 |
1 |
0.32 |
41.6 |
12 |
6.5 |
19 |
2 |
100.0 |
100.0 |
1 |
100.0 |
100.0 |
1 |
100.0 |
100.0 |
1 |
0.25 |
48.0 |
7 |
4.0 |
19 |
3 |
100.0 |
100.0 |
1 |
100.0 |
100.0 |
1 |
100.0 |
100.0 |
1 |
0.28 |
43.9 |
9 |
5.0 |
20 |
0 |
100.0 |
100.0 |
1 |
100.0 |
100.0 |
1 |
100.0 |
100.0 |
1 |
0.34 |
34.9 |
16 |
8.5 |
20 |
1 |
96.7 |
48.4 |
13 |
10.2 |
5.1 |
14 |
96.7 |
48.4 |
13 |
0.36 |
38.8 |
14 |
13.7 |
20 |
2 |
97.3 |
48.9 |
8 |
73.7 |
37.2 |
17 |
97.3 |
48.9 |
9 |
0.34 |
32.3 |
12 |
11.7 |
20 |
3 |
98.1 |
80.7 |
6 |
29.9 |
25.8 |
9 |
98.1 |
60.2 |
7 |
0.49 |
39.0 |
13 |
10.2 |
21 |
0 |
100.0 |
100.0 |
1 |
100.0 |
100.0 |
1 |
100.0 |
100.0 |
1 |
0.21 |
30.6 |
12 |
6.5 |
21 |
1 |
100.0 |
100.0 |
1 |
100.0 |
100.0 |
1 |
100.0 |
100.0 |
1 |
0.23 |
35.7 |
14 |
7.5 |
21 |
2 |
100.0 |
100.0 |
1 |
100.0 |
100.0 |
1 |
100.0 |
100.0 |
1 |
0.22 |
33.4 |
11 |
6.0 |
21 |
3 |
100.0 |
100.0 |
1 |
100.0 |
100.0 |
1 |
100.0 |
100.0 |
1 |
0.24 |
41.3 |
9 |
5.0 |
22 |
0 |
100.0 |
100.0 |
1 |
100.0 |
100.0 |
1 |
100.0 |
100.0 |
1 |
0.24 |
36.7 |
8 |
4.5 |
22 |
1 |
100.0 |
100.0 |
1 |
100.0 |
100.0 |
1 |
100.0 |
100.0 |
1 |
0.21 |
43.5 |
8 |
4.5 |
22 |
2 |
100.0 |
100.0 |
1 |
100.0 |
100.0 |
1 |
100.0 |
100.0 |
1 |
0.25 |
40.4 |
10 |
5.5 |
22 |
3 |
100.0 |
100.0 |
1 |
100.0 |
100.0 |
1 |
100.0 |
100.0 |
1 |
0.26 |
37.7 |
8 |
4.5 |
23 |
0 |
100.0 |
100.0 |
1 |
100.0 |
100.0 |
1 |
100.0 |
100.0 |
1 |
0.29 |
32.1 |
11 |
6.0 |
23 |
1 |
100.0 |
100.0 |
1 |
100.0 |
100.0 |
1 |
100.0 |
100.0 |
1 |
0.28 |
38.9 |
14 |
7.5 |
23 |
2 |
100.0 |
100.0 |
1 |
100.0 |
100.0 |
1 |
100.0 |
100.0 |
1 |
0.24 |
44.2 |
9 |
5.0 |
23 |
3 |
100.0 |
100.0 |
1 |
100.0 |
100.0 |
1 |
100.0 |
100.0 |
1 |
0.29 |
40.3 |
13 |
7.0 |
24 |
0 |
100.0 |
100.0 |
1 |
100.0 |
100.0 |
1 |
100.0 |
100.0 |
1 |
0.20 |
33.0 |
11 |
6.0 |
24 |
1 |
87.0 |
44.9 |
14 |
6.1 |
3.0 |
19 |
87.7 |
43.8 |
15 |
0.22 |
32.1 |
12 |
14.0 |
24 |
2 |
100.0 |
100.0 |
1 |
100.0 |
100.0 |
1 |
100.0 |
100.0 |
1 |
0.24 |
35.1 |
10 |
5.5 |
24 |
3 |
99.5 |
94.5 |
4 |
96.9 |
79.8 |
10 |
99.5 |
93.9 |
10 |
0.22 |
40.1 |
11 |
9.5 |
25 |
0 |
98.4 |
49.4 |
3 |
29.7 |
16.5 |
15 |
99.2 |
49.8 |
15 |
0.28 |
36.0 |
11 |
11.0 |
25 |
1 |
98.4 |
49.9 |
4 |
38.9 |
19.5 |
5 |
98.4 |
49.3 |
4 |
0.34 |
35.3 |
9 |
6.7 |
25 |
2 |
100.0 |
100.0 |
1 |
100.0 |
100.0 |
1 |
100.0 |
100.0 |
