Synthetic-Aperture Radar image based positioning in GPS-denied environments using Deep Cosine Similarity Neural Networks

Seonho Park; Maciej Rysz; Kaitlin L. Fair; Panos M. Pardalos

doi:10.3934/ipi.2021013

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doi: 10.3934/ipi.2021013

Synthetic-Aperture Radar image based positioning in GPS-denied environments using Deep Cosine Similarity Neural Networks

Seonho Park ^1, , Maciej Rysz ^2,, , Kaitlin L. Fair ^3, and Panos M. Pardalos ^1,

1.	Department of Industrial and Systems Engineering, University of Florida, Gainesville, FL 32611, USA
2.	Department of Information Systems and Analytics, Miami University, Oxford, OH 45056, USA
3.	Air Force Research Laboratory (AFRL/RWWI), Eglin Air Force Base, FL 32542, USA

^* Corresponding author: Maciej Rysz

Received September 2020 Revised November 2020 Published January 2021

Fund Project: Distribution A: Approved for public release, distribution is unlimited, 96TW-2020-0170

Navigating unmanned aerial vehicles in precarious environments is of great importance. It is necessary to rely on alternative information processing techniques to attain spatial information that is required for navigation in such settings. This paper introduces a novel deep learning-based approach for navigating that exclusively relies on synthetic aperture radar (SAR) images. The proposed method utilizes deep neural networks (DNNs) for image matching, retrieval, and registration. To this end, we introduce Deep Cosine Similarity Neural Networks (DCSNNs) for mapping SAR images to a global descriptive feature vector. We also introduce a fine-tuning algorithm for DCSNNs, and DCSNNs are used to generate a database of feature vectors for SAR images that span a geographic area of interest, which, in turn, are compared against a feature vector of an inquiry image. Images similar to the inquiry are retrieved from the database by using a scalable distance measure between the feature vector outputs of DCSNN. Methods for reranking the retrieved SAR images that are used to update position coordinates of an inquiry SAR image by estimating from the best retrieved SAR image are also introduced. Numerical experiments comparing with baselines on the Polarimetric SAR (PolSAR) images are presented.

Keywords: Synthetic Aperture Radar (SAR), polarimetric SAR (PolSAR), Deep Cosine Similarity Neural Networks, image graphs, image retrieval, image registration, scale-invariant feature transform (SIFT), SAR-SIFT, remote sensing.

Mathematics Subject Classification: Primary: 68T07, 68U10; Secondary: 65D18.

Citation: Seonho Park, Maciej Rysz, Kaitlin L. Fair, Panos M. Pardalos. Synthetic-Aperture Radar image based positioning in GPS-denied environments using Deep Cosine Similarity Neural Networks. Inverse Problems & Imaging, doi: 10.3934/ipi.2021013

References:

