Supplementary Material
Table S1. Parameters in the framework.
Shorted code Purpose Value in the
framework
Module of framework Eps Hyperparameter. The radius for a point (or pixel) to
search for its neighbors.
3 DBSCAN
MinPts Hyperparameter. The number of neighbors a point (or pixel) has within Eps.
29 DBSCAN
NDVIthresh Framework-unique. The threshold of NDVI to filter
the annual maximum NDVI map.
= 0.25 for center-pivot fields;
= 0.15 for non- center-pivot fields.
DBSCAN
nhigh Framework-unique. If a cluster obtained from DBSCAN consisted of more than nhigh pixels, the cluster was defiend as a large cluster and would be re-clustered using DBSCAN.
5,000 DBSCAN
nlow Framework-unique. If a cluster obtained from DBSCAN consisted of less than nhigh pixels, the cluster was defined as a small cluster, that consisted of too few pixels to represent a field and would be eliminated from the framework.
20 DBSCAN
Learning rate Hyperparameter. Learning rate of Alexnet. 0.001 Alexnet Momentum
coefficient
Hyperparameter. Momentum coefficient of Alexnet to reduce the fluctuation of loss degradation and speed up the model training.
0.9 Alexnet
Mini-batch size Hyperparameter. The mini-batch size to train Alexnet.
16 Alexnet
Nclu Hyperparameter. The number of clusters to run spectral clustering.
= 2 to cluster multiple non- center-pivot fields (label 5);
Automatically searching by the framework to cluster merged fields (label 6)
Spectral clustering
pthresh Framework-unique. The pixel threshold indicated
the potential number of pixels a center-pivot field might have. It was used to set the candidate values of Nclu and to decide when to stop the multiple iterations of spectral clustering for multiple non- center-pivot fields. If an object was classified as multiple non-center-pivot fields by Alexnet but consisted of less than pthresh pixels, spectral clustering would not be implemented.
500 Spectral
clustering
Threshold of the Framework-unique. The pixel threshold. If the 8 Spectral 1
2
number of boundary pixels
number of boundary pixels of two geographically adjacent clusters exceeded this threshold, the Pearson correlation coefficient of the pixel coordinates (with x and y indicating the rows and columns of pixels in the object) was computed.
clustering
Threshold of Pearson correlation coefficient of the pixel coordinates
Framework-unique. The Pearson correlation coefficient threshold. If the Pearson correlation coefficient of two geographically adjacent clusters exceeded this threshold, the two clusters were merged as one field.
0.8 Spectral
clustering
The number of trees
Hyperparameter. The number of trees to construct the random forest.
300 Random
forest Max features Hyperparameter. The number of features to
consider when looking for the best split, log2N , N is the number of input features. N = 4 in this study.
2 Random
forest
Function to measure the quality of a split
Hyperparameter. The function to measure the quality of a split.
Entropy Random forest
Fig.S1. Schematic of DBSCAN clustering. DBSCAN took the annual maximum NDVI image as input (lef image), which resulted in clusters consisting of different field objects (shown by different colors in the DBSCAN cluster image). Seven examples of field objects obtained by DBSCAN were shown here (a to g).
These field objects might consist of one circle (d and e) or fan-shaped CPF (c), multiple CPFs (a and b), or non-CPFs (f and g). Alexnet took the field object NDVI image as input to classify the type of field object if it represented: noisy objects that did not form a valid field, a single circular CPF, a single fan-shaped CPF (incomplete CPF), a single non-CPF, multiple non-CPFs, or multiple merged fields.
2 3
4 5 6 7 8 9 10 11
Fig.S2. The architecture of Alexnet employed in this study. The input NDVI images obtained from DBSCAN (Fig.S1) were resized to form a 2272271 input matrix, which resulted in an output of six ground truth labels. Five convolutional layers and three fully connected layers were implemented in a stepwise manner until the output layer for predicting the class of the input image was produced. A kernel size of 11 was selected, indicating a matrix with 11 × 11 pixels. The stride (S) was set to 4, signifying that the kernel was moved four pixels in each step, which was set to reduce the dimension of the feature maps. Padding (P) of 1 indicated a one-pixel border added to the image with a zero pixel value and was set to utilize the boundary information of a feature map, while P = 0 indicated no padding was applied.
1213 14 15 16 17 18 19 20 21 22
Fig.S3. Examples of spectral clustering with different iterations (N_iter) applied. The different field colors indicate different clusters, showing: (a) and (b) a field object obtained by DBSCAN and classified as label 5 (multiple non-CPFs) by Alexnet and (c) a field object obtained from DBSCAN and classified as label 6 (merged fields) by Alexnet. In example (a), the number of clusters (Nclu) used to run spectral clustering was fixed as 2 in all three iterations since Alexnet kept classifying the sub-clusters as label 5. Afer three iterations the process stopped, as each of the clusters in the third iteration consisted of less than 500 pixels. In (b), a field object consisting of 12 CPFs was classified as label 5 by Alexnet. In the first iteration of spectral clustering, Nclu was set to 2 accordingly and the field object was clustered into two clusters, each of which consisted of six CPFs. Then Alexnet classified the two clusters afer the first iteration as label 6. In the second iteration of spectral clustering, the framework automatically searched for the optimal Nclu values (which was six for both clusters). The two clusters were re-clustered into six subclusters individually. Each of the sub-clusters indicated an individual CPF. The iteration stopped afer iteration 2 since no cluster was classified as label 5 or 6. In (c), a field object obtained by DBSCAN was classified as label 6. The optimal Nclu suggested by the framework was three and thus the spectral clustering was run using Nclu = 3. The CPF was correctly segmented and separated from the remaining parts of the input field object. The two non-CPFs consisted of less than 500 pixels, and hence the clustering procedure stopped. In the whole process, afer up to five iterations of spectral clustering were applied, each pixel will have two types of label, i.e., the Alexnet label (indicating the shape of the field 4 2324
25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41
that a pixel belonged to) and the cluster label (pixels sharing the same cluster label forming a field). The final outputs of the framework were polygons covering individual fields and field shape maps showing if a field represented a single circular CPF; a single fan-shaped CPF; non-CPFs; or merged fields.
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