# Quantitative Retrieval of Organic Soil Properties from Visible Near-Infrared Shortwave Infrared (Vis-NIR-SWIR) Spectroscopy Using Fractal-Based Feature Extraction

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## Abstract

**:**

^{2}) = 0.85, root mean square error (RMSE) = 56.7 g/kg, the ratio of percent deviation (RPD) = 2.59; for pH: R

^{2}= 0.82, RMSE = 0.49 g/kg, RPD = 2.31; and for N: R

^{2}= 0.77, RMSE = 3.01 g/kg, RPD = 2.09. Even better results could be achieved when fractal features were combined with PCA components. Fractal features generated by the proposed method can improve estimation accuracies of soil properties and simultaneously maintain the original spectral curve shape.

## 1. Introduction

## 2. Materials and Methods

#### 2.1. The LUCAS Topsoil Database

^{A}) spectra, continuum removal, Savitzky-Golay filter with a window size of 50, second order polynomial and first derivative. Thirteen soil properties have been analysed in a central laboratory [22], including the percentage of coarse fragments, particle size distribution (% clay, silt and sand content), pH (in CaCl

_{2}and H

_{2}O), soil organic carbon (g/kg), carbonate content (g/kg), phosphorous content (mg/kg), total nitrogen content (g/kg), extractable potassium content (mg/kg), and cation exchange capacity (cmol(+)/kg). Three key soil fertility properties, soil organic carbon (SOC), total nitrogen content (N) and pH in CaCl

_{2}(pH), were selected as our studied properties.

#### 2.2. Fractal Feature Extraction Method

#### 2.2.1. Concept of Fractal Dimension

#### 2.2.2. Variation Method for Fractal Dimension

_{u}and X

_{t+u}are two reflectance values located at points u and t+u, and these two points are separated by the lag of t. The variogram can be calculated as the mean sum of squares of all differences between pairs of values with a given distance divided by two.

#### 2.2.3. Fractal Feature Generation

_{f}can be calculated as:

_{f}) correspondingly decreases, which can be used as a means of dimension reduction.

_{f}numbers of fractal dimension values can be obtained by moving along the spectral curve at step size p. For each segment, the number of points are marked as n and can be calculated by Equation (5). The reflectance value as Z

_{j}(j = 1, 2,…, n) and the corresponding fractal dimension value can be calculated according to Equation (4) as D

_{m}(m = 1, 2,…, N

_{f}), and fractal features at scale s by:

#### 2.3. Gradient-Boosting Regression Model

^{2}) or to minimize the root mean square error (RMSE), each successive tree is trained on the errors left over by the collection of earlier trees. XGBoost is a scalable and flexible gradient-boosting library [50,51,52], which is adopted to build the soil spectral quantitative model in our study. XGBoost uses more regularised model formalisation to control over-fitting, which gives it better performance. Mathematically, the model can be viewed as:

#### 2.4. Evaluation

^{2}and the ratio of percent deviation (RPD).

## 3. Results

#### 3.1. Fractal Features for Soil Spectroscopy

_{p}(t) and lag t, one problem is how many lag increments are necessary to produce reliable results. Theoretically only a minimum of two points is necessary to make such a plot [46]. However, the results of such an analysis tend to not be reliable or representative. In this study, the value of lag increments was set as 5, and the Pearson correlations of soil properties and fractal dimensions are shown in Table 1. The Pearson is a standardized covariance and ranges from −1 to +1, which indicates a perfect negative (−1) or positive (+1) linear relationship respectively. A value of zero is not related to the independency between the two variables, it only suggests no linear association. It can be seen that SOC, N and pH have negative relationships with fractal dimension. SOC and N have similar correlations with fractal dimension. Among these three estimators, the variogram-based fractal dimension calculation method achieved the best correlation between fractal dimension values and soil properties SOC (correlation coefficient (r) = −0.54), N (r = −0.50) and pH (r = −0.12).