[1]	Dataset: UAVSAR POLSAR, NASA 2020., Retrieved from ASF DAAC, 2020. Google Scholar
[2]	A. Babenko, A. Slesarev, A. Chigorin and V. Lempitsky, Neural codes for image retrieval, in European Conference on Computer Vision, Springer, 2014 (2014), 584–599. doi: 10.1007/978-3-319-10590-1_38. Google Scholar
[3]	G. Balamurugan, J. Valarmathi and V. Naidu, Survey on UAV navigation in GPS denied environments, in 2016 International Conference on Signal Processing, Communication, Power and Embedded System (SCOPES), IEEE, 2016,198–204. doi: 10.1109/SCOPES.2016.7955787. Google Scholar
[4]	J. Bhatti and T. E. Humphreys, Hostile control of ships via false GPS signals: Demonstration and detection, NAVIGATION: Journal of the Institute of Navigation, 64 (2017), 51-66. doi: 10.1002/navi.183. Google Scholar
[5]	F. Caballero, L. Merino, J. Ferruz and A. Ollero, Vision-based odometry and SLAM for medium and high altitude flying UAVs, Journal of Intelligent and Robotic Systems, 54 (2009), 137-161. doi: 10.1007/978-1-4020-9137-7_9. Google Scholar
[6]	Y. Cao, M. Long, J. Wang, H. Zhu and Q. Wen, Deep Quantization Network for Efficient Image Retrieval, in Thirtieth AAAI Conference on Artificial Intelligence, 2016. Google Scholar
[7]	A. Cesetti, E. Frontoni, A. Mancini, P. Zingaretti and S. Longhi, A vision-based guidance system for UAV navigation and safe landing using natural landmarks, Journal of Intelligent and Robotic Systems, 57 (2010), 233-257. doi: 10.1007/978-90-481-8764-5_12. Google Scholar
[8]	G. Conte and P. Doherty, Vision-based unmanned aerial vehicle navigation using geo-referenced information, EURASIP Journal on Advances in Signal Processing, 2009 (2009), Article number: 387308. doi: 10.1155/2009/387308. Google Scholar
[9]	N. Dalal and B. Triggs, Histograms of oriented gradients for human detection, in 2005 IEEE Computer Society Conference on Computer Vision and Pattern Recognition (CVPR'05), vol. 1, IEEE, 2005,886–893. doi: 10.1109/CVPR.2005.177. Google Scholar
[10]	F. Dellinger, J. Delon, Y. Gousseau, J. Michel and F. Tupin, SAR-SIFT: A SIFT-like algorithm for SAR images, IEEE Transactions on Geoscience and Remote Sensing, 53 (2015), 453-466. doi: 10.1109/TGRS.2014.2323552. Google Scholar
[11]	J. Deng, W. Dong, R. Socher, L.-J. Li, K. Li and L. Fei-Fei, Imagenet: A large-scale hierarchical image database, in 2009 IEEE Conference on Computer Vision and Pattern Recognition, Ieee, 2009,248–255. doi: 10.1109/CVPR.2009.5206848. Google Scholar
[12]	L. R. Dice, Measures of the amount of ecologic association between species, Ecology, 26 (1945), 297-302. doi: 10.2307/1932409. Google Scholar
[13]	J. Duchi, E. Hazan and Y. Singer, Adaptive subgradient methods for online learning and stochastic optimization, Journal of Machine Learning Research, 12 (2011), 2121-2159. Google Scholar
[14]	M. A. Fischler and R. C. Bolles, Random sample consensus: A paradigm for model fitting with applications to image analysis and automated cartography, Communications of the ACM, 24 (1981), 381-395. doi: 10.1145/358669.358692. Google Scholar
[15]	A. Gordo, J. Almazan, J. Revaud and D. Larlus, End-to-end learning of deep visual representations for image retrieval, International Journal of Computer Vision, 124 (2017), 237-254. doi: 10.1007/s11263-017-1016-8. Google Scholar
[16]	A. Grant, P. Williams, N. Ward and S. Basker, GPS jamming and the impact on maritime navigation, The Journal of Navigation, 62 (2009), 173-187. doi: 10.1017/S0373463308005213. Google Scholar
[17]	H. Jegou, M. Douze and C. Schmid, Product quantization for nearest neighbor search, IEEE Transactions on Pattern Analysis and Machine Intelligence, 33 (2011), 117-128. doi: 10.1109/TPAMI.2010.57. Google Scholar
[18]	M. Kaiser, N. Gans and W. Dixon, Vision-based estimation for guidance, navigation, and control of an aerial vehicle, IEEE Transactions on Aerospace and Electronic Systems, 46 (2010), 1064-1077. doi: 10.1109/TAES.2010.5545174. Google Scholar
[19]	W.-C. Kang, W.-J. Li and Z.-H. Zhou, Column Sampling Based Discrete Supervised Hashing, Thirtieth AAAI Conference on Artificial Intelligence, 2016. Google Scholar
[20]	D. P. Kingma and J. Ba, Adam: A method for stochastic optimization, arXiv preprint, arXiv: 1412.6980. Google Scholar
[21]	A. Krizhevsky, I. Sutskever and G. E. Hinton, Imagenet classification with deep convolutional neural networks, in Communications of the ACM, 60 (2017). doi: 10.1145/3065386. Google Scholar
[22]	P. Li and P. Ren, Partial randomness hashing for large-scale remote sensing image retrieval, IEEE Geoscience and Remote Sensing Letters, 14 (2017), 464-468. doi: 10.1109/LGRS.2017.2651056. Google Scholar
[23]	W.-J. Li, S. Wang and W.-C. Kang, Feature learning based deep supervised hashing with pairwise labels, arXiv preprint, arXiv: 1511.03855. Google Scholar
[24]	Y. Li, Y. Zhang, X. Huang, H. Zhu and J. Ma, Large-scale remote sensing image retrieval by deep hashing neural networks, IEEE Transactions on Geoscience and Remote Sensing, 56 (2017), 950-965. doi: 10.1109/TGRS.2017.2756911. Google Scholar
[25]	H. Liu, R. Wang, S. Shan and X. Chen, Deep supervised hashing for fast image retrieval, in Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, 2016, 2064–2072. doi: 10.1109/CVPR.2016.227. Google Scholar
[26]	J.-Z. Liu and X.-C. Yu, Research on SAR image matching technology based on SIFT, ISPRS08, B1. Google Scholar
