Figure 1.
Samples of: bulk carrier (top); container ship (middle); and oil tanker (bottom) in TerraSAR-X images.
Figure 1.
Samples of: bulk carrier (top); container ship (middle); and oil tanker (bottom) in TerraSAR-X images.
Figure 2.
Three-dimensional principle components computed by PCA and three-dimensional embedding computed by MVU on DS1: (a) visualization of the three-dimensional principle components, their projections on two-dimensional subspace, and eigenvalues from the matrices of PCA; and (b) visualization of the three-dimensional embedding, their projections on two-dimensional subspace, and eigenvalues from the matrices of MVU.
Figure 2.
Three-dimensional principle components computed by PCA and three-dimensional embedding computed by MVU on DS1: (a) visualization of the three-dimensional principle components, their projections on two-dimensional subspace, and eigenvalues from the matrices of PCA; and (b) visualization of the three-dimensional embedding, their projections on two-dimensional subspace, and eigenvalues from the matrices of MVU.
Figure 3.
Image preprocessing by the three-step segmentation: (a) the original SAR image; (b) the binary image after the binaryzation and rotation; (c) the cumulations curve along x direction; (d) the bounding box around the ship; (e) the cumulations curve along y direction; and (f) the SAR image chip.
Figure 3.
Image preprocessing by the three-step segmentation: (a) the original SAR image; (b) the binary image after the binaryzation and rotation; (c) the cumulations curve along x direction; (d) the bounding box around the ship; (e) the cumulations curve along y direction; and (f) the SAR image chip.
Figure 4.
The classification accuracy versus the block stride and number of bins: (a) the classification accuracy versus the block stride, where we set the block stride to be 1, 5, 9, 13, 17 and 21; and (b) the classification accuracy versus the number of bins, where we set the number of bins to be 3, 6, 9, 12, 15, 18 and 21.
Figure 4.
The classification accuracy versus the block stride and number of bins: (a) the classification accuracy versus the block stride, where we set the block stride to be 1, 5, 9, 13, 17 and 21; and (b) the classification accuracy versus the number of bins, where we set the number of bins to be 3, 6, 9, 12, 15, 18 and 21.
Figure 5.
The classification accuracy versus the cell size and block size: (a) the classification accuracy versus the cell size, where we set the cell size to be 3, 5, 7, 9, 11 and 13; and (b) the classification accuracy versus the block size, where we set the block size to be 2, 3, 4, 5, 6 and 7. When the block size is bigger than the image size, we decrease the corresponding cell size to adapt to the image size.
Figure 5.
The classification accuracy versus the cell size and block size: (a) the classification accuracy versus the cell size, where we set the cell size to be 3, 5, 7, 9, 11 and 13; and (b) the classification accuracy versus the block size, where we set the block size to be 2, 3, 4, 5, 6 and 7. When the block size is bigger than the image size, we decrease the corresponding cell size to adapt to the image size.
Figure 6.
The classification accuracy versus the regularization parameters and : (a) the classification accuracy versus , where we set to be 0.15, 0.2, 0.25, 0.3, 0.35, 0.4, 0.45, 0.5 and 0.55; and (b) the classification accuracy versus , where we set to be 10−6, 10−5, 10−4, 10−3 and 10−2.
Figure 6.
The classification accuracy versus the regularization parameters and : (a) the classification accuracy versus , where we set to be 0.15, 0.2, 0.25, 0.3, 0.35, 0.4, 0.45, 0.5 and 0.55; and (b) the classification accuracy versus , where we set to be 10−6, 10−5, 10−4, 10−3 and 10−2.
Figure 7.
The classification accuracy versus the regularization parameters and : (a) the classification accuracy versus , where we set to be 0.002, 0.004, …, 0.018 and 0.02; and (b) the classification accuracy versus , where we set to be 0.1, 0.2, …, 0.9 and 1.
Figure 7.
The classification accuracy versus the regularization parameters and : (a) the classification accuracy versus , where we set to be 0.002, 0.004, …, 0.018 and 0.02; and (b) the classification accuracy versus , where we set to be 0.1, 0.2, …, 0.9 and 1.
Figure 8.
