# Crop Rotation Modeling for Deep Learning-Based Parcel Classification from Satellite Time Series

^{*}

## Abstract

**:**

## 1. Introduction

#### 1.1. Single-Year Crop-Type Classification

#### 1.2. Multi-Year Agricultural Optimization

#### 1.3. Multi-Year Crop Type Classification

- We propose a straightforward training scheme to leverage multi-year data and show its impact on yearly agricultural parcel classification.
- We introduce a modified attention-based temporal encoder able to model both inter- and intra-annual dynamics of agricultural parcels, yielding a large improvement in terms of precision.
- We present the first open-access multi-year dataset [35] for crop classification based on Sentinel-2 images, along with the full implementation of our model.
- Our code in open-source at the following repository: https://github.com/felixquinton1/deep-crop-rotation, accessed on 11 November 2021.

## 2. Materials and Methods

#### 2.1. Dataset

^{2}in the South East of France (centered around 4.31N, 46.44E in WGS84). This area, in the Auvergne-Rhône-Alpes region, is a major producer of cereal with over 54,000 ha of corn and 30,000 ha of wheat. Extensive livestock production makes meadow the most crop type with over 60% of declared parcels in the LPIS. The most frequent crop rotations are permanent cultures (meadows, vineyards, and pasture) and alternating between corn, wheat, and rapeseed.

^{2}) small or with very narrow shapes to reflect the resolution of the Sentinel-2 satellite. Each parcel has a ground truth cultivated crop type for each year corresponding to the main culture as reported by the French LPIS, whose precision is estimated at over 97% as reported by the French Payment Agency. Note that we ignore secondary cultures for parcels with multiple growth cycles. In order to limit class imbalance, we only keep crop types among a list of 20 of the most cultivated species in the area of interest. In sum, our dataset is composed of 103,602 parcels, each associated with three image time sequences and three crop annotations corresponding to the farmers’ declarations for 2018, 2019, and 2020.

#### 2.2. Pixel-Set and Temporal Attention Encoders

#### 2.3. Multi-Year Modeling

- We only consider the last two previous years because of the limited span of our available data. However, it would be straightforward to extend our approach to a longer duration.
- We consider that the history of a parcel is completely described by its past cultivated crop types, and we do not take the past satellite observations into account. In other words, the label at year i is independent from past observations conditionally to its past labels [39] (Chapter 2). This design choice allows the model to stay tractable in terms of memory requirements.
- The labels of the past two years are summed and not concatenated. The information about the order in which the crops were cultivated is then lost, but this results in a more compact model.

#### 2.4. Baseline Models

**Single-Year:**M

_{single}. We simply do not provide the labels of previous years, and directly map the current year’s observations to a vector of class scores [18].

**Conditional Random Fields:**M

_{CRF}. Based on the work of [32,33], we implement a simple chain-CRF probabilistic model. We use the prediction of the previous PSE+LTAE, calibrated with the method of Guo et al. [40] to approximate the posterior probability $p\in {[0,1]}^{L}$ of a parcel having the label k for year i:${p}_{k}=P({l}^{i}=k\mid {x}^{i})$ (see Section 3.3 for more details). We then model the second order transition probability $p({l}^{i}=k\mid {l}^{i-1},{l}^{i-2})$ with a three-dimensional tensor $T\in {[0,1]}^{L\times L\times L}$ that can be approximated based on the observed transitions in the training set. As suggested by Bailly et al., we use a Laplace regularization [41] (Chapter 13) to increase robustness. The resulting probability for a given year i is given by:

**Observation Bypass:**M

_{obs}. Instead of concatenating the labels of previous years to the embedding ${e}^{i}$, we concatenate the average of the descriptors of the last two years ${e}^{i-1}$ for ${e}^{i-2}$:

**Label Concatenation:**M

_{dec-concat}. Instead of concatenating the sum of the last two previous years, we propose to concatenate each one-hot-encoded vector ${l}^{i-1}$ and ${l}^{i-2}$ with the learned descriptor ${z}^{i}$. This approach is similar to Equation (2), but leads to a larger descriptor and a higher parameter count.

