1The authors are with the Department of Mechanical Engineering, Clemson University, Clemson, South Carolina 29634. J. R. Saylor's e-mail address is jrsaylor@ces.clemson.edu.
Several thresholding algorithms are applied to the analysis of drop images, and their performance is compared. Images were obtained by use of a digital camera setup in which drops were illuminated from behind, resulting in an image of the drop silhouette. Each algorithm was evaluated based on the accuracy of the drop diameter obtained from the thresholded image and on the size of the depth of field. Because of the difficulty associated with creating drops that have a known diameter, solid spheres composed of a glass with an index of refraction close to that of water were used in computing the depth of field and in determining the accuracy of measured diameter. The application of this study is to the automatic measurement of raindrops and images were obtained during several storms. With each thresholding algorithm this raindrop imagery was used to compute the probability density function of drop diameter, and the rain rate. The performance of each thresholding algorithm was quantified by comparison of these measurements with simultaneous measurements obtained by use of a Joss–Waldvogel disdrometer.
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Slope and Intercept of the Lines Shown in Fig. 10 and 95% Confidence Level of the Linear Fit Presented in Eq. (21)
Thresholding Algorithm
Slope s (cm mm−1)
Intercept i (cm)
95% Confidence Level C95 (cm)
Double
1.88
2.07
±1.55
Entropy
1.85
−1.64
±0.95
Fixed 110
1.41
1.77
±0.66
Iterative
1.60
−1.27
±1.01
MP
1.89
0.70
±0.91
Table 2
Slope and Intercept of the Lines Shown in Fig. 12
Thresholding Algorithm
Slope s′
Intercept i′ (mm)
Double
0.92
−0.20
Entropy
0.93
0.02
Fixed 110
0.96
−0.17
Iterative
0.95
0.03
MP
0.90
−0.17
Table 3
Tabulation of 〈Dm〉, Db, σ1, and σ2 for Each D Investigateda
Algorithm
D (mm)
〈Dm〉 (mm)
Db (mm)
σ1 (mm)
σ2 (mm)
Double
3
2.6056
0.3944
0.1030
0.0255
4
3.4401
0.5599
0.1512
0.0273
5
4.3410
0.6590
0.2472
0.0380
6
5.2543
0.7457
0.3415
0.0464
7
6.2177
0.7823
0.3746
0.0506
8
7.2049
0.7951
0.4490
0.0460
Entropy
3
2.8488
0.1512
0.0410
0.0799
4
3.7410
0.2590
0.0675
0.0269
5
4.6521
0.3479
0.1082
0.0905
6
5.6078
0.3922
0.1309
0.1057
7
6.5519
0.4481
0.1517
0.0384
8
7.5106
0.4894
0.1937
0.2511
Fixed 110
3
2.7562
0.2438
0.0708
0.0184
4
3.6502
0.3498
0.1188
0.0240
5
4.5831
0.4169
0.1763
0.0244
6
5.5543
0.4457
0.2261
0.0313
7
6.5437
0.4563
0.2224
0.0350
8
7.5404
0.4596
0.2915
0.1547
Iterative
3
2.8888
0.1112
0.0426
0.0134
4
3.8185
0.1815
0.0647
0.0167
5
4.7480
0.2520
0.1133
0.0202
6
5.7282
0.2718
0.1290
0.0212
7
6.6682
0.3318
0.1633
0.0313
8
7.6453
0.3547
0.2536
0.1520
Moment
3
2.5607
0.4393
0.0241
0.0201
Preservation
4
3.3953
0.6047
0.0516
0.0224
5
4.2620
0.7380
0.0741
0.0712
6
5.1722
0.8278
0.1268
0.3276
7
6.0843
0.9157
0.1581
0.0992
8
7.0065
0.9935
0.1745
0.3389
aA set of these statistics is presented for each algorithm explored.