The classification accuracy versus the regularization parameters and : (a) the classification accuracy versus , where we set to be 0, 0.1, …, 0.9 and 1; and (b) the classification accuracy versus , where we set to be 0, 0.025, …, 0.225 and 0.25.
Figure 8.
The classification accuracy versus the regularization parameters and : (a) the classification accuracy versus , where we set to be 0, 0.1, …, 0.9 and 1; and (b) the classification accuracy versus , where we set to be 0, 0.025, …, 0.225 and 0.25.
Figure 9.
The classification accuracy versus the sub-dictionary size . We set the sub-dictionary size to be 4, 5, 6, 7, 8, 9, 10 and 11.
Figure 9.
The classification accuracy versus the sub-dictionary size . We set the sub-dictionary size to be 4, 5, 6, 7, 8, 9, 10 and 11.
Figure 10.
The distribution of sparse codes with respect to the dictionary, which is learnt by TDDL: (a) the distribution of sparse codes of the training set; and (b) the distribution of sparse codes of the testing set.
Figure 10.
The distribution of sparse codes with respect to the dictionary, which is learnt by TDDL: (a) the distribution of sparse codes of the training set; and (b) the distribution of sparse codes of the testing set.
Figure 11.
The distribution of sparse codes with respect to the dictionary, which is learnt by TDDL with intrinsic constraints only: (a) the distribution of sparse codes of the training set; and (b) the distribution of sparse codes of the testing set.
Figure 11.
The distribution of sparse codes with respect to the dictionary, which is learnt by TDDL with intrinsic constraints only: (a) the distribution of sparse codes of the training set; and (b) the distribution of sparse codes of the testing set.
Figure 12.
The distribution of sparse codes with respect to the dictionary, which is learnt by TDDL-SIC: (a) the distribution of sparse codes of the training set; and (b) the distribution of sparse codes of the testing set.
Figure 12.
The distribution of sparse codes with respect to the dictionary, which is learnt by TDDL-SIC: (a) the distribution of sparse codes of the training set; and (b) the distribution of sparse codes of the testing set.
Table 1.
The image details of DS1 and DS2.
Table 1.
The image details of DS1 and DS2.
Dataset | Sensor | Model | Polarization | Azimuth Resolution | Range Resolution |
---|
DS1 | TerraSAR-X | stripmap | VV | 2.0 m | 1.0 m |
DS2 | TerraSAR-X | spotlight | VV | 1.0 m | 1.0 m |
Table 2.
The numbers of ship samples in training set and testing set.
Table 2.
The numbers of ship samples in training set and testing set.
| DS1 | DS2 |
---|
| BC | CS | OT | BC | CS | OT |
Training Set | 75 | 25 | 25 | 75 | 75 | 75 |
Testing Set | 75 | 25 | 25 | 75 | 75 | 75 |
Table 3.
The parameters used in MSHOG feature.
Table 3.
The parameters used in MSHOG feature.
Parameter | Cell Size (Pixels) | Block Size (Cells) | Block Stride (Pixels) | Number of Bins | Dimensions |
---|
Value | | | 9 | 12 | 20 |
Table 4.
The parameters used in TDDL-SIC.
Table 4.
The parameters used in TDDL-SIC.
Parameter | | | | | | | |
---|
Values | 0.35 | 0.001 | 0.01 | 0.8 | 0.1 | 0.025 | 7 |
Table 5.
Comparison on classification accuracy (%) of 2DC, SF, SS, LRCSG, PSHOG and MSHOG on DS1 with SVM classifier.
Table 5.
Comparison on classification accuracy (%) of 2DC, SF, SS, LRCSG, PSHOG and MSHOG on DS1 with SVM classifier.
| 2DC | SF | SS | LRCSG | PSHOG | MSHOG |
---|
BC | 94.8 | 98.2 | 94.4 | 97.4 | 96.3 | 96.1 |
CS | 92.1 | 80.5 | 91.8 | 92.3 | 91.1 | 93.5 |
OT | 81.7 | 75.9 | 81.3 | 76.2 | 82.8 | 92.3 |
Total | 91.6 | 90.2 | 91.2 | 92.1 | 92.5 | 94.8 |
Table 6.
Comparison on classification accuracy (%) of 2DC, SF, SS, LRCSG, PSHOG and MSHOG on DS2 with SVM classifier.
