Ljiljana Platiša, Bart Goossens, Ewout Vansteenkiste, Subok Park, Brandon D. Gallas, Aldo Badano, and Wilfried Philips, "Channelized Hotelling observers for the assessment of volumetric imaging data sets," J. Opt. Soc. Am. A 28, 1145-1163 (2011)
Current clinical practice is rapidly moving in the direction of volumetric imaging.
For two-dimensional (2D) images, task-based medical image quality is often assessed
using numerical model observers. For three- dimensional (3D) images, however, these
models have been little explored so far. In this work, first, two novel designs of a
multislice channelized Hotelling observer (CHO) are proposed for the task of
detecting 3D signals in 3D images. The novel designs are then compared and evaluated
in a simulation study with five different CHO designs: a single-slice model, three
multislice models, and a volumetric model. Four different random background
statistics are considered, both Gaussian (noncorrelated and correlated Gaussian
noise) and non-Gaussian (lumpy and clustered lumpy backgrounds). Overall, the results
show that the volumetric model outperforms the others, while the disparity between
the models decreases for greater complexity of the detection task. Among the
multislice models, the second proposed CHO could most closely approach the volumetric
model, whereas the first new CHO seems to be least affected by the number of training
samples.
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The following notation applies: M, number of voxels in the
image; , number of voxels in the FOV (LB, CLB); , spread parameter of the 3D Gaussian signal; , magnitude of the 3D Gaussian signal; , standard deviation of the 3D Gaussian kernel (CNB) or spread
parameter of the 3D Gaussian lump (LB); , peak intensity level in the background image; , mean number of lumps in the FOV (LB, CLB); , , and , characteristic lengths of the asymmetrical lumps in the
x, y, and z directions,
respectively (CLB).
For each image category and its related signal size, the parameters of the LG
channels are determined: the size of the channels, ; the number of 2D LG channels, ; and the number of 3D LG channels, . The parameters of 2D and 3D LG channels are selected in the
experiments with ssCHO and vCHO models, respectively. The models are
investigated in the space of five families of LG channels defined by the value
of the channel spread parameter, . For each family, the number of LG channels is varied in the
range of . The experiments are conducted with trainer pairs and tester pairs and for the second largest among four considered
values of signal magnitude given in Table 1. The
results of these experiments are illustrated in Fig. 3.
The total number of each of WNB and CNB images is 11,000 image pairs, and the
total number of each of LB and CLB images is 7000 image pairs. For all study
configurations, the number of tester image pairs is fixed to . No overlap exists between the trainer images and the tester
images.
Table 4
Terms of Eq. (17) for Three
Different Types of Model Observer Efficiency, η
Type of Efficiency
SNR of a given CHO
SNR of the IO
SNR of the CHO trained with image pairs, (see Table 3)
SNR of the CHO trained with the maximum considered
number of trainer pairs,
SNR of the ssCHO
SNR of the vCHO
Table 5
Efficiency of CHO Models Applied on CNB Images with Different Spread of the
Signal: Efficiency of the CHO Model Relative to the IO Performance () and Efficiency of ssCHO Relative to the vCHO Performance ()a
ssCHO
vCHO
(%)
(%)
(%)
(%)
(%)
(%)
8
0.25
69
85
86
91
62
0.5
59
71
71
82
98
60
0.75
55
66
66
77
93
59
1
53
63
63
75
91
59
5
0.01
13
28
27
35
82
16
0.015
13
27
27
36
78
17
0.02
14
27
26
37
77
18
0.025
14
26
26
37
76
18
3
0.0025
12
36
35
46
88
13
0.0035
12
36
36
47
86
14
0.0045
12
36
35
47
85
14
0.0055
12
36
35
47
85
15
Three different values of signal spread parameter are considered: , , and . For each , the exact same backgrounds are used and their lump spread
parameter is . For msCHO models, the efficiency for the ROI size of are given. The values of and are calculated using Eq. (17) and as explained in Subsection 4C. The calculations are done for the MRMC configuration
with the number of trainer image pairs .
