# Mapping Rice Cropping Systems in Vietnam Using an NDVI-Based Time-Series Similarity Measurement Based on DTW Distance

^{1}

^{2}

^{3}

^{4}

^{5}

^{*}

## Abstract

**:**

^{2}being as high as 0.809; however, the mapped rice accuracy decreased at the provincial scale due to the reduced number of rice planting areas per province. An analysis of the results indicates that the 500-m resolution MODIS data are limited in terms of mapping scattered rice parcels. The results demonstrate that the DTW-based similarity measure of the NDVI time series can be effectively used to map large-area rice cropping systems with diverse cultivation processes.

## 1. Introduction

**Figure 1.**Cloud coverage in images. Among the 46 MODIS images, the cloud coverage of 33 MODIS images exceeds 20%, and that of 16 images exceeds 40%. During the rainy season of Vietnam (May to November, namely, day 120 to day 304), the mean cloud coverage was 47%.

## 2. Study Area and Materials

#### 2.1. Brief Introduction to the Study Area

^{2}. Vietnam is long and narrow, with high elevations in the west and low elevations in the east. Vietnam experiences a tropical monsoon climate characterized by high temperatures and rainy seasons. The annual average temperature is approximately 24 °C, and the average annual rainfall ranges from 1500 mm to 2000 mm.

#### 2.2. MODIS NDVI Time-Series Data

#### 2.3. Digital Elevation Model (DEM) Data

#### 2.4. Ancillary Data

## 3. Data Preprocessing

**Figure 3.**Comparison between S-G algorithm filtering, Logistic algorithm filtering, and Gaussian algorithm filtering, where the black line denotes the original NDVI curves, which are sampled from a clear sky rice growth point; the red line denotes the S-G-algorithm-fitted NDVI curve with our manually generated gap NDVI curve; the Logistic fitted curve is denoted by the blue line; and the Gaussian-algorithm-fitted simulated gap NDVI is denoted by the green line.

_{i}, i = 1,…, N with a linear combination of nearby values in a window, as shown in Equation (2):

## 4. Methods

_{1}, NDVI

_{2},…, NDVI

_{n}>. Then, a sequence was identified as <NDVI

_{1}(x, y), NDVI

_{2}(x, y),…, NDVI

_{n}(x, y)>. Because the MOD09A1 annual period includes 46 images, n equals 46. We then calculated the DTW distance of the sequence with the standard rice growth NDVI time series of each region, and a DTW distance was calculated for each pixel with the standard rice growth NDVI time series, thereby determining the similarity of each pixel’s NDVI time series with the standard rice growth NDVI time series. Using this similarity measure, we distinguished the rice from other crops.

#### 4.1. Building Standard NDVI Time-Series Base

#### 4.2. Dynamic Time Warping Based on Time-Series Similarity Measurements

_{1},c

_{2},…,c

_{m}} and Q = {q

_{1},q

_{2},…,q

_{n}}, with respective lengths of m and n. We construct an m × n matrix A

_{m × n}and define the distance between each element as a

_{ij}= d(C

_{i},Q

_{j}) = $\sqrt{{\left({\mathrm{C}}_{\mathrm{i}}-{\mathrm{Q}}_{j}\right)}^{2}}$. In the matrix A

_{m × n}, a winding path is set by a group of adjacent matrix elements, and notes for W = {w

_{1}, w

_{2},..., w

_{k}} and the kth element in W are defined as w

_{k}= (a

_{ij})

_{k}; this path must satisfy the following conditions:

- Monotonicity constraint: w
_{k}= a_{ij}, w_{k+1}= a_{i’j’}, then i’ ≥ i and j’ ≥ j - Endpoint constraint: w
_{1}= a_{11}, w_{k}= a_{mn} - Continuity constraint: w
_{k}= a_{ij}, w_{k+1}= a_{i’j’}; then i’ ≤ i + 1 and j’ ≤ j + 1.