[27]	D. G. Lowe, Object recognition from local scale-invariant features, in Proceedings of the Seventh IEEE International Conference on Computer Vision, vol. 2, Ieee, 1999, 1150–1157. doi: 10.1109/ICCV.1999.790410. Google Scholar
[28]	D. G. Lowe, Distinctive image features from scale-invariant keypoints, International Journal of Computer Vision, 60 (2004), 91-110. doi: 10.1023/B:VISI.0000029664.99615.94. Google Scholar
[29]	J. MacQueen et al., Some methods for classification and analysis of multivariate observations, in Proceedings of the Fifth Berkeley Symposium on Mathematical Statistics and Probability, vol. 1, Oakland, CA, USA, 1967,281–297. Google Scholar
[30]	A. Nemra and N. Aouf, Robust INS/GPS sensor fusion for UAV localization using SDRE nonlinear filtering, IEEE Sensors Journal, 10 (2010), 789-798. doi: 10.1109/JSEN.2009.2034730. Google Scholar
[31]	D. Nistér, O. Naroditsky and J. Bergen, Visual odometry, in Proceedings of the 2004 IEEE Computer Society Conference on Computer Vision and Pattern Recognition, 2004. CVPR 2004., vol. 1, Ieee, 2004, I–I. Google Scholar
[32]	D. O. Nitti, F. Bovenga, M. T. Chiaradia, M. Greco and G. Pinelli, Feasibility of using synthetic aperture radar to aid UAV navigation, Sensors, 15 (2015), 18334-18359. doi: 10.3390/s150818334. Google Scholar
[33]	H. Noh, A. Araujo, J. Sim, T. Weyand and B. Han, Large-scale image retrieval with attentive deep local features, in Proceedings of the IEEE International Conference on Computer Vision, 2017, 3456–3465. doi: 10.1109/ICCV.2017.374. Google Scholar
[34]	C. Oliver and S. Quegan, Understanding Synthetic Aperture Radar Images, SciTech Publishing, 2004. Google Scholar
[35]	S. Park, S. H. Jung and P. M. Pardalos, Combining stochastic adaptive cubic regularization with negative curvature for nonconvex optimization, Journal of Optimization Theory and Applications, 184 (2020), 953-971. doi: 10.1007/s10957-019-01624-6. Google Scholar
[36]	A. Paszke, S. Gross, F. Massa, A. Lerer, J. Bradbury, G. Chanan, T. Killeen, Z. Lin, N. Gimelshein, L. Antiga et al., Pytorch: An imperative style, high-performance deep learning library, in Advances in Neural Information Processing Systems, 2019, 8024–8035. Google Scholar
[37]	M. Shan, F. Wang, F. Lin, Z. Gao, Y. Z. Tang and B. M. Chen, Google map aided visual navigation for UAVs in GPS-denied environment, in 2015 IEEE International Conference on Robotics and Biomimetics (ROBIO), IEEE, 2015,114–119. doi: 10.1109/ROBIO.2015.7418753. Google Scholar
[38]	F. Shen, C. Shen, W. Liu and H. Tao Shen, Supervised discrete hashing, in Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, 2015, 37–45. doi: 10.1109/CVPR.2015.7298598. Google Scholar
[39]	D.-G. Sim, R.-H. Park, R.-C. Kim, S. U. Lee and I.-C. Kim, Integrated position estimation using aerial image sequences, IEEE Transactions on Pattern Analysis and Machine Intelligence, 24 (2002), 1-18. Google Scholar
[40]	K. Simonyan and A. Zisserman, Very deep convolutional networks for large-scale image recognition, arXiv preprint, arXiv: 1409.1556. Google Scholar
[41]	S. Suri, P. Schwind, P. Reinartz and J. Uhl, Combining mutual information and scale invariant feature transform for fast and robust multisensor SAR image registration, in 75th Annual ASPRS Conference, 2009. Google Scholar
[42]	G. Tolias, R. Sicre and H. Jégou, Particular object retrieval with integral max-pooling of CNN activations, arXiv preprint, arXiv: 1511.05879. Google Scholar
[43]	B. Wang, J. Zhang, L. Lu, G. Huang and Z. Zhao, A uniform SIFT-like algorithm for SAR image registration, IEEE Geoscience and Remote Sensing Letters, 12 (2015), 1426-1430. Google Scholar
[44]	B. Wessel, M. Huber and A. Roth, Registration of near real-time SAR images by image-to-image matching, in Proc. Photogramm. Image Anal., 2007,179. Google Scholar
[45]	P. Williams and M. Crump, All-source navigation for enhancing UAV operations in GPS-denied environments, in Proceedings of the 28th International Congress of the Aeronautical Sciences, 2012. Google Scholar
[46]	K. M. Yi, E. Trulls, V. Lepetit and P. Fua, LIFT: Learned invariant feature transform, in European Conference on Computer Vision, Springer, 2016 (2016), 467–483. doi: 10.1007/978-3-319-46466-4_28. Google Scholar
[47]	J. Yue-Hei Ng, F. Yang and L. S. Davis, Exploiting local features from deep networks for image retrieval, in Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition Workshops, 2015, 53–61. Google Scholar
[48]	S. Zhao, F. Lin, K. Peng, B. Chen and T. Lee, Homography-based vision-aided inertial navigation of UAVs in unknown environments, in AIAA Guidance, Navigation, and Control Conference, 2012, 5033. doi: 10.2514/6.2012-5033. Google Scholar
[49]	L. Zheng, Y. Yang and Q. Tian, SIFT meets CNN: A decade survey of instance retrieval, IEEE Transactions on Pattern Analysis and Machine Intelligence, 40 (2018), 1224-1244. doi: 10.1109/TPAMI.2017.2709749. Google Scholar
[50]	H. Zhu, M. Long, J. Wang and Y. Cao, Deep hashing network for efficient similarity retrieval, in Thirtieth AAAI Conference on Artificial Intelligence, 2016. Google Scholar
[51]	B. Zitova and J. Flusser, Image registration methods: A survey, Image and Vision Computing, 21 (2003), 977-1000. doi: 10.1016/S0262-8856(03)00137-9. Google Scholar