Table 6
Efficiency of Five CHO Models for Different Levels of the Signal while the Number of Trainer Images Increase: a
0.25
0.5
0.75
1
0.25
0.5
0.75
1
0.25
0.5
0.75
1
(%) for ssCHO
(%) for vCHO
0.55
1.02
1.48
1.94
0.70
1.31
1.92
2.53
41
74
84
88
55
82
87
88
100
56
81
89
92
61
84
90
93
200
69
91
95
97
73
92
96
97
500
89
96
98
99
90
97
98
99
1000
96
99
99
100
94
99
99
100
2000
99
100
100
100
99
100
100
100
(%) for
(%) for
(%) for
0.61
1.12
1.62
2.11
0.61
1.12
1.62
2.11
0.63
1.20
1.75
2.30
13
51
69
75
23
58
72
78
0
0
3
5
100
34
71
81
85
37
70
82
87
11
26
36
42
200
44
83
91
93
54
86
93
95
16
43
60
68
500
78
94
96
97
81
94
97
98
41
70
80
85
1000
88
97
98
99
89
97
98
99
61
85
92
94
2000
97
99
99
100
97
99
99
100
85
95
97
98
For CNB images, the efficiency of CHO models ssCHO, , , , and vCHO, trained with fewer image pairs relative to their
performance for the largest considered number of trainer images, , are calculated using Eq. (17) and as explained in Subsection 4C. For three msCHO models, the efficiency for the ROI size
of is given.
Table 7
Efficiency of msCHO Models for Different-Sized ROIs while the Number of
Trainer Images Increase: a
R
3
5
11
64
3
5
11
64
3
5
11
64
(%) for
(%) for
(%) for
1.49
1.49
1.62
1.73
1.49
1.49
1.62
1.73
1.60
1.65
1.75
—
84
83
69
19
82
81
72
25
55
36
3
—
100
88
87
81
49
87
86
82
52
77
68
36
—
200
95
94
91
68
95
94
93
73
88
80
60
—
500
97
97
96
88
97
97
97
87
94
89
80
—
1000
99
99
98
94
99
99
98
94
98
96
92
—
2000
100
100
99
98
100
100
99
98
99
99
97
—
For CNB images, the efficiency of msCHO models , , and , trained with fewer image pairs relative to their performance
for the largest considered number of trainer images, , are calculated using Eq. (17) and as explained in Subsection 4C. In particular, the efficiency for the signal magnitude
of for four different ROI sizes, , is presented. Here, implies that the CHO is applied to all slices in the
image.
The following notation applies: M, number of voxels in the
image; , number of voxels in the FOV (LB, CLB); , spread parameter of the 3D Gaussian signal; , magnitude of the 3D Gaussian signal; , standard deviation of the 3D Gaussian kernel (CNB) or spread
parameter of the 3D Gaussian lump (LB); , peak intensity level in the background image; , mean number of lumps in the FOV (LB, CLB); , , and , characteristic lengths of the asymmetrical lumps in the
x, y, and z directions,
respectively (CLB).
For each image category and its related signal size, the parameters of the LG
channels are determined: the size of the channels, ; the number of 2D LG channels, ; and the number of 3D LG channels, . The parameters of 2D and 3D LG channels are selected in the
experiments with ssCHO and vCHO models, respectively. The models are
investigated in the space of five families of LG channels defined by the value
of the channel spread parameter, . For each family, the number of LG channels is varied in the
range of . The experiments are conducted with trainer pairs and tester pairs and for the second largest among four considered
values of signal magnitude given in Table 1. The
results of these experiments are illustrated in Fig. 3.
The total number of each of WNB and CNB images is 11,000 image pairs, and the
total number of each of LB and CLB images is 7000 image pairs. For all study
configurations, the number of tester image pairs is fixed to . No overlap exists between the trainer images and the tester
images.