**Figure 4.**Example of DTW distance. The distance between each element of sequence C = {3, 2, 2, 1, 4, 3, 4} and sequence Q = {1, 4, 3, 2, 1, 4} is used to build a matrix, and the DTW uses a dynamic programming technique to find the minimal distance between two time series. The DTW distance is 2 + 1 + 0 + 0 + 0 + 0 + 0 + 1 + 0 = 4.

_{i}and q

_{j}denote the absolute value of the NDVI value in the NDVI time series. In Vietnam, the crop phenological stages are not fixed, and the planting dates depend on rainfall conditions. The planting date for irrigated rice exhibits greater variance, and geographical factors extend the variance of the length of each phenological stage. Thus, the absolute value between the NDVI time series of rice growth pixels may differ from the reference NDVI time series. As Figure 5 illustrates, suppose that NDVI1 is the reference NDVI time series and that NDVI2 is the NDVI time series of a pixel. Because the rice planting data for the pixels correspond to dates after those of the rice planting data of the reference NDVI time series, the phases are not aligned with the reference data; however, the DTW algorithm aligns the phases between these two NDVI time series by stretching or shrinking the time dimension. As a result, the DTW distance similarity measure allows for the identification of similar rice types despite dislocations of the NDVI time series because the DTW distance is small, and when applying a proper threshold to the DTW distance, they are the same type.

**Figure 5.**Illustration of DTW-corrected distances. The NDVI2 cycle’s planting date is later than that of the NDVI1 cycle.

## 5. Results

#### 5.1. Standard NDVI Time-Series Base and DTW Distance

Region | Time Series Shape | Time Series Shape | Time Series Shape |
---|---|---|---|

North East & Red River Delta | Irrigated Double Rice Cropping in North East region | Irrigated Double Rice Cropping in Red River Delta | |

North West | Rain-fed Single Rice Cropping | Irrigated Double Rice Cropping | |

North Central Coast | Irrigated Double Rice Cropping | Irrigated Single Rice Cropping I | Rain-fed Single Rice Cropping |

South Central Coast, Central Highlands & South East | Irrigated Double Rice Cropping | Irrigated Triple Rice Cropping | Rain-fed Single Rice Cropping |

Mekong River Delta | Irrigated Triple Rice Cropping I | Irrigated Double Rice Cropping I | Irrigated Single Rice Cropping |

Irrigated Double Rice Cropping II | Irrigated Triple Rice Cropping II | Irrigated Triple Rice Cropping III |

**Figure 6.**The results for the DTW distance: (

**a**) The DTW distance of single rice cropping in the Mekong River Delta; (

**b**) the DTW distance of double rice cropping I in the Mekong River Delta; (

**c**) the DTW distance of double rice cropping II in the Mekong River Delta; (

**d**) the DTW distance of triple rice cropping I in the Mekong River Delta; (

**e**) the DTW distance of triple rice cropping II in the Mekong River Delta; (

**f**) the DTW distance of triple rice cropping III in the Mekong River Delta.

#### 5.2. DTW Threshold and Rice Distribution Map

North East | North West | Red River Delta | North Central Coast | South Central Coast, Central Highlands & South East | Mekong River Delta | |
---|---|---|---|---|---|---|

Single rice | 3.8 | 3.7 | 3.4 | I. 3.3 II. 3.6 | 3.5 | 3.6 |

Double rice | 3.8 | 4 | 3.4 | 3.7 | 3.6 | I. 3.9 II. 3.4 |

Triple rice | 3.5 | 3.5 | I. 3.7 II. 3.5 III. 3.2 |

#### 5.3. Accuracy Assessment

^{2}value is 0.809, indicating that the two data points fit well. However, at the province scale, the results are not ideal. We separate the results into three components using the statistical data. The first component is rice-planted areas smaller than 500 km

^{2}in the statistical data, representing 21 provinces. The second component includes rice-planted areas from 500 km

^{2}to 1000 km

^{2}in the statistical data, representing 18 provinces, and the third component is the statistical rice-planted areas from 1000 km