**Single-Year Label Bypass:**M

_{dec-one-year}. In order to evaluate the impact of describing the history of parcels as the past two cultivated crops, we only concatenate the label of the previous year to the learned descriptor ${e}^{i}$.

#### 2.5. Training Protocol

#### 2.5.1. Mixed-Year Training

_{2018}, M

_{2019}, and M

_{2020}. In contrast, the model M

_{mixed}is trained with all parcels across all years with no information regarding of the year of acquisition. All models share the same PSE+LTAE configuration [18]. We visualize the training protocols in Figure 5, and report the results in Table 2. In the rest of the paper, we use mixed year training for all models.

#### 2.5.2. Cross-Validation

#### 2.6. Evaluation Metrics

## 3. Results

#### 3.1. Training Protocol

#### 3.2. Influence of Crop Rotation Modeling

_{obs}barely improves the quality of the single-year model, while this model has indeed access to more information than M

_{single}, the same model is used to extract SITS descriptors for all three years. This means that the model’s ambiguities and errors will be the same for all three representations, which prevent M

_{obs}from largely improving its prediction. Our approach injects new information to the model by concatenating the labels of previous years, which is independent of the model’s limitations. Our method is more susceptible to the propagation of mistakes in the farmers’ declarations, but provides the largest increase in performance in practice.

_{dec}model obtains an mIoU of 84.7% and an overall accuracy of 98.1% on the training set.

_{dec}in Figure 8, and its performance for each crop in Table 4. We also compute $\Delta =\mathrm{IoU}\left({M}_{\mathrm{dec}}\right)-\mathrm{IoU}\left({M}_{\mathrm{single}}\right)$ the gain compared to the single-year model $\mathrm{IoU}\left({M}_{\mathrm{single}}\right)$, as well as the ratio of improvement $\rho =\Delta /(1-\mathrm{mIoU}\left({M}_{\mathrm{single}}\right))$. This last number indicates the proportion of IoU that have been gained by modeling crop rotations. We observe that our model provides a large performance increase across all classes but four. The improvement is particularly stark for classes with strong temporal stability such as vineyards.

**Permanent Culture.**Classes within this group are such that at least 90% of the observed successions are constant over three years. Contains Meadow, Vineyard, and Wood Pasture.**Structured Culture.**A crop is said to be structured if, when grown in 2018, over 75% of the observed three year successions fall into 10 different rotations or less, and is not permanent. Contains Rapeseed, Sunflower, Soybean, Alfalfa, Leguminous, Flowers/Fruits/vegetables, and Potato.**Other.**All other classes.

#### 3.3. Model Calibration

## 4. Discussion

#### 4.1. Choice of Backbone Network

#### 4.2. Operational Setting

#### 4.3. Scope of the Study

#### 4.4. Applicability of Our Model

## 5. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Abbreviations

CNN | Convolutional Neural Network |

MLP | Multi Layer Perceptron |

RNN | Recurrent Neural Network |

PSE | Pixel Set encoder |

TAE | Temporal Attention Encoder |

LTAE | Lightweight Temporal Attention Encodeur |

ECE | Expected Calibration Error |

CAP | Common Agricultural Policy |

LPIS | Land-Parcel Identification System |

SITS | Satellite Image Time Series |

CRF | Conditional Random Fields |

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**Figure 1.**Multi-Year Sentinel-2 Data. Details of our area of interest for the three years studied in this article. The crop type of each parcel is represented by the color of a polygon following their contour according to the legend above. This color code is used throughout this article for all figures representing cultivated crops.