show all references

References:

[1]	Dataset: UAVSAR POLSAR, NASA 2020., Retrieved from ASF DAAC, 2020. Google Scholar
[2]	A. Babenko, A. Slesarev, A. Chigorin and V. Lempitsky, Neural codes for image retrieval, in European Conference on Computer Vision, Springer, 2014 (2014), 584–599. doi: 10.1007/978-3-319-10590-1_38. Google Scholar
[3]	G. Balamurugan, J. Valarmathi and V. Naidu, Survey on UAV navigation in GPS denied environments, in 2016 International Conference on Signal Processing, Communication, Power and Embedded System (SCOPES), IEEE, 2016,198–204. doi: 10.1109/SCOPES.2016.7955787. Google Scholar
[4]	J. Bhatti and T. E. Humphreys, Hostile control of ships via false GPS signals: Demonstration and detection, NAVIGATION: Journal of the Institute of Navigation, 64 (2017), 51-66. doi: 10.1002/navi.183. Google Scholar
[5]	F. Caballero, L. Merino, J. Ferruz and A. Ollero, Vision-based odometry and SLAM for medium and high altitude flying UAVs, Journal of Intelligent and Robotic Systems, 54 (2009), 137-161. doi: 10.1007/978-1-4020-9137-7_9. Google Scholar
[6]	Y. Cao, M. Long, J. Wang, H. Zhu and Q. Wen, Deep Quantization Network for Efficient Image Retrieval, in Thirtieth AAAI Conference on Artificial Intelligence, 2016. Google Scholar
[7]	A. Cesetti, E. Frontoni, A. Mancini, P. Zingaretti and S. Longhi, A vision-based guidance system for UAV navigation and safe landing using natural landmarks, Journal of Intelligent and Robotic Systems, 57 (2010), 233-257. doi: 10.1007/978-90-481-8764-5_12. Google Scholar
[8]	G. Conte and P. Doherty, Vision-based unmanned aerial vehicle navigation using geo-referenced information, EURASIP Journal on Advances in Signal Processing, 2009 (2009), Article number: 387308. doi: 10.1155/2009/387308. Google Scholar
[9]	N. Dalal and B. Triggs, Histograms of oriented gradients for human detection, in 2005 IEEE Computer Society Conference on Computer Vision and Pattern Recognition (CVPR'05), vol. 1, IEEE, 2005,886–893. doi: 10.1109/CVPR.2005.177. Google Scholar
[10]	F. Dellinger, J. Delon, Y. Gousseau, J. Michel and F. Tupin, SAR-SIFT: A SIFT-like algorithm for SAR images, IEEE Transactions on Geoscience and Remote Sensing, 53 (2015), 453-466. doi: 10.1109/TGRS.2014.2323552. Google Scholar
[11]	J. Deng, W. Dong, R. Socher, L.-J. Li, K. Li and L. Fei-Fei, Imagenet: A large-scale hierarchical image database, in 2009 IEEE Conference on Computer Vision and Pattern Recognition, Ieee, 2009,248–255. doi: 10.1109/CVPR.2009.5206848. Google Scholar
[12]	L. R. Dice, Measures of the amount of ecologic association between species, Ecology, 26 (1945), 297-302. doi: 10.2307/1932409. Google Scholar
[13]	J. Duchi, E. Hazan and Y. Singer, Adaptive subgradient methods for online learning and stochastic optimization, Journal of Machine Learning Research, 12 (2011), 2121-2159. Google Scholar
[14]	M. A. Fischler and R. C. Bolles, Random sample consensus: A paradigm for model fitting with applications to image analysis and automated cartography, Communications of the ACM, 24 (1981), 381-395. doi: 10.1145/358669.358692. Google Scholar
[15]	A. Gordo, J. Almazan, J. Revaud and D. Larlus, End-to-end learning of deep visual representations for image retrieval, International Journal of Computer Vision, 124 (2017), 237-254. doi: 10.1007/s11263-017-1016-8. Google Scholar
[16]	A. Grant, P. Williams, N. Ward and S. Basker, GPS jamming and the impact on maritime navigation, The Journal of Navigation, 62 (2009), 173-187. doi: 10.1017/S0373463308005213. Google Scholar
[17]	H. Jegou, M. Douze and C. Schmid, Product quantization for nearest neighbor search, IEEE Transactions on Pattern Analysis and Machine Intelligence, 33 (2011), 117-128. doi: 10.1109/TPAMI.2010.57. Google Scholar
[18]	M. Kaiser, N. Gans and W. Dixon, Vision-based estimation for guidance, navigation, and control of an aerial vehicle, IEEE Transactions on Aerospace and Electronic Systems, 46 (2010), 1064-1077. doi: 10.1109/TAES.2010.5545174. Google Scholar
[19]	W.-C. Kang, W.-J. Li and Z.-H. Zhou, Column Sampling Based Discrete Supervised Hashing, Thirtieth AAAI Conference on Artificial Intelligence, 2016. Google Scholar
[20]	D. P. Kingma and J. Ba, Adam: A method for stochastic optimization, arXiv preprint, arXiv: 1412.6980. Google Scholar
[21]	A. Krizhevsky, I. Sutskever and G. E. Hinton, Imagenet classification with deep convolutional neural networks, in Communications of the ACM, 60 (2017). doi: 10.1145/3065386. Google Scholar
[22]	P. Li and P. Ren, Partial randomness hashing for large-scale remote sensing image retrieval, IEEE Geoscience and Remote Sensing Letters, 14 (2017), 464-468. doi: 10.1109/LGRS.2017.2651056. Google Scholar
[23]	W.-J. Li, S. Wang and W.-C. Kang, Feature learning based deep supervised hashing with pairwise labels, arXiv preprint, arXiv: 1511.03855. Google Scholar
[24]	Y. Li, Y. Zhang, X. Huang, H. Zhu and J. Ma, Large-scale remote sensing image retrieval by deep hashing neural networks, IEEE Transactions on Geoscience and Remote Sensing, 56 (2017), 950-965. doi: 10.1109/TGRS.2017.2756911. Google Scholar
[25]	H. Liu, R. Wang, S. Shan and X. Chen, Deep supervised hashing for fast image retrieval, in Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, 2016, 2064–2072. doi: 10.1109/CVPR.2016.227. Google Scholar