^{2}to 7000 km

^{2}, representing 22 provinces. The comparison between the statistical data and the MODIS-derived rice areas for 21 provinces of the first component, where rice planting might be scattered or small, is shown in Figure 8b; the R

^{2}between the two datasets in this component is 0.086, which shows that they are significantly unrelated. The comparison between the statistical data and the MODIS-derived rice areas for 18 provinces of the second component is shown in Figure 8c; the R

^{2}of the comparison for this component is 0.226, which is greater than that in the first comparison; however, the result remains unsatisfactory. For the third component for 22 provinces where rice planting is relatively intensive, the comparison between the statistical data and the MODIS-derived rice areas is shown in Figure 8d, and the R

^{2}between the two datasets was 0.661.

Agriculture District/Province | Statistic Area | MODIS Extracted Area | Agriculture District/Province | Statistic Area | MODIS Extracted Area | ||||||
---|---|---|---|---|---|---|---|---|---|---|---|

Total Area | Total Area | Single Rice | Double Rice | Triple Rice | Total Area | Total Area | Single Rice | Double Rice | Triple Rice | ||

Red River Delta | 11,501 | 15,574 | 165 | 7704.5 | 0 | North East & North West | 6664 | 6241.8 | 1209.7 | 2516 | 0 |

North Central & South Central (Coastal) | 12,141 | 13,205.1 | 6539.8 | 2116.8 | 479.2 | South East | 1263 | 697.9 | 533.6 | 1.3 | 53.9 |

Central Highlands | 2178 | 3212.4 | 2982.3 | 101.7 | 8.9 | Mekong River Delta | 39,459 | 40,633.3 | 1315.5 | 8607.8 | 7367.4 |

**Figure 8.**Comparison between extraction results and the statistical data: (

**a**) comparison of statistical data and MODIS-derived rice areas for the 63 provinces in Vietnam; (

**b**) comparison of planted areas of less than 500 km

^{2}for a total of 22 provinces using statistical data with the MODIS-derived rice areas; (

**c**) comparison of statistical data of planted areas from 500 km

^{2}to 1000 km

^{2}for a total of 18 provinces and MODIS-derived rice areas; (

**d**) comparison of statistical data of planted areas from 1000 km

^{2}to 7000 km

^{2}for a total of 23 provinces and MODIS-derived rice areas.

**Table 4.**Accuracy assessment of the classified rice crops based on field survey points. We separated the provinces into three groups based on the number of rice field points. The first group comprises 23 provinces with less than two field samples, the second group comprises 20 provinces with between three and seven field samples, and the third group comprises 18 provinces with between eight and 28 field samples.

No. of Field Survey Points | No. of Correctly Classified Rice Points | No. of Rice Points | No. of Correctly Classified Non-Rice Points | No. of Non-Rice Points | Overall Accuracy (%) | Accuracy of Rice Classification (%) | Rice Field Omission Errors (%) | Rice Field Commission Errors (%) | |
---|---|---|---|---|---|---|---|---|---|

Entire area | 1200 | 191 | 365 | 708 | 835 | 74.9 | 52.3 | 47.7 | 34.8 |

First part | 324 | 4 | 26 | 274 | 298 | 85.8 | 15.4 | 84.6 | 92.3 |

Second part | 391 | 41 | 109 | 237 | 282 | 71.1 | 37.6 | 62.4 | 41.3 |

Third part | 485 | 146 | 230 | 197 | 255 | 70.7 | 63.5 | 36.5 | 25.2 |

**Figure 9.**Fractal rice field in the North East region, in which rice was planted nearby the river: (

**a**) the Landsat TM image for 5 April 2009, in the North East region. The grid in black is the corresponding extent of a pixel in MODIS pixel.; (

**b**) The Google Earth image obtained on 18 December 2013; (

**c**) the NDVI curve of three points in the rice area; (

**d**) the segmentation result based on multiresolution segmentation and the TM image.

**Figure 10.**Decreasing trends of extraction accuracy when the patches per MODIS pixel are increased, which denotes a greater heterogeneity of the land cover.

