# Novel Unsupervised Classification of Collapsed Buildings Using Satellite Imagery, Hazard Scenarios and Fragility Functions

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## Abstract

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## 1. Introduction

## 2. The IHF Classification Method

#### 2.1. Fundamentals

#### 2.2. Discussion of the IHF Method

## 3. Application of the IHF Method to the 2011 Great East Japan Earthquake and Tsunami

#### 3.1. A Problem of Bi-Dimensional Dataset Features Using a Linear Threshold

#### 3.2. Generalization of the Discriminant Function

#### 3.3. Discussion of the Case Study

## 4. Conclusions and Prospects

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## References

- Maruyama, Y.; Yamazaki, F.; Matsuzaki, S.; Miura, H.; Estrada, M. Evaluation of Building Damage and Tsunami Inundation Based on Satellite Images and GIS Data Following the 2010 Chile Earthquake. Earthq. Spectra
**2012**, 28, S165–S178. [Google Scholar] [CrossRef] - Liu, W.; Yamazaki, F.; Gokon, H.; Koshimura, S. Extraction of Tsunami-Flooded Areas and Damaged Buildings in the 2011 Tohoku-Oki Earthquake from TerraSAR-X Intensity Images. Earthq. Spectra
**2013**, 29, S183–S200. [Google Scholar] [CrossRef] - Hashemi-Parast, S.O.; Yamazaki, F.; Liu, W. Monitoring and evaluation of the urban reconstruction process in Bam, Iran, after the 2003 M w 6.6 earthquake. Nat. Hazards
**2017**, 85, 197–213. [Google Scholar] [CrossRef] - Nakmuenwai, P.; Yamazaki, F.; Liu, W. Automated Extraction of Inundated Areas from Multi-Temporal Dual-Polarization RADARSAT-2 Images of the 2011 Central Thailand Flood. Remote Sens.
**2017**, 9, 78. [Google Scholar] [CrossRef] - Moya, L.; Yamazaki, F.; Liu, W.; Yamada, M. Detection of collapsed buildings due to the 2016 Kumamoto, Japan, earthquake from Lidar data. Nat. Hazards Earth Syst. Sci. Discuss.
**2017**, 2017, 1–20. [Google Scholar] [CrossRef] - Dong, L.; Shan, J. A comprehensive review of earthquake-induced building damage detection with remote sensing techniques. ISPRS J. Photogramm. Remote Sens.
**2013**, 84, 85–99. [Google Scholar] [CrossRef] - Balz, T.; Liao, M. Building-damage detection using post-seismic high-resolution SAR satellite data. Int. J. Remote Sens.
**2010**, 31, 3369–3391. [Google Scholar] [CrossRef] - Chen, Q.; Li, L.; Jiang, P.; Liu, X. Building collapse extraction using modified freeman decomposition from post-disaster polarimetric SAR image. In Proceedings of the 2016 IEEE International Geoscience and Remote Sensing Symposium (IGARSS), Beijing, China, 10–15 July 2016; pp. 5769–5772. [Google Scholar]
- Dong, H.; Xu, X.; Gui, R.; Song, C.; Sui, H. Metric learning based collapsed building extraction from post-earthquake PolSAR imagery. In Proceedings of the 2016 IEEE International Geoscience and Remote Sensing Symposium (IGARSS), Beijing, China, 10–15 July 2016; pp. 4742–4745. [Google Scholar]
- Bai, Y.; Adriano, B.; Mas, E.; Gokon, H.; Koshimura, S. Object-based Building Damage Assessment Methodology Using Only Post Event ALOS-2/PALSAR-2 Dual Polarimetric SAR Intensity Images. J. Disaster Res.