Table 4
Rain Rates (mm h−1) Obtained for Each of the 15 h of Recorded Rain Dataa
Hour
Date, Rain Hour Processed
Algorithm
Double
Entropy
Fixed 110
Iterative
MP
JWD
1
28 July, 1st hour
34.565
62.312
41.986
52.691
49.724
28.925
2
25 June, 20th hour
25.595
56.997
34.114
45.323
41.666
20.534
3
27 July, 1st hour
23.762
45.974
29.236
31.231
37.232
20.085
4
1 July, 0th hour
25.296
52.640
31.282
44.874
37.743
19.594
5
25 June, 12th hour
20.229
46.677
27.995
45.845
34.179
17.601
6
28 July, 0th hour
19.344
35.754
22.514
30.854
24.401
13.596
7
25 June, 22nd hour
17.161
29.520
19.315
23.812
24.355
10.933
8
27 July, 0th hour
10.325
27.245
14.432
19.081
18.917
10.293
9
14 June, 19th hour
13.832
32.229
17.227
22.890
22.180
8.735
10
14 June, 18th hour
8.849
18.233
10.758
12.396
13.665
7.238
11
13 July, 18th hour
8.626
20.653
10.881
19.273
13.281
6.596
12
4 July, 15th hour
5.600
14.291
7.210
9.831
9.834
5.070
13
1 July, 19th hour
2.869
9.132
3.891
4.558
5.688
3.239
14
30 June, 12th hour
1.393
4.860
2.172
4.332
3.427
1.658
15
30 June, 23rd hour
2.646
7.174
3.771
5.160
5.161
0.917
aAll the hours of rain data are from the year 2004; 0th hour is midnight to 1 a.m.
Table 5
Parameters Relevant to the Linear Fits of RA to RJ in Figs. 14 and 15
Thresholding Algorithm
Slope (m)
Intercept c (mm h−1)
95% Confidence Interval (mm h−1)
Correlation Coefficient
Double
1.20
0.66
±3.15
0.984
Entropy
2.24
4.78
±7.16
0.976
Fixed 110
1.50
0.98
±3.19
0.989
Iterative
1.92
2.42
±8.70
0.954
MP
1.77
2.17
±4.05
0.988
Table 6
Total Number of Examined Drops Accepted as In Focus H( D) and Number of Out-of-Focus Drops Incorrectly Accepted Ho(D) for Each Thresholding Algorithm and Each Diameter Range
Diameter Range (mm)
H(D)
Ho(D) for Thresholding Algorithm
Double
Entropy
Fixed 110
Iterative
MP
0.4–0.6
60
59
59
56
60
60
0.9–1.1
50
29
49
14
35
33
1.4–1.6
40
0
26
2
10
12
1.9–2.1
30
0
4
2
3
6
2.9–3.1
20
0
0
0
0
0
Table 7
Rain Rates (mm h−1) Obtained for Rain That Occurred During the 0th Hour of 1 July with the Simple Boundary Counting Algorithm and the Boundary Counting Algorithms with Image Smoothing a
Thresholding Algorithm
Boundary Counting
Boundary Counting with Closing
Boundary Counting with Yu–Yan Smoothing
Double
25.296
3.397
24.100
Entropy
53.176
3.640
51.982
Fixed 110
31.467
6.059
30.910
Iterative
44.987
2.940
43.448
MP
38.076
10.286
36.850
aThe rain rate R calculated from the JWD for this hour was 19.594 mm h−1.
Tables (7)
Table 1
Slope and Intercept of the Lines Shown in Fig. 10 and 95% Confidence Level of the Linear Fit Presented in Eq. (21)
Thresholding Algorithm
Slope s (cm mm−1)
Intercept i (cm)
95% Confidence Level C95 (cm)
Double
1.88
2.07
±1.55
Entropy
1.85
−1.64
±0.95
Fixed 110
1.41
1.77
±0.66
Iterative
1.60
−1.27
±1.01
MP
1.89
0.70
±0.91
Table 2
Slope and Intercept of the Lines Shown in Fig. 12
Thresholding Algorithm
Slope s′
Intercept i′ (mm)
Double
0.92
−0.20
Entropy
0.93
0.02
Fixed 110
0.96
−0.17
Iterative
0.95
0.03
MP
0.90
−0.17
Table 3
Tabulation of 〈Dm〉, Db, σ1, and σ2 for Each D Investigateda
Algorithm
D (mm)
〈Dm〉 (mm)
Db (mm)
σ1 (mm)
σ2 (mm)
Double
3
2.6056
0.3944
0.1030
0.0255
4
3.4401
0.5599
0.1512
0.0273
5
4.3410
0.6590
0.2472
0.0380
6
5.2543
0.7457
0.3415
0.0464
7
6.2177
0.7823
0.3746
0.0506
8
7.2049
0.7951
0.4490
0.0460
Entropy
3
2.8488
0.1512
0.0410
0.0799
4
3.7410
0.2590
0.0675
0.0269
5
4.6521
0.3479
0.1082
0.0905
6
5.6078
0.3922
0.1309
0.1057
7
6.5519
0.4481
0.1517
0.0384
8
7.5106
0.4894
0.1937
0.2511
Fixed 110
3
2.7562
0.2438
0.0708
0.0184
4
3.6502
0.3498
0.1188
0.0240
5
4.5831
0.4169
0.1763
0.0244
6
5.5543
0.4457
0.2261
0.0313
7
6.5437
0.4563
0.2224
0.0350
8
7.5404
0.4596
0.2915
0.1547
Iterative
3
2.8888
0.1112
0.0426
0.0134
4
3.8185
0.1815
0.0647
0.0167
5
4.7480
0.2520
0.1133
0.0202
6
5.7282
0.2718
0.1290
0.0212
7
6.6682
0.3318
0.1633
0.0313
8
7.6453
0.3547
0.2536
0.1520
Moment
3
2.5607
0.4393
0.0241
0.0201
Preservation
4
3.3953
0.6047
0.0516
0.0224
5
4.2620
0.7380
0.0741
0.0712
6
5.1722
0.8278
0.1268
0.3276
7
6.0843
0.9157
0.1581
0.0992
8
7.0065
0.9935
0.1745
0.3389
aA set of these statistics is presented for each algorithm explored.
