# Object-Based Time-Constrained Dynamic Time Warping Classification of Crops Using Sentinel-2
## 4 Discussion  
Our study reported on the first operational implementation of DTW as a ready-to-use workflow in an OBIA environment focused on crop mapping applications that yielded high overall accuracies. We compared single-band DTW (using NDVI time series) with multi-band DTW (using NDVI, GNDVI, NDRE, SAVI, and NDWI) and found that multi-band significantly increase the overall accuracy for California, while slightly decreasing it for Texas. Furthermore, we evaluated the impact of time constraints in DTW over the final classification accuracy and had best results using time delays of 30 and 45 days. Poorest results were obtained by Euclidean distance or DTW without time constraints. As reported in Belgiu and Csillik Belgiu and Csillik (2018), an object-based DTW has the advantage of generating vector digital spatial data that can be further used in agricultural monitoring activities. Therefore, it can successfully support (if not replace) labor-intensive and error-prone manual digitization of crop fields from satellite imagery. Furthermore, the object-based DTW reported here reduced the computational time required by DTW to classify target classes from SITS, since it uses objects rather than pixels as input spatial analysis units. As a comparison, [PERSON] and Csillik Belgiu and Csillik (2018) analyzed a similar region in size as TA1 but with fewer images (21) using a pixel-based approach with \(dtwSat\) package Belgiu and Csillik (2018) in R and the execution time was 30 hours without the segmentation step. \begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline  & \multicolumn{2}{c}{**CropScape**} & \multicolumn{4}{c}{**Single-band DTW30**} & \multicolumn{4}{c}{**Multi-band DTW30**} \\ \hline
**Crop** & **UA\({}^{*}\)** & **PA\({}^{*}\)** & **UA** & **UA+** & **PA** & **PA+** & **UA** & **UA+** & **PA** & **PA+** \\ \hline Wheat & 27.6 & 31.9 & 43.5 & **51.5** & 18.7 & **37.0** & 18.0 & **33.0** & 14.6 & **35.1** \\ Alfalfa & 12.5 & 8.4 & 1.8 & **12.6** & 22.3 & **23.8** & 1.2 & **12.6** & 14.6 & **16.8** \\ Other hay & 34.5 & 46.4 & 34.1 & **48.5** & 21.6 & **51.2** & 25.6 & **43.0** & 25.0 & **52.7** \\ Sugarbeets & 14.0 & 53.3 & 30.4 & **33.5** & 8.6 & **54.0** & 22.7 & **26.7** & 2.9 & **53.4** \\ Onions & 28.6 & 21.4 & 11.6 & **30.9** & 14.3 & **25.7** & 8.2 & **29.8** & 9.2 & **23.3** \\ Sod & 34.7 & 52.8 & 17.6 & **38.9** & 48.8 & **71.9** & 22.1 & **41.1** & 35.4 & **63.6** \\ Fallow & 19.5 & 19.2 & 13.6 & **23.8** & 0 & **19.2** & 7.3 & **20.8** & 0 & **19.2** \\ Vegetables & 79.9 & 54.9 & 66.2 & **103.8** & 2.2 & **54.9** & 60.9 & **100.5** & 2.2 & **54.9** \\ Water & 7 & 7.8 & 0 & **7.0** & 36.7 & **37.5** & 0 & **7.0** & 13.3 & **15.4** \\ \hline \hline \end{tabular}
\end{table} 
Table 8: Errors for UAs and PAs for single-band DTW30 and multi-band DTW30 for California, compared with those from CropScape. With \({}^{*}\) are shown the CropScape errors at the scale of California and UA+ and PA+ represent the combined errors, shown in bold. \begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline  & \multicolumn{2}{c}{**CropScape**} & \multicolumn{4}{c}{**Single-band DTW45**} & \multicolumn{4}{c}{**Multi-band DTW30**} \\ \hline
**Crop** & **UA\({}^{*}\)** & **PA\({}^{*}\)** & **UA** & **UA+** & **PA** & **PA+** & **UA** & **UA+** & **PA** & **PA+** \\ \hline Corn & 9.7 & 16.2 & 4.0 & **10.5** & 7.7 & **17.9** & 3.5 & **10.3** & 13.2 & **20.9** \\ Cotton & 16.6 & 10.7 & 13.4 & **21.3** & 17.2 & **20.3** & 27.6 & **32.2** & 7.4 & **13.0** \\ Wheat & 16.9 & 13.5 & 1.9 & **17.0** & 9.4 & **16.5** & 2.0 & **17.0** & 12.9 & **18.7** \\ Alfalfa & 13.0 & 26.1 & 12.8 & **18.2** & 0 & **26.1** & 15.0 & **19.8** & 0 & **26.1** \\ Fallow & 30.5 & 57.0 & 33.3 & **45.2** & 51.2 & **76.6** & 44.2 & **53.7** & 41.5 & **70.5** \\ Grass & 30.7 & 17.1 & 22.7 & **38.2** & 2.3 & **17.3** & 16.0 & **34.6** & 2.3 & **17.3** \\ Double & 75.2 & 83.9 & 20.3 & **77.9** & 15 & **85.2** & 2.2 & **75.2** & 26.7 & **88.0** \\ \hline \hline \end{tabular}
\end{table}