[26]	J.-Z. Liu and X.-C. Yu, Research on SAR image matching technology based on SIFT, ISPRS08, B1. Google Scholar
[27]	D. G. Lowe, Object recognition from local scale-invariant features, in Proceedings of the Seventh IEEE International Conference on Computer Vision, vol. 2, Ieee, 1999, 1150–1157. doi: 10.1109/ICCV.1999.790410. Google Scholar
[28]	D. G. Lowe, Distinctive image features from scale-invariant keypoints, International Journal of Computer Vision, 60 (2004), 91-110. doi: 10.1023/B:VISI.0000029664.99615.94. Google Scholar
[29]	J. MacQueen et al., Some methods for classification and analysis of multivariate observations, in Proceedings of the Fifth Berkeley Symposium on Mathematical Statistics and Probability, vol. 1, Oakland, CA, USA, 1967,281–297. Google Scholar
[30]	A. Nemra and N. Aouf, Robust INS/GPS sensor fusion for UAV localization using SDRE nonlinear filtering, IEEE Sensors Journal, 10 (2010), 789-798. doi: 10.1109/JSEN.2009.2034730. Google Scholar
[31]	D. Nistér, O. Naroditsky and J. Bergen, Visual odometry, in Proceedings of the 2004 IEEE Computer Society Conference on Computer Vision and Pattern Recognition, 2004. CVPR 2004., vol. 1, Ieee, 2004, I–I. Google Scholar
[32]	D. O. Nitti, F. Bovenga, M. T. Chiaradia, M. Greco and G. Pinelli, Feasibility of using synthetic aperture radar to aid UAV navigation, Sensors, 15 (2015), 18334-18359. doi: 10.3390/s150818334. Google Scholar
[33]	H. Noh, A. Araujo, J. Sim, T. Weyand and B. Han, Large-scale image retrieval with attentive deep local features, in Proceedings of the IEEE International Conference on Computer Vision, 2017, 3456–3465. doi: 10.1109/ICCV.2017.374. Google Scholar
[34]	C. Oliver and S. Quegan, Understanding Synthetic Aperture Radar Images, SciTech Publishing, 2004. Google Scholar
[35]	S. Park, S. H. Jung and P. M. Pardalos, Combining stochastic adaptive cubic regularization with negative curvature for nonconvex optimization, Journal of Optimization Theory and Applications, 184 (2020), 953-971. doi: 10.1007/s10957-019-01624-6. Google Scholar
[36]	A. Paszke, S. Gross, F. Massa, A. Lerer, J. Bradbury, G. Chanan, T. Killeen, Z. Lin, N. Gimelshein, L. Antiga et al., Pytorch: An imperative style, high-performance deep learning library, in Advances in Neural Information Processing Systems, 2019, 8024–8035. Google Scholar
[37]	M. Shan, F. Wang, F. Lin, Z. Gao, Y. Z. Tang and B. M. Chen, Google map aided visual navigation for UAVs in GPS-denied environment, in 2015 IEEE International Conference on Robotics and Biomimetics (ROBIO), IEEE, 2015,114–119. doi: 10.1109/ROBIO.2015.7418753. Google Scholar
[38]	F. Shen, C. Shen, W. Liu and H. Tao Shen, Supervised discrete hashing, in Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, 2015, 37–45. doi: 10.1109/CVPR.2015.7298598. Google Scholar
[39]	D.-G. Sim, R.-H. Park, R.-C. Kim, S. U. Lee and I.-C. Kim, Integrated position estimation using aerial image sequences, IEEE Transactions on Pattern Analysis and Machine Intelligence, 24 (2002), 1-18. Google Scholar
[40]	K. Simonyan and A. Zisserman, Very deep convolutional networks for large-scale image recognition, arXiv preprint, arXiv: 1409.1556. Google Scholar
[41]	S. Suri, P. Schwind, P. Reinartz and J. Uhl, Combining mutual information and scale invariant feature transform for fast and robust multisensor SAR image registration, in 75th Annual ASPRS Conference, 2009. Google Scholar
[42]	G. Tolias, R. Sicre and H. Jégou, Particular object retrieval with integral max-pooling of CNN activations, arXiv preprint, arXiv: 1511.05879. Google Scholar
[43]	B. Wang, J. Zhang, L. Lu, G. Huang and Z. Zhao, A uniform SIFT-like algorithm for SAR image registration, IEEE Geoscience and Remote Sensing Letters, 12 (2015), 1426-1430. Google Scholar
[44]	B. Wessel, M. Huber and A. Roth, Registration of near real-time SAR images by image-to-image matching, in Proc. Photogramm. Image Anal., 2007,179. Google Scholar
[45]	P. Williams and M. Crump, All-source navigation for enhancing UAV operations in GPS-denied environments, in Proceedings of the 28th International Congress of the Aeronautical Sciences, 2012. Google Scholar
[46]	K. M. Yi, E. Trulls, V. Lepetit and P. Fua, LIFT: Learned invariant feature transform, in European Conference on Computer Vision, Springer, 2016 (2016), 467–483. doi: 10.1007/978-3-319-46466-4_28. Google Scholar
[47]	J. Yue-Hei Ng, F. Yang and L. S. Davis, Exploiting local features from deep networks for image retrieval, in Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition Workshops, 2015, 53–61. Google Scholar
[48]	S. Zhao, F. Lin, K. Peng, B. Chen and T. Lee, Homography-based vision-aided inertial navigation of UAVs in unknown environments, in AIAA Guidance, Navigation, and Control Conference, 2012, 5033. doi: 10.2514/6.2012-5033. Google Scholar
[49]	L. Zheng, Y. Yang and Q. Tian, SIFT meets CNN: A decade survey of instance retrieval, IEEE Transactions on Pattern Analysis and Machine Intelligence, 40 (2018), 1224-1244. doi: 10.1109/TPAMI.2017.2709749. Google Scholar
[50]	H. Zhu, M. Long, J. Wang and Y. Cao, Deep hashing network for efficient similarity retrieval, in Thirtieth AAAI Conference on Artificial Intelligence, 2016. Google Scholar
[51]	B. Zitova and J. Flusser, Image registration methods: A survey, Image and Vision Computing, 21 (2003), 977-1000. doi: 10.1016/S0262-8856(03)00137-9. Google Scholar