Table 4
Rain Rates (mm h−1) Obtained for Each of the 15 h of Recorded Rain Dataa
Hour
Date, Rain Hour Processed
Algorithm
Double
Entropy
Fixed 110
Iterative
MP
JWD
1
28 July, 1st hour
34.565
62.312
41.986
52.691
49.724
28.925
2
25 June, 20th hour
25.595
56.997
34.114
45.323
41.666
20.534
3
27 July, 1st hour
23.762
45.974
29.236
31.231
37.232
20.085
4
1 July, 0th hour
25.296
52.640
31.282
44.874
37.743
19.594
5
25 June, 12th hour
20.229
46.677
27.995
45.845
34.179
17.601
6
28 July, 0th hour
19.344
35.754
22.514
30.854
24.401
13.596
7
25 June, 22nd hour
17.161
29.520
19.315
23.812
24.355
10.933
8
27 July, 0th hour
10.325
27.245
14.432
19.081
18.917
10.293
9
14 June, 19th hour
13.832
32.229
17.227
22.890
22.180
8.735
10
14 June, 18th hour
8.849
18.233
10.758
12.396
13.665
7.238
11
13 July, 18th hour
8.626
20.653
10.881
19.273
13.281
6.596
12
4 July, 15th hour
5.600
14.291
7.210
9.831
9.834
5.070
13
1 July, 19th hour
2.869
9.132
3.891
4.558
5.688
3.239
14
30 June, 12th hour
1.393
4.860
2.172
4.332
3.427
1.658
15
30 June, 23rd hour
2.646
7.174
3.771
5.160
5.161
0.917
aAll the hours of rain data are from the year 2004; 0th hour is midnight to 1 a.m.
Table 5
Parameters Relevant to the Linear Fits of RA to RJ in Figs. 14 and 15
Thresholding Algorithm
Slope (m)
Intercept c (mm h−1)
95% Confidence Interval (mm h−1)
Correlation Coefficient
Double
1.20
0.66
±3.15
0.984
Entropy
2.24
4.78
±7.16
0.976
Fixed 110
1.50
0.98
±3.19
0.989
Iterative
1.92
2.42
±8.70
0.954
MP
1.77
2.17
±4.05
0.988
Table 6
Total Number of Examined Drops Accepted as In Focus H( D) and Number of Out-of-Focus Drops Incorrectly Accepted Ho(D) for Each Thresholding Algorithm and Each Diameter Range
Diameter Range (mm)
H(D)
Ho(D) for Thresholding Algorithm
Double
Entropy
Fixed 110
Iterative
MP
0.4–0.6
60
59
59
56
60
60
0.9–1.1
50
29
49
14
35
33
1.4–1.6
40
0
26
2
10
12
1.9–2.1
30
0
4
2
3
6
2.9–3.1
20
0
0
0
0
0
Table 7
Rain Rates (mm h−1) Obtained for Rain That Occurred During the 0th Hour of 1 July with the Simple Boundary Counting Algorithm and the Boundary Counting Algorithms with Image Smoothing a
Thresholding Algorithm
Boundary Counting
Boundary Counting with Closing
Boundary Counting with Yu–Yan Smoothing
Double
25.296
3.397
24.100
Entropy
53.176
3.640
51.982
Fixed 110
31.467
6.059
30.910
Iterative
44.987
2.940
43.448
MP
38.076
10.286
36.850
aThe rain rate R calculated from the JWD for this hour was 19.594 mm h−1.