**2017**, 12, 259–271. [Google Scholar] [CrossRef] - Gokon, H.; Koshimura, S.; Matsuoka, M. Object-Based Method for Estimating Tsunami-Induced Damage Using TerraSAR-X Data. J. Disaster Res.
**2016**, 11, 225–235. [Google Scholar] [CrossRef] - Matsuoka, M.; Nojima, N. Building Damage Estimation by Integration of Seismic Intensity Information and Satellite L-band SAR Imagery. Remote Sens.
**2010**, 2, 2111–2126. [Google Scholar] [CrossRef] - Karimzadeh, S.; Mastuoka, M. Building Damage Assessment Using Multisensor Dual-Polarized Synthetic Aperture Radar Data for the 2016 M 6.2 Amatrice Earthquake, Italy. Remote Sens.
**2017**, 9, 330. [Google Scholar] [CrossRef] - Gokon, H.; Koshimura, S.; Meguro, K. Verification of a Method for Estimating Building Damage in Extensive Tsunami Affected Areas Using L-Band SAR Data. J. Disaster Res.
**2017**, 12, 251–258. [Google Scholar] [CrossRef] - Liu, W.; Yamazaki, F. Extraction of collapsed buildings in the 2016 Kumamoto earthquake using multi-temporal PALSAR-2 data. J. Disaster Res.
**2017**, 12, 241–250. [Google Scholar] [CrossRef] - Wieland, M.; Liu, W.; Yamazaki, F. Learning Change from Synthetic Aperture Radar Images: Performance Evaluation of a Support Vector Machine to Detect Earthquake and Tsunami-Induced Changes. Remote Sens.
**2016**, 8, 792. [Google Scholar] [CrossRef] - Gokon, H.; Post, J.; Stein, E.; Martinis, S.; Twele, A.; Mück, M.; Geiß, C.; Koshimura, S.; Matsuoka, M. A Method for Detecting Buildings Destroyed by the 2011 Tohoku Earthquake and Tsunami Using Multitemporal TerraSAR-X Data. IEEE Geosci. Remote Sens. Lett.
**2015**, 12, 1277–1281. [Google Scholar] [CrossRef] - Jia, L.; Li, M.; Wu, Y.; Zhang, P.; Chen, H.; An, L. Semisupervised SAR Image Change Detection Using a Cluster-Neighborhood Kernel. IEEE Geosci. Remote Sens. Lett.
**2014**, 11, 1443–1447. [Google Scholar] [CrossRef] - Frank, J.; Rebbapragada, U.; Bialas, J.; Oommen, T.; Havens, T.C. Effect of Label Noise on the Machine-Learned Classification of Earthquake Damage. Remote Sens.
**2017**, 9, 803. [Google Scholar] [CrossRef] - Janalipour, M.; Mohammadzadeh, A. A Fuzzy-GA Based Decision Making System for Detecting Damaged Buildings from High-Spatial Resolution Optical Images. Remote Sens.
**2017**, 9, 349. [Google Scholar] [CrossRef] - Bai, Y.; Adriano, B.; Mas, E.; Koshimura, S. Machine Learning Based Building Damage Mapping from ALOS-2/PALSAR-2 SAR Imagery: Case Study of 2016 Kumamoto Earthquake. J. Disaster Res.
**2017**, 12, 646–655. [Google Scholar] [CrossRef] - Bai, Y.; Gao, C.; Singh, S.; Koch, M.; Adriano, B.; Mas, E.; Koshimura, S. A Framework of Rapid Regional Tsunami Damage Recognition from Post-event TerraSAR-X Imagery Using Deep Neural Networks. IEEE Geosci. Remote Sens. Lett.
**2018**, 15, 43–47. [Google Scholar] [CrossRef] - Ohta, Y.; Murakami, H.; Watoh, Y.; Koyama, M. A Model for Evaluating Life Span Characteristics of Entrapped Occupants by an Earthquake. In Proceedings of the 13th World Conference on Earthquake Engineering, Vancouver, BC, Canada, 1–6 August 2004; p. 9. [Google Scholar]
- Yamazaki, F.; Murao, O. Vulnerability Functions for Japanese Buildings Based on Damage Data from the 1995 Kobe Earthquake. In Implications of Recent Earthquakes on Seismic Risk; Imperial College Press: London, UK, 2000; Volume 2, pp. 91–102. [Google Scholar]