## 6. Conclusions

## Supplementary Files

Supplementary File 1## Acknowledgments

## Author Contributions

## Conflicts of Interest

## References

- Fairhurst, T.; Dobermann, A. Rice in the global food supply. World
**2002**, 502, 454, 349–511, 675. [Google Scholar] - Kuenzer, C.; Knauer, K. Remote sensing of rice crop areas. Int. J. Remote Sens.
**2013**, 34, 2101–2139. [Google Scholar] [CrossRef] - Ricepedia. The Online Authority on Rice: Rice Species. Available online: http://ricepedia.org/ (accessed on 15 March 2015).
- General Statistics Office of Vietnam. Statistical Yearbook of Vietnam. Available online: http://www.gso.gov.vn/ (accessed on 15 March 2015).
- Bouman, B.A.M. Crop modeling and remote-sensing for yield prediction. Neth. J. Agric. Sci.
**1995**, 43, 143–161. [Google Scholar] - Thiruvengadachari, S.; Sakhtivadivel, R. Satellite Remote Sensing for Assessment of Irrigation System Performance: A Case Study in India; IWMI Research Report: Colombo, CMB, Sri Lanka, 1997. [Google Scholar]
- Casanova, D.; Epema, G.F.; Goudriaan, J. Monitoring rice reflectance at field level for estimating biomass and lai. Field Crop. Res.
**1998**, 55, 83–92. [Google Scholar] [CrossRef] - Dawson, T.P.; Curran, P.J.; North, P.R.J.; Plummer, S.E. The propagation of foliar biochemical absorption features in forest canopy reflectance: A theoretical analysis. Remote Sens. Environ.
**1999**, 67, 147–159. [Google Scholar] [CrossRef] - Chang, K.W.; Shen, Y.; Lo, J.C. Predicting rice yield using canopy reflectance measured at booting stage. Agron. J.
**2005**, 97, 872–878. [Google Scholar] [CrossRef] - Hatfield, J.L.; Gitelson, A.A.; Schepers, J.S.; Walthall, C.L. Application of spectral remote sensing for agronomic decisions. Agron. J.
**2008**, 100, S117–S131. [Google Scholar] [CrossRef] - Shen, S.; Yang, S.; Li, B.; Tan, B.; Li, Z.; le Toan, T. A scheme for regional rice yield estimation using ENVISAT ASAR data. Sci. China Ser. D-Earth Sci.
**2009**, 52, 1183–1194. [Google Scholar] [CrossRef] - Fang, H.; Wu, B.; Liu, H.; Huang, X. Using NOAA AVHRR and Landsat TM to estimate rice area year-by-year. Int. J. Remote Sens.
**1998**, 19, 521–525. [Google Scholar] [CrossRef] - Liu, J.; Liu, M.; Tian, H.; Zhuang, D.; Zhang, Z.; Zhang, W.; Tang, X.; Deng, X. Spatial and temporal patterns of China’s cropland during 1990–2000: An analysis based on Landsat-TM data. Remote Sens. Environ.
**2005**, 98, 442–456. [Google Scholar] [CrossRef] - Turner, M.D.; Congalton, R.G. Classification of multi-temporal Spot-XS satellite data for mapping rice fields on a west African floodplain. Int. J. Remote Sens.
**1998**, 19, 21–41. [Google Scholar] [CrossRef] - Panigrahy, S.; Sharma, S.A. Mapping of crop rotation using multi-date Indian remote sensing satellite digital data. ISPRS J. Photogramm. Remote Sens.
**1997**, 52, 85–91. [Google Scholar] [CrossRef] - Quarmby, N.A.; Townshend, J.R.G.; Settle, J.J.; White, K.H.; Milnes, M.; Hindle, T.L.; Silleos, N. Linear mixture modelling applied to AVHRR data for crop area estimation. Int. J. Remote Sens.
**1992**, 13, 415–425. [Google Scholar] [CrossRef] - Li, Q.Z.; Zhang, H.X.; Du, X.; Wen, N.; Tao, Q.S. County-level rice area estimation in southern China using remote sensing data. J. Appl. Remote Sens.
