demonstrates that the image gradient representation, phase
filtering, robust estimation and robustness iteration are all
effective. The superiority of the proposed method mainly ben-
efits from the integration of using four additional measures to
exclude the corrupted phase shift angles that deviate from the
theoretical plane model. As shown in Table 1, the results im-
prove for all the test methods with the larger window size due
to the increasing image information. The
UCC
method seems
to be sensitive to small correlation windows, while Foroosh’s
method is the most stable in terms of the influence of the
window size. Considering that a larger correlation window
would exacerbate the “fattening” effect in practical cases that
object boundaries are not reconstructed correctly (Heo
et al.
,
2011), the correlation window size in the following tests was
set as 64 × 64 pixels. In addition, a comparison of computa-
tional time of all the subpixel methods in the case of 128×128
pixels is provided in Table 2. All these seven methods are
programmed in Matlab on a computer with 3.0 GHz CPU. The
total computational counts with respect to each method are
50*60 = 3000 times. As can be seen, the proposed method,
which integrates Stone’s method with additional measures
to improve the accuracy and robustness, spends a little more
computational time than the original Stone’s method, but
takes less computational time than UCC method. The compu-
tation time of the proposed method is dominated by robust
estimation and robust iteration. Fortunately, the use of
HMSS
algorithm effectively saves the computational time on robust
estimation processing, which ensure the proposed method is
reliable and acceptable in view of both accuracy and compu-
tational efficiency. Future efforts will focus on ways to en-
hance the computational efficiency of the proposed method.
Table 1. Comparison Results in terms of RMS and MeanStd of Different Methods (Unit: Pixels).
Size
Method
Foroosh
PEF
UCC
Hoge
Stone
CCF-O
Row
32
RMS
0.1238
0.0636
0.3008
0.0595
0.1305
0.0881
MeanStd
0.0675
0.0631
0.1227
0.0558
0.1264
0.0578
64
RMS
0.1125
0.0261
0.1766
0.0281
0.0709
0.0673
MeanStd
0.0457
0.0258
0.0908
0.0277
0.0702
0.0314
128
RMS
0.1101
0.0103
0.0504
0.0163
0.0263
0.0598
MeanStd
0.0363
0.0098
0.0179
0.0157
0.0252
0.0179
Column
32
RMS
0.1456
0.0772
0.3191
0.0902
0.1480
0.1239
MeanStd
0.0873
0.0764
0.1368
0.0827
0.1398
0.0921
64
RMS
0.1309
0.0291
0.2616
0.0471
0.0778
0.0786
MeanStd
0.0591
0.0287
0.1180
0.0437
0.0754
0.0516
128
RMS
0.1208
0.0112
0.0779
0.0197
0.0264
0.0614
MeanStd
0.0474
0.0106
0.0391
0.0179
0.0251
0.0308
Size
Method
Stone_GR
Stone_PF
Stone_RE
Stone_RI
Proposed
Row
32
RMS
0.1173
0.0877
0.0594
0.0806
0.0436
MeanStd
0.1113
0.0834
0.0459
0.0770
0.0330
64
RMS
0.0616
0.0408
0.0229
0.0335
0.0123
MeanStd
0.0591
0.0403
0.0197
0.0332
0.0098
128
RMS
0.0210
0.0134
0.0085
0.0117
0.0040
MeanStd
0.0195
0.0130
0.0079
0.0116
0.0033
Column
32
RMS
0.1326
0.1008
0.0790
0.0977
0.0583
MeanStd
0.1240
0.0918
0.0624
0.0894
0.0518
64
RMS
0.0667
0.0428
0.0253
0.0374
0.0187
MeanStd
0.0634
0.0414
0.0215
0.0365
0.0152
128
RMS
0.0215
0.0138
0.0096
0.0124
0.0048
MeanStd
0.0198
0.0127
0.0089
0.0118
0.0041
Table 2. Computational Time of Different Methods in the case
of 128×128 Pixels (Unit: Seconds).
Method Foroosh PEF UCC Hoge Stone CCF-O Proposed
Total
Time
11.327 7.901 22.175 12.618 11.605 8.749 19.344
Table 3. Tracking Errors of Four Different Methods in the
Static Test (Unit: Pixels).
Test positions Methods NCC LK Shape-based Proposed
T3
Left
x
0.0406 0.0363 0.1367
0.0236
y
0.0304 0.0269 0.0484
0.0175
Right
x
0.0453 0.0310 0.1271
0.0226
y
0.0416 0.0215 0.0545
0.0141
T10
Left
x
0.0379 0.0337 0.0474
0.0252
y
0.0408 0.0239 0.0293
0.0171
Right
x
0.0515 0.0310 0.2169
0.0218
y
0.0398 0.0169 0.2052
0.0114
T5
Left
x
0.0353 0.0284 0.0463
0.0246
y
0.0411 0.0271 0.0402
0.0123
Right
x
0.0405 0.0301 0.0501
0.0217
y
0.0460 0.0212 0.0391
0.0140
T14
Left
x
0.0517 0.0306 0.0525
0.0192
y
0.0419 0.0224 0.0346
0.0157
Right
x
0.0407 0.0345 0.0513
0.0202
y
0.0348 0.0145 0.0358
0.0129
PHOTOGRAMMETRIC ENGINEERING & REMOTE SENSING
September 2018
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