Table 4
Terms of Eq. (17) for Three
Different Types of Model Observer Efficiency, η
Type of Efficiency
SNR of a given CHO
SNR of the IO
SNR of the CHO trained with image pairs, (see Table 3)
SNR of the CHO trained with the maximum considered
number of trainer pairs,
SNR of the ssCHO
SNR of the vCHO
Table 5
Efficiency of CHO Models Applied on CNB Images with Different Spread of the
Signal: Efficiency of the CHO Model Relative to the IO Performance () and Efficiency of ssCHO Relative to the vCHO Performance ()a
ssCHO
vCHO
(%)
(%)
(%)
(%)
(%)
(%)
8
0.25
69
85
86
91
62
0.5
59
71
71
82
98
60
0.75
55
66
66
77
93
59
1
53
63
63
75
91
59
5
0.01
13
28
27
35
82
16
0.015
13
27
27
36
78
17
0.02
14
27
26
37
77
18
0.025
14
26
26
37
76
18
3
0.0025
12
36
35
46
88
13
0.0035
12
36
36
47
86
14
0.0045
12
36
35
47
85
14
0.0055
12
36
35
47
85
15
Three different values of signal spread parameter are considered: , , and . For each , the exact same backgrounds are used and their lump spread
parameter is . For msCHO models, the efficiency for the ROI size of are given. The values of and are calculated using Eq. (17) and as explained in Subsection 4C. The calculations are done for the MRMC configuration
with the number of trainer image pairs .
Table 6
Efficiency of Five CHO Models for Different Levels of the Signal while the Number of Trainer Images Increase: a
0.25
0.5
0.75
1
0.25
0.5
0.75
1
0.25
0.5
0.75
1
(%) for ssCHO
(%) for vCHO
0.55
1.02
1.48
1.94
0.70
1.31
1.92
2.53
41
74
84
88
55
82
87
88
100
56
81
89
92
61
84
90
93
200
69
91
95
97
73
92
96
97
500
89
96
98
99
90
97
98
99
1000
96
99
99
100
94
99
99
100
2000
99
100
100
100
99
100
100
100
(%) for
(%) for
(%) for
0.61
1.12
1.62
2.11
0.61
1.12
1.62
2.11
0.63
1.20
1.75
2.30
13
51
69
75
23
58
72
78
0
0
3
5
100
34
71
81
85
37
70
82
87
11
26
36
42
200
44
83
91
93
54
86
93
95
16
43
60
68
500
78
94
96
97
81
94
97
98
41
70
80
85
1000
88
97
98
99
89
97
98
99
61
85
92
94
2000
97
99
99
100
97
99
99
100
85
95
97
98
For CNB images, the efficiency of CHO models ssCHO, , , , and vCHO, trained with fewer image pairs relative to their
performance for the largest considered number of trainer images, , are calculated using Eq. (17) and as explained in Subsection 4C. For three msCHO models, the efficiency for the ROI size
of is given.
Table 7
Efficiency of msCHO Models for Different-Sized ROIs while the Number of
Trainer Images Increase: a
R
3
5
11
64
3
5
11
64
3
5
11
64
(%) for
(%) for
(%) for
1.49
1.49
1.62
1.73
1.49
1.49
1.62
1.73
1.60
1.65
1.75
—
84
83
69
19
82
81
72
25
55
36
3
—
100
88
87
81
49
87
86
82
52
77
68
36
—
200
95
94
91
68
95
94
93
73
88
80
60
—
500
97
97
96
88
97
97
97
87
94
89
80
—
1000
99
99
98
94
99
99
98
94
98
96
92
—
2000
100
100
99
98
100
100
99
98
99
99
97
—
For CNB images, the efficiency of msCHO models , , and , trained with fewer image pairs relative to their performance
for the largest considered number of trainer images, , are calculated using Eq. (17) and as explained in Subsection 4C. In particular, the efficiency for the signal magnitude
of for four different ROI sizes, , is presented. Here, implies that the CHO is applied to all slices in the
image.