**2014**, 8. [Google Scholar] [CrossRef] - Roberts, D.A. Large area mapping of land-cover change in Rondônia using multi-temporal spectral mixture analysis and decision tree classifiers. J. Geophys. Res.
**2002**, 107. [Google Scholar] [CrossRef] - Xiao, X.; Boles, S.; Liu, J.; Zhuang, D.; Frolking, S.; Li, C.; Salas, W.; Moore, B. Mapping paddy rice agriculture in southern China using multi-temporal MODIS images. Remote Sens. Environ.
**2005**, 95, 480–492. [Google Scholar] [CrossRef] - Xiao, X.M.; Boles, S.; Frolking, S.; Li, C.S.; Babu, J.Y.; Salas, W.; Moore, B. Mapping paddy rice agriculture in south and southeast Asia using multi-temporal MODIS images. Remote Sens. Environ.
**2006**, 100, 95–113. [Google Scholar] [CrossRef] - Xiao, X.; Boles, S.; Frolking, S.; Salas, W.; Moore, B.; Li, C.; He, L.; Zhao, R. Observation of flooding and rice transplanting of paddy rice fields at the site to landscape scales in China using vegetation sensor data. Int. J. Remote Sens.
**2002**, 23, 3009–3022. [Google Scholar] [CrossRef] - Gumma, M.K.; Thenkabail, P.S.; Maunahan, A.; Islam, S.; Nelson, A. Mapping seasonal rice cropland extent and area in the high cropping intensity environment of Bangladesh using MODIS 500 m data for the year 2010. ISPRS J. Photogramm. Remote Sens.
**2014**, 91, 98–113. [Google Scholar] [CrossRef] - Chen, C.F.; Son, N.T.; Chang, L.Y. Monitoring of rice cropping intensity in the upper Mekong delta, Vietnam using time-series MODIS data. Adv. Space Res.
**2012**, 49, 292–301. [Google Scholar] [CrossRef] - Kontgis, C.; Schneider, A.; Ozdogan, M. Mapping rice paddy extent and intensification in the Vietnamese Mekong river delta with dense time stacks of Landsat data. Remote Sens. Environ.
**2015**, 169, 255–269. [Google Scholar] [CrossRef] - Geerken, R.; Zaitchik, B.; Evans, J.P. Classifying rangeland vegetation type and coverage from NDVI time series using Fourier filtered cycle similarity. Int. J. Remote Sens.
**2005**, 26, 5535–5554. [Google Scholar] [CrossRef] - Keogh, E.J.; Pazzani, M.J. Derivative dynamic time warping. In Proceedings of the SIAM International Conference on Data Mining, Columbus, OH, USA, 21 June 2001; pp. 5–7.
- Keogh, E.; Ratanamahatana, C.A. Exact indexing of dynamic time warping. Knowl. Inf. Syst.
**2005**, 7, 358–386. [Google Scholar] [CrossRef] - Berndt, D.J.; Clifford, J. Using Dynamic Time Warping to Find Patterns in Time Series. In Proceedings of the KDD Workshop, Seattle, WA, USA, 12 August 1994; pp. 359–370.
- Chen, Y.-L.; Wu, S.-Y.; Wang, Y.-C. Discovering multi-label temporal patterns in sequence databases. Inf. Sci.
**2011**, 181, 398–418. [Google Scholar] [CrossRef] - Kim, S.-W.; Shin, M. Subsequence matching under time warping in time-series databases: Observation, optimization, and performance results. Comput. Syst. Sci. Eng.
**2008**, 23, 31–42. [Google Scholar] [CrossRef] - Rebai, I.; BenAyed, Y. Text-to-speech synthesis system with Arabic diacritic recognition system. Comput. Speech Lang.
**2015**, 34, 43–60. [Google Scholar] [CrossRef] - Dockstader, S.L.; Bergkessel, K.A.; Tekalp, A.M. Feature extraction for the analysis of gait and human motion. In Proceedings of the 16th International Conference on Pattern Recognition, Quebec, QC, Canada, 15 August 2002; pp. 5–8.
- Lee, A.J.T.; Chen, Y.-A.; Ip, W.-C. Mining frequent trajectory patterns in spatial-temporal databases. Inf. Sci.