1 |
0.23 |
39.8 |
11 |
6.0 |
25 |
3 |
97.8 |
49.1 |
1 |
29.6 |
14.9 |
15 |
97.6 |
48.8 |
7 |
0.31 |
33.4 |
10 |
8.8 |
26 |
0 |
91.9 |
50.0 |
2 |
10.5 |
12.6 |
20 |
91.2 |
49.9 |
2 |
0.38 |
51.6 |
13 |
10.5 |
26 |
1 |
76.0 |
39.7 |
11 |
11.2 |
8.2 |
7 |
76.0 |
39.7 |
11 |
0.37 |
48.3 |
12 |
10.8 |
26 |
2 |
100.0 |
100.0 |
1 |
100.0 |
100.0 |
1 |
100.0 |
100.0 |
1 |
0.36 |
39.8 |
11 |
6.0 |
26 |
3 |
79.5 |
40.5 |
13 |
16.6 |
10.2 |
20 |
79.5 |
40.4 |
13 |
0.45 |
48.3 |
9 |
12.2 |
27 |
0 |
93.4 |
46.8 |
9 |
56.7 |
28.4 |
4 |
94.0 |
47.0 |
11 |
0.32 |
41.9 |
12 |
10.0 |
27 |
1 |
92.7 |
67.5 |
5 |
50.0 |
60.7 |
4 |
92.7 |
67.5 |
5 |
0.39 |
40.0 |
8 |
6.3 |
27 |
2 |
100.0 |
100.0 |
1 |
100.0 |
100.0 |
1 |
100.0 |
100.0 |
1 |
0.30 |
36.0 |
8 |
4.5 |
27 |
3 |
99.3 |
91.0 |
3 |
50.0 |
27.0 |
10 |
99.3 |
49.9 |
6 |
0.37 |
32.4 |
11 |
8.7 |
28 |
0 |
100.0 |
100.0 |
1 |
100.0 |
100.0 |
1 |
100.0 |
100.0 |
1 |
0.24 |
25.1 |
13 |
7.0 |
28 |
1 |
94.0 |
49.1 |
7 |
78.1 |
46.0 |
6 |
93.7 |
48.6 |
7 |
0.25 |
28.9 |
13 |
9.8 |
28 |
2 |
100.0 |
100.0 |
1 |
100.0 |
100.0 |
1 |
100.0 |
100.0 |
1 |
0.21 |
37.9 |
6 |
3.5 |
28 |
3 |
98.1 |
67.6 |
12 |
20.2 |
10.2 |
26 |
98.1 |
49.1 |
16 |
0.27 |
34.4 |
11 |
14.5 |
29 |
0 |
100.0 |
100.0 |
1 |
100.0 |
100.0 |
1 |
100.0 |
100.0 |
1 |
0.20 |
34.5 |
11 |
6.0 |
29 |
1 |
97.3 |
48.8 |
2 |
11.8 |
8.2 |
17 |
97.3 |
48.7 |
2 |
0.29 |
32.3 |
12 |
9.5 |
29 |
2 |
100.0 |
100.0 |
1 |
100.0 |
100.0 |
1 |
100.0 |
100.0 |
1 |
0.29 |
32.3 |
12 |
6.5 |
29 |
3 |
100.0 |
100.0 |
1 |
100.0 |
100.0 |
1 |
100.0 |
100.0 |
1 |
0.27 |
34.1 |
12 |
6.5 |
30 |
0 |
100.0 |
100.0 |
1 |
100.0 |
100.0 |
1 |
100.0 |
100.0 |
1 |
0.25 |
29.8 |
12 |
6.5 |
30 |
1 |
100.0 |
100.0 |
1 |
100.0 |
100.0 |
1 |
100.0 |
100.0 |
1 |
0.22 |
35.1 |
12 |
6.5 |
30 |
2 |
98.0 |
67.5 |
11 |
95.1 |
48.2 |
17 |
98.0 |
63.8 |
14 |
0.25 |
35.8 |
11 |
12.5 |
30 |
3 |
96.4 |
64.7 |
7 |
83.3 |
49.1 |
4 |
98.9 |
75.0 |
4 |
0.31 |
34.2 |
12 |
8.5 |
31 |
0 |
100.0 |
100.0 |
1 |
100.0 |
100.0 |
1 |
100.0 |
100.0 |
1 |
0.22 |
28.3 |
13 |
7.0 |
31 |
1 |
99.4 |
81.0 |
6 |
92.2 |
47.3 |
7 |
99.4 |
77.9 |
7 |
0.24 |
30.7 |
13 |
9.8 |
31 |
2 |
100.0 |
100.0 |
1 |
100.0 |
100.0 |
1 |
100.0 |
100.0 |
1 |
0.28 |
27.2 |
13 |
7.0 |
31 |
3 |
100.0 |
100.0 |
1 |
100.0 |
100.0 |
1 |
100.0 |
100.0 |
1 |
0.30 |
22.4 |
14 |
7.5 |