#### 3.2. Effects of Different Step and Window Size on Extracted Fractal Features

^{2}derived by step–window pairs for SOC using rodogram, madogram and variogram methods are shown in Figure 6(A2–A4) respectively, as is the case for N and pH in Figure 6B,C. For a comparable study, the regression model was also applied to raw spectral values and PCA-transformed data.

^{2}varies from 0.64 to 0.83 (rodogram), 0.70 to 0.84 (madogram) and 0.72 to 0.84 (variogram). For pH, R

^{2}varies from 0.61 to 0.80 (rodogram), 0.63 to 0.80 (madogram) and 0.63 to 0.82 (variogram. However, for N there is comparatively less accuracy. R

^{2}varies from 0.52 to 0.74 (rodogram), 0.53 to 0.75 (madogram) and 0.55 to 0.76 (variogram). Models with raw spectra were developed by evenly selecting desired number of spectral measurements. The Hughes phenomenon can be seen well in models built with raw spectra. R

^{2}increased first and then declined with the increase of feature numbers. It can be seen that models with raw spectra had the poorest performance. For SOC and N, fractal features outperformed PCA-transformed features and raw spectra. Fractal features for pH achieved similar accuracies compared to PCA-transformed features.

#### 3.3. Modelling Soil Properties with Fractal Features

^{2}was used as the evaluation metric for validation data.

^{2}= 0.851, RMSE = 56.7 g/kg, RPD = 2.59) was 2.5 nm for the former and 105.0 nm for the latter with variogram estimator. The best performance step–window sizes for N (R

^{2}= 0.776, RMSE = 3.01 g/kg, RPD = 2.09) were step size at 2.5 nm and window size at 65.0 nm with the variogram estimator. The best performance step–window size for N (R

^{2}= 0.822, RMSE = 0.49, RPD = 2.31) were step size at 7.5 nm and window size at 45.0 nm with the variogram estimator. From Table 2, it can be seen that fractal-based feature extraction methods tend to keep a much larger number of features compared to PCA. To achieve similar performance of PCA, fractal-based approaches need to retain ~200 features, such as 190 for SOC (R

^{2}= 0.819, RMSE = 62.49 g/kg, RPD = 2.34) where step size and window size were respectively 10.0 nm and 105.0 nm, 128 features for N (R

^{2}= 0.736, RMSE = 3.26 g/kg, RPD = 1.92) where step size and window size were respectively 15.0 nm and 135.0 nm, and 131 features for pH (R

^{2}= 0.807, RMSE = 0.50, RPD = 2.22) where step size and window size were respectively 15.0 nm and 50.0 nm.

^{2}= 0.86, RMSE = 55.16 g/kg, RPD = 2.7), N (R

^{2}= 0.78, RMSE = 2.96 g/kg, RPD = 2.19) and pH (R

^{2}= 0.85, RMSE = 0.44, RPD = 2.59), as shown in Figure 7.

#### 3.4. Comparison with PLS Regression

^{2}= 0.834) was achieved when the number of components was 60 (Figure 8).

^{2}for the estimation of OC contents was 0.846 (Figure 9).

^{2}= 0.851) for the estimation of SOC contents of these three methods. We also applied methods A and B to the estimation of N and pH contents. For N, the same case applied; method C showed the highest R

^{2}. Although method A (PLS regression) achieved the best performance for the estimation of pH contents, when focusing on extracted features, fractal features had similar performance compared with PLS components, the R

^{2}for method C being 0.821 and for method B, 0.823. The only difference between these two methods was the ingested features. The results are summarised in Table 3, and it can be seen that fractal features can achieve similar or even better results compared with PLS components.