Table 6.
Comparison on classification accuracy (%) of 2DC, SF, SS, LRCSG, PSHOG and MSHOG on DS2 with SVM classifier.
| 2DC | SF | SS | LRCSG | PSHOG | MSHOG |
---|
BC | 96 | 96.7 | 90 | 100 | 96.3 | 98.1 |
CS | 93.4 | 79.3 | 89.4 | 96.2 | 91.7 | 92.2 |
OT | 72.8 | 77.6 | 81.2 | 73.8 | 80.4 | 84.6 |
Total | 87.4 | 84.5 | 86.9 | 90.0 | 89.5 | 91.6 |
Table 7.
Comparison of the classification accuracy (%) of TDDL, TDDL with intrinsic constraints only and TDDL-SIC on DS1.
Table 7.
Comparison of the classification accuracy (%) of TDDL, TDDL with intrinsic constraints only and TDDL-SIC on DS1.
| TDDL | TDDL with Intrinsic Constraints Only | TDDL-SIC |
---|
| BC | CS | OT | BC | CS | OT | BC | CS | OT |
BC | 100 | 0 | 0 | 100 | 0 | 0 | 100 | 0 | 0 |
CS | 4.2 | 87.6 | 8.2 | 0 | 88.3 | 11.7 | 0 | 96.5 | 3.5 |
OT | 3 | 15.9 | 81.1 | 0.4 | 7.8 | 91.8 | 0.1 | 4.2 | 95.7 |
Total | 93.7 | 96 | 98.4 |
Table 8.
Comparison on classification accuracy (%) of SVM, K-NN, SRC and TDDL-SIC with MSHOG feature on DS1.
Table 8.
Comparison on classification accuracy (%) of SVM, K-NN, SRC and TDDL-SIC with MSHOG feature on DS1.
| SVM | K-NN | SRC | TDDL-SIC |
---|
BC | 96.1 | 94.8 | 98.2 | 100 |
CS | 93.5 | 91.4 | 93.1 | 96.5 |
OT | 92.3 | 86.6 | 87.0 | 95.7 |
Total | 94.8 | 92.5 | 94.9 | 98.4 |
Table 9.
Comparison on classification accuracy (%) of SVM, K-NN, SRC and TDDL-SIC with MSHOG feature on DS2.
Table 9.
Comparison on classification accuracy (%) of SVM, K-NN, SRC and TDDL-SIC with MSHOG feature on DS2.
| SVM | K-NN | SRC | TDDL-SIC |
---|
BC | 98.1 | 97.4 | 100 | 100 |
CS | 92.2 | 90.5 | 93.1 | 96.5 |
OT | 84.6 | 88.9 | 87.3 | 96.1 |
Total | 91.6 | 92.3 | 93.4 | 97.5 |
Table 10.
Comparison of the classification accuracy (%) of FS, SCA, FSSR, JFCS and “MSHOG+TDDL-SIC” on DS1.
Table 10.
Comparison of the classification accuracy (%) of FS, SCA, FSSR, JFCS and “MSHOG+TDDL-SIC” on DS1.
| FS | SCA | FSSR | JFCS | MSHOG+TDDL-SIC |
---|
BC | 98.2 | 94.4 | 97.8 | 98.1 | 100 |
CS | 80.5 | 91.8 | 92.7 | 89.6 | 96.5 |
OT | 75.9 | 81.3 | 85.1 | 85.2 | 95.7 |
Total | 90.2 | 91.2 | 94.2 | 93.9 | 98.4 |
Table 11.
Comparison of the classification accuracy (%) of FS, SCA, FSSR, JFCS and “MSHOG+TDDL-SIC” on DS2.
Table 11.
Comparison of the classification accuracy (%) of FS, SCA, FSSR, JFCS and “MSHOG+TDDL-SIC” on DS2.
| FS | SCA | FSSR | JFCS | MSHOG+TDDL-SIC |
---|
BC | 96.7 | 90 | 100 | 100 | 100 |
CS | 79.3 | 89.4 | 95 | 93.3 | 96.5 |
OT | 77.6 | 81.2 | 86.8 | 89 | 96.1 |
Total | 84.5 | 86.9 | 93.9 | 94.1 | 97.5 |