**2009**, 179, 2218–2231. [Google Scholar] [CrossRef] - Niennattrakul, V.; Srisai, D.; Ratanamahatana, C.A. Shape-based template matching for time series data. Knowl. Based Syst.
**2012**, 26, 1–8. [Google Scholar] [CrossRef] - Petitjean, F.; Ketterlin, A.; Gançarski, P. A global averaging method for dynamic time warping, with applications to clustering. Pattern Recognit.
**2011**, 44, 678–693. [Google Scholar] [CrossRef] - Petitjean, F.; Inglada, J.; Gancarski, P. Satellite image time series analysis under time warping. IEEE Trans. Geosci. Remote Sens.
**2012**, 50, 3081–3095. [Google Scholar] [CrossRef] - Izakian, H.; Pedrycz, W.; Jamal, I. Fuzzy clustering of time series data using dynamic time warping distance. Eng. Appl. Artif. Intell.
**2015**, 39, 235–244. [Google Scholar] [CrossRef] - Jeong, Y.S.; Jayaraman, R. Support vector-based algorithms with weighted dynamic time warping kernel function for time series classification. Knowl. Based Syst.
**2015**, 75, 184–191. [Google Scholar] [CrossRef] - Maclean, J.L.; Dawe, D.C.; Hardy, B.; Hettel, G.P. Rice Almanac: Source Book for the Most Important Economic Activity on Earth, 2nd ed.; CABI Publishing: Wallingford, Oxon, UK, 2002; pp. 102–105. [Google Scholar]
- Toshihiro, S.; Cao, V. P.; Aikihiko, K.; Khang, D.N.; Masayuki, Y. Analysis of rapid expansion of inland aquaculture and triple rice-cropping areas in a coastal area of the Vietnamese Mekong Delta using MODIS time-series imagery. Landscape Urban Plan.
**2009**, 92, 34–46. [Google Scholar] - Son, N.-T.; Chen, C.-F.; Chen, C.-R.; Duc, H.-N.; Chang, L.-Y. A phenology-based classification of time-series MODIS data for rice crop monitoring in Mekong delta, Vietnam. Remote Sens.
**2013**, 6, 135–156. [Google Scholar] [CrossRef] - Greg, E. LAADS Web. Available online: http://ladsweb.nascom.nasa.gov/ (accessed on 25 December 2015).
- U.S. Department of the Interior; U.S. Geological Survey. MOD09A1|LP DAAC: NASA Land Data Products and Services. Available online: http://lpdaac.usgs.gov/dataset_discovery/modis/modis_products_table/mod09a1/ (accessed on 25 December 2015).
- Huete, A.; Didan, K.; Miura, T.; Rodriguez, E.P.; Gao, X.; Ferreira, L.G. Overview of the radiometric and biophysical performance of the MODIS vegetation indices. Remote Sens. Environ.
**2002**, 83, 195–213. [Google Scholar] [CrossRef] - Lhermitte, S.; Verbesselt, J.; Verstraeten, W.W.; Coppin, P. A comparison of time series similarity measures for classification and change detection of ecosystem dynamics. Remote Sens. Environ.
**2011**, 115, 3129–3152. [Google Scholar] [CrossRef] - CGIAR-CSI SRTM 90m DEM Digital Elevation Database. Available online: http://srtm.csi.cgiar.org/ (accessed on 25 December 2015).
- Statistical Documentation and Service Centre—General Statistics Office of Vietnam. Available online: http://www.gso.gov.vn/ (accessed on 25 December 2015).