**Figure 2.**Area of Interest. The studied parcels are taken from the 31TFM Sentinel-2 tile, covering an area of 110 × 110 km and containing over 103,602 parcels meeting our size, shape, and stability criteria. (

**a**) Large view of the tile. (

**b**) Detail of the area.

**Figure 3.**Intra-Year Dynamics. Evolution of two areas across three seasons of the year 2020. The top parcels contains mainly meadow parcels, while the bottom one comprises more diverse crops. The aspect of most parcel drastically changes across one year’s worth of acquisition, corresponding to different phases in the growth cycle. (

**a**) Winter. (

**b**) Spring. (

**c**) Summer.

**Figure 4.**Multi-Year Modeling. Different approaches to model crop rotation dynamics: (

**a**) the model only has access to the current year’s observation; (

**b**) a chain-CRF is used to model the influence of past cultivated crop; (

**c**) the model has access to the observation of the past two years; (

**d**) proposed approach: the model has access to the last two declared crops.

**Figure 5.**Training Protocol. A single model is trained with parcels taken from all three years (

**a**), and three specialized models whose training set only comprises observation for a given year (

**b**).

**Figure 6.**Learned Representations. Illustrations of the learned SITS representations of the mixed-year model M

_{mixed}(

**a**) and the specialized M

_{2020}(

**b**). T-SNE algorithm is used to plot in 2D the representation for 100 parcels over 10 classes and 3 years. We observe that M

_{mixed}produced cluster of embeddings that are consistent from one year to another, and with clearer demarcation between classes.

**Figure 7.**Qualitative Illustration. Detail of the area of interest with the ground truth in (

**a**) and the qualification of the prediction in (

**b**) with correct prediction in blue and errors in red.

**Figure 8.**Confusion Matrix. Confusion matrix of the prediction of ${\mathcal{M}}_{\mathrm{dec}}$ for the year 2020. The area of each entry corresponds to the square root of the number of predictions.

**Figure 9.**Model calibration. Empirical rate of correct prediction by predicted confidence. We quantize the predicted confidence into 100 bins for visualization purposes. For a perfectly calibrated prediction, the blue histogram would exactly follow the orange line. We observe that a simple post-processing step can considerably improves calibration. (

**a**) No calibration, ECE = 1.4%. (

**b**) Calibration, ECE = 0.8%.

**Table 1.**Crop distribution. We indicate the number of parcels declarations in the LPIS for each class across all 103,602 parcels and all 3 years.

Class | Count | Class | Count |
---|---|---|---|

Meadow | 184,489 | Triticale | 5114 |

Maize | 42,006 | Rye | 569 |

Wheat | 27,921 | Rapeseed | 7624 |

Barley Winter | 10,516 | Sunflower | 1886 |

Vineyard | 15,461 | Soybean | 6072 |

Sorghum | 820 | Alfalfa | 2682 |

Oat Winter | 529 | Leguminous | 1454 |

Mixed cereal | 1061 | Flo./fru./veg. | 1079 |

Oat Summer | 330 | Potato | 230 |

Barley Summer | 538 | Wood pasture | 425 |

**Table 2.**Quantitative evaluation. Performance (mIoU and OA) of the different specialized models ${M}_{2018}$, ${M}_{2019}$, ${M}_{2020}$ and of the mixed-years model ${M}_{\mathrm{mixed}}$ evaluated on each year individually and all available years simultaneously with 5-fold cross-validation. The best performances are shown in bold. Boxed values correspond to evaluations where the training set and the evaluation set are drawn from the same year. The mixed-year model performs better for all years, even compared to specialized models.

Model | 2018 | 2019 | 2020 | 3 Years | ||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|

OA | mIoU | OA | mIoU | OA | mIoU | OA | mIoU | |||||

${M}_{2018}$ | 97.0 | 64.7 | 90.3 | 45.5 | 90.8 | 43.4 | 92.7 | 49.1 | ||||

${M}_{2019}$ | 88.9 | 39.5 | 97.2 | 70.1 | 88.7 | 40.1 | 91.6 | 48.0 | ||||

${M}_{2020}$ | 91.4 | 44.2 | 93.7 | 51.8 | 96.7 | 67.3 | 93.9 | 54.0 | ||||

${M}_{\mathrm{mixed}}$ | 97.3 | 69.2 | 97.4 | 72.2 | 96.8 | 68.7 | 97.2 | 70.4 |

**Table 3.**Performance by model. Performances (mIoU and OA) of the models M

_{single}, M

_{obs}, M

_{CRF}, and M

_{dec}tested for the year 2020. Our proposed model M

_{dec}achieve higher performance than M

_{single}with a 6.3% mIoU gap.