- Porter, K.; Kennedy, R.; Bachman, R. Creating Fragility Functions for Performance-Based Earthquake Engineering. Earthq. Spectra
**2007**, 23, 471–489. [Google Scholar] [CrossRef] - Koshimura, S.; Oie, T.; Yanagisawa, H.; Imamura, F. Developing Fragility Functions For Tsunami Damage Estimation Using Numerical Model And Post-Tsunami Data From Banda Aceh, Indonesia. Coast. Eng. J.
**2009**, 51, 243–273. [Google Scholar] [CrossRef] - Mas, E.; Koshimura, S.; Suppasri, A.; Matsuoka, M.; Matsuyama, M.; Yoshii, T.; Jimenez, C.; Yamazaki, F.; Imamura, F. Developing Tsunami fragility curves using remote sensing and survey data of the 2010 Chilean Tsunami in Dichato. Nat. Hazards Earth Syst. Sci.
**2012**, 12, 2689–2697. [Google Scholar] [CrossRef] - Suppasri, A.; Mas, E.; Charvet, I.; Gunasekera, R.; Imai, K.; Fukutani, Y.; Abe, Y.; Imamura, F. Building damage characteristics based on surveyed data and fragility curves of the 2011 Great East Japan tsunami. Nat. Hazards
**2013**, 66, 319–341. [Google Scholar] [CrossRef] - Cornell, C.A. Engineering seismic risk analysis. Bull. Seismol. Soc. Am.
**1968**, 58, 1583–1606. [Google Scholar] - McGuire, R. Seismic Hazard and Risk Analysis; Engineering Monographs on Miscellaneous Earthquake Engineering Topics; Earthquake Engineering Research Institute: Oakland, CA, USA, 2004. [Google Scholar]
- Martinelli, A.; Cifani, G.; Cialone, G.; Corazza, L.; Petracca, A.; Petrucci, G. Building vulnerability assessment and damage scenarios in Celano (Italy) using a quick survey data-based methodology. Soil Dyn. Earthq. Eng.
**2008**, 28, 875–889. [Google Scholar] [CrossRef] - Zülfikar, A.C.; Fercan, N.Ö.Z.; Tunç, S.; Erdik, M. Real-time earthquake shake, damage, and loss mapping for Istanbul metropolitan area. Earth Planets Space
**2017**, 69, 9. [Google Scholar] [CrossRef] - Karimzadeh, S.; Feizizadeh, B.; Matsuoka, M. From a GIS-based hybrid site condition map to an earthquake damage assessment in Iran: Methods and trends. Int. J. Disaster Risk Reduct.
**2017**, 22, 23–36. [Google Scholar] [CrossRef] - Frolova, N.I.; Larionov, V.I.; Bonnin, J.; Sushchev, S.P.; Ugarov, A.N.; Kozlov, M.A. Seismic risk assessment and mapping at different levels. Nat. Hazards
**2017**, 88, 43–62. [Google Scholar] [CrossRef] - Moya, L.; Mas, E.; Koshimura, S. Evaluation of tsunami fragility curves for building damage level allocation. Res. Rep. Tsunami Eng.
**2017**, 34, 33–41. [Google Scholar] - Shabestari, K.T.; Yamazaki, F. Near-fault spatial variation in strong ground motion due to rupture directivity and hanging wall effects from the Chi-Chi, Taiwan earthquake. Earthq. Eng. Struct. Dyn.
**2003**, 32, 2197–2219. [Google Scholar] [CrossRef] - Kato, T.; Terada, Y.; Nishimura, H.; Nagai, T.; Koshimura, S. Tsunami records due to the 2010 Chile Earthquake observed by GPS buoys established along the Pacific coast of Japan. Earth Planets Space
**2011**, 63, e5–e8. [Google Scholar] [CrossRef] - Ozawa, S.; Nishimura, T.; Suito, H.; Kobayashi, T.; Tobita, M.; Imakiire, T. Coseismic and postseismic slip of the 2011 magnitude-9 Tohoku-Oki earthquake. Nature
**2011**, 471, 