Figure 1. Overview of the system for SAR aided navigating by SAR image representation, matching and registration

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Figure 2. Example of a patch graph. (a) a SAR map from the UAVSAR dataset (b) patches extracted from the SAR map and its associated graph (c) visualization of the adjacency matrix. White cells show zero edge values whereas black cells show nonzero values

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Figure 3. Overview of Product Quantization (PQ) with DCSNN

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Figure 4. Comparison between keypoints generated by (a) SAR-SIFT and (b) SIFT

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Figure 5. (a) SAR-SIFT based keypoints on two adjacent SAR patches (b) image matching of the keypoints via RANSAC

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Figure 6. PolSAR data from UAVSAR dataset for our experiments. (From left) VVVV(R), HVHV(G), HHHH(B) channels, and total RGB image. Best viewed in color. (a) PolSAR map for Hayward Fault Zone in California, US. (b) PolSAR map for Yukon–Kuskokwim Delta in Alaska, US

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Figure 7. Precision recall curves on Hayward Fault Zone (Top rows) and Yukon–Kuskokwim Delta (Bottom rows) PolSAR maps. From left column, the feature length is $ 24 $, $ 48 $, $ 96 $, and $ 120 $. AlexNet is used as a backbone

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Figure 8. Examples of the retrieved SAR patches before and after reranking processes. First column represents examples of inquiry SAR patches. The first two rows ((a) and (b)) are from Hayward Fault Zone PolSAR and the later two rows ((c) and (d)) are from Yukon-Kuskokwim Delta PolSAR data. Having green box indicates it is correctly retrieved, whereas having red box indicates that it is incorrectly retrieved

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Table 1. Descriptions of the PolSAR map from UAVSAR [1]

Region (Dataset Name)	Usage	Acquired Date	Pixel Size (Height×Width)	#Patches
Hayward Fault Zone	Training	Oct 9, 2018	$23506\times3300$	6440
Hayward Fault Zone	Test	May 30, 2019	$23476\times3300$	6412
Yukon–Kuskokwim Delta	Training	Aug 28, 2018	$19066\times3300$	5180
Yukon–Kuskokwim Delta	Test	Sep 17, 2019	$19148\times3300$	5208