Model | Description | OA | mIoU |
---|---|---|---|

${M}_{\mathrm{sin}\mathrm{gle}}$ | single-year observation | 96.8 | 68.7 |

${M}_{\mathrm{obs}}$ | bypassing 2 years of observation | 96.8 | 69.3 |

${M}_{\mathrm{CRF}}$ | using past 2 declarations in a CRF | 96.8 | 72.3 |

M_{dec-one-year} | concatenating last declaration only | 97.5 | 74.3 |

M_{dec-concat} | concatenating past 2 declarations | 97.5 | 74.4 |

${M}_{\mathrm{dec}}$ | proposed method | 97.5 | 75.0 |

**Table 4.**Performance by class. IoU per class of our model M

_{dec}for the year 2020, as well as the improvement Δ compared to the single-year model M

_{single}, and the ratio of improvement ρ. All values are given in %, and we sort the classes according to decreasing ρ.

Class | IoU | $\mathbf{\Delta}$ | $\mathit{\rho}$ | Class | IoU | $\mathbf{\Delta}$ | $\mathit{\rho}$ |
---|---|---|---|---|---|---|---|

Wood Pasture | 92.4 | +48.2 | 86.3 | Oat Summer | 52.8 | +3.6 | 7.0 |

Vineyard | 99.3 | +1.4 | 68.7 | Rapeseed | 98.3 | +0.1 | 6.6 |

Alfalfa | 68.7 | +23.9 | 49.9 | Maize | 95.7 | +0.2 | 6.3 |

Flo./Fru./Veg. | 83.4 | +14.5 | 46.5 | Wheat | 91.9 | +0.3 | 3.9 |

Meadow | 98.4 | +0.9 | 36.9 | Barley Summer | 64.3 | +1.1 | 3.1 |

Leguminous | 45.2 | +14.6 | 21.1 | Potato | 57.1 | +0.5 | 1.2 |

Rye | 54.7 | +6.4 | 12.4 | Sunflower | 92.2 | −0.1 | −0.3 |

Oat Winter | 57.7 | +4.5 | 9.7 | Sorghum | 56.6 | −0.2 | −0.4 |

Triticale | 68.7 | 2.6 | 7.8 | Soybean | 91.8 | −0.2 | −3.1 |

Mix. Cereals | 31.0 | +5.1 | 6.8 | Barley Winter | 92.8 | −0.6 | −8.5 |

**Table 5.**Improvement Relative to Structure. Classwise IoU and mean improvement of our model compared to the single-year model according to the rotation structure of the cultivated crops.

Category | mIoU | Mean $\mathbf{\Delta}$ |
---|---|---|

Permanent | 97.3 | 16.9 |

Structured | 77.7 | 7.6 |

Other | 66.6 | 2.3 |

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## Share and Cite

**MDPI and ACS Style**

Quinton, F.; Landrieu, L.
Crop Rotation Modeling for Deep Learning-Based Parcel Classification from Satellite Time Series. *Remote Sens.* **2021**, *13*, 4599.
https://doi.org/10.3390/rs13224599

**AMA Style**

Quinton F, Landrieu L.
Crop Rotation Modeling for Deep Learning-Based Parcel Classification from Satellite Time Series. *Remote Sensing*. 2021; 13(22):4599.
https://doi.org/10.3390/rs13224599

**Chicago/Turabian Style**

Quinton, Félix, and Loic Landrieu.
2021. "Crop Rotation Modeling for Deep Learning-Based Parcel Classification from Satellite Time Series" *Remote Sensing* 13, no. 22: 4599.
https://doi.org/10.3390/rs13224599