373–376. [Google Scholar] [CrossRef] [PubMed] - Matsuoka, M.; Yamamoto, N. Web-based Quick Estimation System of Strong Ground Motion Maps Using Engineering Geomorphologic Classification Map and Observed Seismic Records. In Proceedings of the 15th World Conference on Earthquake Engineering, Lisbon, Portugal, 24–28 September 2012; p. 10. [Google Scholar]
- Irikura, K.; Miyakoshi, K.; Kamae, K.; Yoshida, K.; Somei, K.; Kurahashi, S.; Miyake, H. Applicability of source scaling relations for crustal earthquakes to estimation of the ground motions of the 2016 Kumamoto earthquake. Earth Planets Space
**2017**, 69, 10. [Google Scholar] [CrossRef] - Moya, L.; Mas, E.; Adriano, B.; Koshimura, S.; Yamazaki, F.; Liu, W. An Integrated Method to Extract Collapsed Buildings from Satellite Imagery, Hazard Distribution and Fragility Curves. Int. J. Disaster Risk Reduct.
**2018**. submitted. [Google Scholar] - Alpaydin, E. Introduction to Machine Learning, 3rd ed.; The MIT Press: Cambridge, MA, USA, 2014; Chapter 10. [Google Scholar]
- Bishop, C.M. Pattern Recognition and Machine Learning (Information Science and Statistics); Springer-Verlag New York, Inc.: Secaucus, NJ, USA, 2006. [Google Scholar]
- Ministry of Land, Infrastructure, Transport and Tourism (MLIT). Results of the Survey on Disaster Caused by the Great East Japan Earthquake (First Report). Available online: http://www.mlit.go.jp/report/press/city07_hh_000053.html (accessed on 22 December 2017).
- Murao, O.; Nakazato, H. Vulnerability functions for buildings based on damage survey data in Sri Lanka after the 2004 Indian Ocean Tsunami. In Proceedings of the International Conference on Sustainable Built Environment (ICSBE-2010), Kandy, Sri Lanka, 13–14 December 2010; pp. 371–378. [Google Scholar]
- Suppasri, A.; Koshimura, S.; Imamura, F. Developing tsunami fragility curves based on the satellite remote sensing and the numerical modeling of the 2004 Indian Ocean tsunami in Thailand. Nat. Hazards Earth Syst. Sci.
**2011**, 11, 173–189. [Google Scholar] [CrossRef] - Reese, S.; Bradley, B.A.; Bind, J.; Smart, G.; Power, W.; Sturman, J. Empirical building fragilities from observed damage in the 2009 South Pacific tsunami. Earth-Sci. Rev.
**2011**, 107, 156–173. [Google Scholar] [CrossRef] - Gokon, H.; Koshimura, S.; Imai, K.; Matsuoka, M.; Namegaya, Y.; Nishimura, Y. Developing fragility functions for the areas affected by the 2009 Samoa earthquake and tsunami. Nat. Hazards Earth Syst. Sci.
**2014**, 14, 3231–3241. [Google Scholar] [CrossRef] - Villar-Vega, M.; Silva, V.; Crowley, H.; Yepes, C.; Tarque, N.; Acevedo, A.B.; Hube, M.A.; Gustavo, C.D.; María, H.S. Development of a Fragility Model for the Residential Building Stock in South America. Earthq. Spectra
**2017**, 33, 581–604. [Google Scholar] [CrossRef] - Fawcett, T. An introduction to ROC analysis. Pattern Recognit. Lett.
**2006**, 27, 861–874. [Google Scholar] [CrossRef] - Python Software Foundation. Python Language Reference, Version 2.7. Available online: https://www.python.org/ (accessed on 22 December 2017).
- Oliphant, T.E. Guide to NumPy, 2nd ed.; CreateSpace Independent Publishing Platform: Austin, TX, USA, 2015. [Google Scholar]