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Region (Dataset Name)	Usage	Acquired Date	Pixel Size (Height×Width)	#Patches
Hayward Fault Zone	Training	Oct 9, 2018	$23506\times3300$	6440
Hayward Fault Zone	Test	May 30, 2019	$23476\times3300$	6412
Yukon–Kuskokwim Delta	Training	Aug 28, 2018	$19066\times3300$	5180
Yukon–Kuskokwim Delta	Test	Sep 17, 2019	$19148\times3300$	5208

Table 2. Mean average precision (mAP) results of DCSNN and binary hashing methods before reranking on Hayward Fault Zone PolSAR map

Methods	Feature length $l$	AlexNet [21]	VGG-11 [40]
Pretrained (BH)	$l=24$	0.0478	0.0313
	$l=48$	0.0761	0.0522
	$l=96$	0.1547	0.1200
	$l=120$	0.1566	0.1219
Pretrained (PQ+AQD)	$l=24$	0.2332	0.1706
	$l=48$	0.3208	0.2055
	$l=96$	0.3231	0.2676
	$l=120$	0.3856	0.3161
DHN [50]	$l=24$	0.1182	0.1255
	$l=48$	0.1642	0.1693
	$l=96$	0.2274	0.2153
	$l=120$	0.3202	0.2449
DPSH [23]	$l=24$	0.0895	0.1220
	$l=48$	0.2825	0.2632
	$l=96$	0.4545	0.4005
	$l=120$	0.5213	0.4334
DHNN-L2 [24]	$l=24$	0.0451	0.1147
	$l=48$	0.0683	0.1291
	$l=96$	0.2044	0.1329
	$l=120$	0.2190	0.1304
DCSNN (ours)	$l=24$	0.2519	0.4889
	$l=48$	0.6145	0.6301
	$l=96$	0.6481	0.5783
	$l=120$	0.6813	0.5819

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Methods	Feature length $l$	AlexNet [21]	VGG-11 [40]
Pretrained (BH)	$l=24$	0.0478	0.0313
	$l=48$	0.0761	0.0522
	$l=96$	0.1547	0.1200
	$l=120$	0.1566	0.1219
Pretrained (PQ+AQD)	$l=24$	0.2332	0.1706
	$l=48$	0.3208	0.2055
	$l=96$	0.3231	0.2676
	$l=120$	0.3856	0.3161
DHN [50]	$l=24$	0.1182	0.1255
	$l=48$	0.1642	0.1693
	$l=96$	0.2274	0.2153
	$l=120$	0.3202	0.2449
DPSH [23]	$l=24$	0.0895	0.1220
	$l=48$	0.2825	0.2632
	$l=96$	0.4545	0.4005
	$l=120$	0.5213	0.4334
DHNN-L2 [24]	$l=24$	0.0451	0.1147
	$l=48$	0.0683	0.1291
	$l=96$	0.2044	0.1329
	$l=120$	0.2190	0.1304
DCSNN (ours)	$l=24$	0.2519	0.4889
	$l=48$	0.6145	0.6301
	$l=96$	0.6481	0.5783
	$l=120$	0.6813	0.5819

Table 3. mAP results of the DCSNN and binary hashing methods before reranking on Yukon–Kuskokwim Delta PolSAR map

Methods	Feature length $l$	AlexNet [21]	VGG-11 [40]
Pretrained (BH)	$l=24$	0.0566	0.0396
	$l=48$	0.1048	0.0550
	$l=96$	0.1927	0.1227
	$l=120$	0.2196	0.1174
Pretrained (PQ+AQD)	$l=24$	0.2684	0.1736
	$l=48$	0.3580	0.2091
	$l=96$	0.3718	0.2579
	$l=120$	0.4184	0.2690
DHN [50]	$l=24$	0.1219	0.1610
	$l=48$	0.2072	0.1910
	$l=96$	0.2715	0.2447
	$l=120$	0.3627	0.2239
DPSH [23]	$l=24$	0.1347	0.1170
	$l=48$	0.2371	0.2516
	$l=96$	0.3649	0.3281
	$l=120$	0.4098	0.3331
DHNN-L2 [24]	$l=24$	0.0621	0.1132
	$l=48$	0.1556	0.1812
	$l=96$	0.2916	0.3166
	$l=120$	0.3227	0.2822
DCSNN (ours)	$l=24$	0.4393	0.4324
	$l=48$	0.5424	0.5196
	$l=96$	0.5734	0.4913
	$l=120$	0.5996	0.4831

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Methods	Feature length $l$	AlexNet [21]	VGG-11 [40]
Pretrained (BH)	$l=24$	0.0566	0.0396
	$l=48$	0.1048	0.0550
	$l=96$	0.1927	0.1227
	$l=120$	0.2196	0.1174
Pretrained (PQ+AQD)	$l=24$	0.2684	0.1736
	$l=48$	0.3580	0.2091
	$l=96$	0.3718	0.2579
	$l=120$	0.4184	0.2690
DHN [50]	$l=24$	0.1219	0.1610
	$l=48$	0.2072	0.1910
	$l=96$	0.2715	0.2447
	$l=120$	0.3627	0.2239
DPSH [23]	$l=24$	0.1347	0.1170
	$l=48$	0.2371	0.2516
	$l=96$	0.3649	0.3281
	$l=120$	0.4098	0.3331
DHNN-L2 [24]	$l=24$	0.0621	0.1132
	$l=48$	0.1556	0.1812
	$l=96$	0.2916	0.3166
	$l=120$	0.3227	0.2822
DCSNN (ours)	$l=24$	0.4393	0.4324
	$l=48$	0.5424	0.5196
	$l=96$	0.5734	0.4913
	$l=120$	0.5996	0.4831