- Leinenkugel, P.; Kuenzer, C.; Dech, S. Comparison and enhancement of MODIS cloud mask products for Southeast Asia. Int. J. Remote Sens.
**2013**, 34, 2730–2748. [Google Scholar] [CrossRef] - Viovy, N.; Arino, O.; Belward, A.S. The best index slope extraction (BISE)—A method for reducing noise in NDVI time-series. Int. J. Remote Sens.
**1992**, 13, 1585–1590. [Google Scholar] [CrossRef] - Ma, M.; Veroustraete, F. Reconstructing pathfinder AVHRR land NDVI time-series data for the northwest of China. Adv. Space Res.
**2006**, 37, 835–840. [Google Scholar] [CrossRef] - Gu, J.; Li, X.; Huang, C.; Okin, G.S. A simplified data assimilation method for reconstructing time-series MODIS NDVI data. Adv. Space Res.
**2009**, 44, 501–509. [Google Scholar] [CrossRef] - Huang, N.E.; Shen, Z.; Long, S.R.; Wu, M.C.; Shih, H.H.; Zheng, Q.; Yen, N.C.; Tung, C.C.; Liu, H.H. The Empirical Mode Decomposition and the Hilbert Spectrum for Nonlinear and Non-Stationary Time Series Analysis. In Proceedings of the Royal Society of London A: Mathematical, Physical and Engineering Sciences, London, UK, 8 March 1998; The Royal Society: London, UK, 1998; pp. 903–995. [Google Scholar]
- Sakamoto, T.; Yokozawa, M.; Toritani, H.; Shibayama, M.; Ishitsuka, N.; Ohno, H. A crop phenology detection method using time-series MODIS data. Remote Sens. Environ.
**2005**, 96, 366–374. [Google Scholar] [CrossRef] - Hird, J.N.; McDermid, G.J. Noise reduction of NDVI time series: An empirical comparison of selected techniques. Remote Sens. Environ.
**2009**, 113, 248–258. [Google Scholar] [CrossRef] - Jonsson, P.; Eklundh, L. Seasonality extraction by function fitting to time-series of satellite sensor data. IEEE Trans. Geosci. Remote Sens.
**2002**, 40, 1824–1832. [Google Scholar] [CrossRef] - Chen, J.; Jonsson, P.; Tamura, M.; Gu, Z.H.; Matsushita, B.; Eklundh, L. A simple method for reconstructing a high-quality NDVI time-series data set based on the Savitzky-Golay filter. Remote Sens. Environ.
**2004**, 91, 332–344. [Google Scholar] [CrossRef] - Jeong, Y.S.; Jeong, M.K.; Omitaomu, O.A. Weighted dynamic time warping for time series classification. Pattern Recognit.
**2011**, 44, 2231–2240. [Google Scholar] [CrossRef]

© 2016 by the authors; licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons by Attribution (CC-BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Guan, X.; Huang, C.; Liu, G.; Meng, X.; Liu, Q.
Mapping Rice Cropping Systems in Vietnam Using an NDVI-Based Time-Series Similarity Measurement Based on DTW Distance. *Remote Sens.* **2016**, *8*, 19.
https://doi.org/10.3390/rs8010019

**AMA Style**

Guan X, Huang C, Liu G, Meng X, Liu Q.
Mapping Rice Cropping Systems in Vietnam Using an NDVI-Based Time-Series Similarity Measurement Based on DTW Distance. *Remote Sensing*. 2016; 8(1):19.
https://doi.org/10.3390/rs8010019

**Chicago/Turabian Style**

Guan, Xudong, Chong Huang, Gaohuan Liu, Xuelian Meng, and Qingsheng Liu.
2016. "Mapping Rice Cropping Systems in Vietnam Using an NDVI-Based Time-Series Similarity Measurement Based on DTW Distance" *Remote Sensing* 8, no. 1: 19.
https://doi.org/10.3390/rs8010019