**Figure 1.**The functions $g\left({h}_{\mathit{\theta}}\left(\mathit{x}\right)\right)=-\mathrm{ln}\left({h}_{\mathit{\theta}}\left(\mathit{x}\right)\right)$ and $g\left({h}_{\mathit{\theta}}\left(\mathit{x}\right)\right)=-\mathrm{ln}(1-{h}_{\mathit{\theta}}\left(\mathit{x}\right))$ that contribute to the elements of the summation in Equation (5).

**Figure 2.**Study area. (

**a**) Location of the coastal area of Miyagi Prefecture (red rectangle) within the Tohoku region of Japan; (

**b**) RGB color composite of the TerraSAR-X images acquired on 13 March 2011 (red) and 21 October 2010 (green and blue); (

**c**) Inundation depth map of the Great East Japan Earthquake and Tsunami. The inundation values are given in units of meters.

**Figure 3.**(

**a**) Scatter plot of the bi-dimensional dataset composed of r and d values. The colored marks denote the densities at the corresponding points; (

**b**) Empirical fragility functions of buildings that collapse due to a tsunami event as proposed by Koshimura et al. [26] (solid line) and by Suppasri et al. [28] (dashed line).

**Figure 4.**Discriminant functions obtained using the fragility function of Koshimura et al. [26]. (

**a**–

**g**) Scatter plots of the bi-dimensional dataset separated by damage state (DS), together with the obtained discriminant functions; (

**h**) Variations of the cost function ($J\left(\mathit{\theta}\right)$) throughout the iterative gradient descent algorithm.

**Figure 5.**Discriminant functions obtained using the fragility function of Suppasri et al. [28]. (

**a**–

**g**) Scatter plots of the bi-dimensional dataset separated by DS, together with the obtained discriminant functions; (

**h**) Variations of the cost function ($J\left(\mathit{\theta}\right)$) throughout the iterative gradient descent algorithm.

**Figure 7.**Parallel coordinate plot of seven normalized features. Red and blue marks denote samples classified as collapsed and non-collapsed buildings, respectively. The black ticks delimit the range of $[average-std,average+std]$ for each normalized feature.

**Table 1.**Accuracy evaluation of the classification results for collapsed and non-collapsed buildings obtained using a linear discriminant function based on the fragility function of Koshimura et al. [26]. NC: non-collapsed; C: collapsed; DS: damage state; PA: producer accuracy; UA: user accuracy.

DS0 | DS1 | DS2 | DS3 | DS4 | DS5 | DS0–DS5 | DS6 | Total | UA | |
---|---|---|---|---|---|---|---|---|---|---|

NC | 1668 | 2190 | 5655 | 4816 | 1179 | 2018 | 17,526 | 664 | 18,190 | 96.3 |

C | 189 | 388 | 994 | 1204 | 516 | 1614 | 4905 | 8140 | 13,045 | 62.4 |

Total | 1857 | 2578 | 6649 | 6020 | 1695 | 3632 | 22,431 | 8804 | 31,235 | |

PA | 89.8 | 84.9 | 85.1 | 80.0 | 69.6 | 55.6 | 78.1 | 92.5 | 82.2 |

**Table 2.**Accuracy evaluation of the classification results for collapsed and non-collapsed buildings obtained using a linear discriminant function based on the fragility function of Suppasri et al. [28].

DS0 | DS1 | DS2 | DS3 | DS4 | DS5 | DS0–DS5 | DS6 | Total | UA | |
---|---|---|---|---|---|---|---|---|---|---|

NC | 1793 | 2448 | 6264 | 5551 | 1475 | 2844 | 20,375 | 1861 | 22,236 | 91.6 |

C | 64 | 130 | 385 | 469 | 220 | 788 | 2056 | 6943 | 8999 | 77.2 |

Total | 1857 | 2578 | 6649 | 6020 | 1695 | 3632 | 22,431 | 8804 | 31,235 | |

PA | 96.6 | 95.0 | 94.2 | 92.2 | 87.0 | 78.3 | 90.8 | 78.9 | 87.5 |

**Table 3.**Accuracy evaluation of the classification results for collapsed and non-collapsed buildings obtained using a non-linear discriminant function based on the fragility function of Koshimura et al. [26].

DS0 | DS1 | DS2 | DS3 | DS4 | DS5 | DS0–DS5 | DS6 | Total | UA | |
---|---|---|---|---|---|---|---|---|---|---|

NC | 1649 | 2158 | 5534 | 4719 | 1153 | 1926 | 17,139 | 615 | 17,754 | 96.5 |

C | 208 | 420 | 1115 | 1301 | 542 | 1706 | 5292 | 8189 | 13,481 | 60.7 |

Total | 1857 | 2578 | 6649 | 6020 | 1695 | 3632 | 22,431 | 8804 | 31,235 | |

PA | 88.8 | 83.7 | 83.2 | 78.4 | 68.0 | 53.0 | 76.4 | 93.0 | 81.1 |

**Table 4.**Accuracy evaluation of the classification results for collapsed and non-collapsed buildings obtained using a non-linear discriminant function based on the fragility function of Suppasri et al. [28].