Table 4. mAP values before and after reranking with SAR-SIFT or SIFT on Hayward Fault Zone PolSAR map

CNN backbone	Feature length $l$	Before reranking	After reranking (SAR-SIFT/SIFT)
AlexNet [21]	$l=24$	0.2519	0.4074/0.3533
	$l=48$	0.6145	0.7394/0.6850
	$l=96$	0.6481	0.7548/0.6998
	$l=120$	0.6813	0.7760/0.7252
VGG-11 [40]	$l=24$	0.4889	0.6512/0.5813
	$l=48$	0.6301	0.7540/0.6923
	$l=96$	0.5783	0.6799/0.6231
	$l=120$	0.5819	0.6787/0.6216

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CNN backbone	Feature length $l$	Before reranking	After reranking (SAR-SIFT/SIFT)
AlexNet [21]	$l=24$	0.2519	0.4074/0.3533
	$l=48$	0.6145	0.7394/0.6850
	$l=96$	0.6481	0.7548/0.6998
	$l=120$	0.6813	0.7760/0.7252
VGG-11 [40]	$l=24$	0.4889	0.6512/0.5813
	$l=48$	0.6301	0.7540/0.6923
	$l=96$	0.5783	0.6799/0.6231
	$l=120$	0.5819	0.6787/0.6216

Table 5. mAP values of the DCSNN before and after reranking with SAR-SIFT or SIFT on Yukon–Kuskokwim Delta PolSAR map

CNN backbone	Feature length $l$	Before reranking	After reranking (SAR-SIFT/SIFT)
AlexNet [21]	$l=24$	0.4393	0.5831/0.5965
	$l=48$	0.5424	0.6591/0.6693
	$l=96$	0.5734	0.6782/0.6888
	$l=120$	0.5996	0.7021/0.7123
VGG-11 [40]	$l=24$	0.4324	0.5909/0.6030
	$l=48$	0.5196	0.6418/0.6521
	$l=96$	0.4913	0.5939/0.6036
	$l=120$	0.4831	0.5840/0.5940

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CNN backbone	Feature length $l$	Before reranking	After reranking (SAR-SIFT/SIFT)
AlexNet [21]	$l=24$	0.4393	0.5831/0.5965
	$l=48$	0.5424	0.6591/0.6693
	$l=96$	0.5734	0.6782/0.6888
	$l=120$	0.5996	0.7021/0.7123
VGG-11 [40]	$l=24$	0.4324	0.5909/0.6030
	$l=48$	0.5196	0.6418/0.6521
	$l=96$	0.4913	0.5939/0.6036
	$l=120$	0.4831	0.5840/0.5940

Table 6. Positioning accuracy examples

Inquiry SAR Patch	Actual Coordinates [$deg$]	Estimated Coordinates [$deg$]	Error [$m$]
Fig. 8(a)	38.0625, -122.2733	38.0625, -122.2734	5.7288
Fig. 8(b)	37.9836, -122.3599	37.9836, -122.3600	5.7347
Fig. 8(c)	61.0926, -164.1878	61.0926, -164.1879	4.2529
Fig. 8(d)	61.0808, -164.1208	61.0808, -164.1208	5.0970

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Inquiry SAR Patch	Actual Coordinates [$deg$]	Estimated Coordinates [$deg$]	Error [$m$]
Fig. 8(a)	38.0625, -122.2733	38.0625, -122.2734	5.7288
Fig. 8(b)	37.9836, -122.3599	37.9836, -122.3600	5.7347
Fig. 8(c)	61.0926, -164.1878	61.0926, -164.1879	4.2529
Fig. 8(d)	61.0808, -164.1208	61.0808, -164.1208	5.0970

Table 7. Mean and standard deviation of positioning error results

Data Name	Success Cases Ratio [%]	Distance Error [$m$]
Hayward Fault Zone	98.50	4.9635$\pm$0.1755
Yukon–Kuskokwim Delta	97.70	4.9522$\pm$0.4038

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Data Name	Success Cases Ratio [%]	Distance Error [$m$]
Hayward Fault Zone	98.50	4.9635$\pm$0.1755
Yukon–Kuskokwim Delta	97.70	4.9522$\pm$0.4038

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American Institute of Mathematical Sciences

Synthetic-Aperture Radar image based positioning in GPS-denied environments using Deep Cosine Similarity Neural Networks

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Synthetic-Aperture Radar image based positioning in GPS-denied environments using Deep Cosine Similarity Neural Networks

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