DS0 | DS1 | DS2 | DS3 | DS4 | DS5 | DS0–DS5 | DS6 | Total | UA | |
---|---|---|---|---|---|---|---|---|---|---|

NC | 1788 | 2419 | 6205 | 5492 | 1444 | 2738 | 20,086 | 1612 | 21,698 | 92.6 |

C | 69 | 159 | 444 | 528 | 251 | 894 | 2345 | 7192 | 9537 | 75.4 |

Total | 1857 | 2578 | 6649 | 6020 | 1695 | 3632 | 22,431 | 8804 | 31,235 | |

PA | 96.3 | 93.8 | 93.3 | 91.2 | 85.2 | 75.4 | 89.5 | 81.7 | 87.3 |

**Table 5.**Accuracy evaluation of the classification results for collapsed and non-collapsed buildings obtained from a 7-dimensional dataset using a non-linear discriminant function based on the fragility function of Suppasri et al. [28].

DS0 | DS1 | DS2 | DS3 | DS4 | DS5 | DS0–DS5 | DS6 | Total | UA | |
---|---|---|---|---|---|---|---|---|---|---|

NC | 1811 | 2484 | 6360 | 5634 | 1484 | 2882 | 20,655 | 2207 | 22,862 | 90.3 |

C | 46 | 94 | 289 | 386 | 211 | 750 | 1776 | 6597 | 8373 | 78.8 |

Total | 1857 | 2578 | 6649 | 6020 | 1695 | 3632 | 22,431 | 8804 | 31,235 | |

PA | 97.5 | 96.4 | 95.7 | 93.6 | 87.6 | 79.4 | 92.1 | 74.9 | 87.2 |

**Table 6.**Performance comparison between the IHF method and that of Wieland et al. [16]. IHF, imagery, hazard and fragility.

Class | Wieland et al. | IHF Method | |||||||
---|---|---|---|---|---|---|---|---|---|

Koshimura et al. | Suppasri et al. | ||||||||

UA | PA | F1 | UA | PA | F1 | UA | PA | F1 | |

C | 0.75 | 0.77 | 0.76 | 0.62 | 0.92 | 0.75 | 0.77 | 0.79 | 0.78 |

NC | 0.76 | 0.74 | 0.75 | 0.96 | 0.78 | 0.86 | 0.92 | 0.91 | 0.91 |

Total | 0.76 | 0.76 | 0.76 | 0.79 | 0.85 | 0.80 | 0.84 | 0.85 | 0.85 |

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## Share and Cite

**MDPI and ACS Style**

Moya, L.; Marval Perez, L.R.; Mas, E.; Adriano, B.; Koshimura, S.; Yamazaki, F.
Novel Unsupervised Classification of Collapsed Buildings Using Satellite Imagery, Hazard Scenarios and Fragility Functions. *Remote Sens.* **2018**, *10*, 296.
https://doi.org/10.3390/rs10020296

**AMA Style**

Moya L, Marval Perez LR, Mas E, Adriano B, Koshimura S, Yamazaki F.
Novel Unsupervised Classification of Collapsed Buildings Using Satellite Imagery, Hazard Scenarios and Fragility Functions. *Remote Sensing*. 2018; 10(2):296.
https://doi.org/10.3390/rs10020296

**Chicago/Turabian Style**

Moya, Luis, Luis R. Marval Perez, Erick Mas, Bruno Adriano, Shunichi Koshimura, and Fumio Yamazaki.
2018. "Novel Unsupervised Classification of Collapsed Buildings Using Satellite Imagery, Hazard Scenarios and Fragility Functions" *Remote Sensing* 10, no. 2: 296.
https://doi.org/10.3390/rs10020296