## 4. Discussion

#### 4.1. The Importance of Fractal Dimension for Soil Spectra

#### 4.2. Modelling Soil Properties with Fractal Features

^{2}than the method using the rodogram estimator. In [58] the classification achieved better results with texture layers derived from the madogram. Since the madogram estimator calculates the sum of the absolute value of the semivariance for all observed lags, it yields a softer effect on the presence of outliers compared to the variogram estimator. However, in our study, soil spectra were well pre-processed by the Savitzky–Golay filter and generated fractal features. Fractal features generated by these three estimators have a similar curve shape and achieved very close estimation accuracies for tested soil properties.

^{2}was found to be located at the bottom of the step–window matrix. However, there is no guarantee as to which step–window pair is the best parameter for soil property estimation. Therefore, a hyper-parameter optimisation method should be adopted for each of the soil properties.

## 5. Conclusions

^{2}= 0.86, RMSE = 55.16 g/kg, RPD = 2.7), N (R

^{2}= 0.78, RMSE = 2.96 g/kg, RPD = 2.19) and pH (R

^{2}= 0.85, RMSE = 0.44, RPD = 2.59). Fractal analysis can be functionalised as an approach to examine the relationship between soil spectra and soil properties, which can characterise statistical self-similarity and further quantify the irregularity of soil spectra [47]. Fractal features, by taking advantage of fractal information encoded in the shape of soil spectral curve, can reflect the impact of various properties on soil spectra except when the properties have less direct spectral response. In this case, fractal features can still be functioned to quantify the corresponding soil property, however, they not perform as well. Fractal features performed well when ingested into quantitative soil spectroscopic models, and the proposed fractal method can not only reduce the dimensionality in the original space, but also simultaneously maintain the spectral shape, which means that methods for raw spectra can also be applied to extracted fractal features, for example, calibrating soil properties using PLS regression with fractal features.

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## References

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**Figure 1.**Distribution of organic soil samples in the Land Use/Land Cover Area Frame Survey (LUCAS) topsoil database. Colours indicate amounts of soil organic carbon (SOC) content.

**Figure 2.**Illustration of fractal dimension calculation. (

**A**) is the spectral curve and (

**B**) is the corresponding log–log plot of variogram and lags and the fitted regression line.

**Figure 3.**Illustration of the meaning of step and window size for multiple fractal feature generation. (step size = 100.0 nm, window size = 200.0 nm).

**Figure 4.**(

**A**) Average spectral reflectance and continuum removal reflectance of LUCAS organic soil samples computed by SOC classes. (

**B**–

**D**) Average fractal energy and continuum removal responses of organic soil samples computed by SOC classes using rodogram, madogram and variogram estimators respectively. The central wavelength number of the corresponding spectral segment is assigned to the fractal feature.

**Figure 5.**The effect of step and window size on generated fractal features. (

**A**)are fractal feature curves when window sizes were at 15.0–95.0 nm (step size fixed at 2.5 nm); (

**B**) is the number of fractal features when step sizes were increased from 10.0 to 50.0 nm (window size fixed at 50.0 nm).

**Figure 6.**Gradient-boosting regression modelling accuracies for SOC, N and pH. (

**A1**), (

**B1**) and (

**C1**) were with principal component analysis (PCA)-transformed features and raw spectra; (

**A2**), (

**B2**) and (

**C2**) were with fractal features derived by the rodogram method with various step-scale pairs. (

**A3**), (

**B3**) and (

**C3**) were with fractal features derived by the madogram method with various step-window pairs. (

**A4**), (

**B4**) and (

**C4**) were with fractal features derived by the variogram method with various step-scale pairs.

**Figure 7.**Best performance of gradient-boosting regression modelling accuracies for SOC, N and pH. (

**A1**), (

**A2**) and (

**A3**) were with PCA-transformed features. (

**B1**), (

**B2**) and (

**B3**) were with fractal features. (

**C1**), (

**C2**) and (

**C3**) were with features combined by PCA-transformed features and fractal features. R

^{2}: coefficient of determination; RMSE: root mean square error; RPD: the ratio of percent deviation.

**Figure 8.**The change of R

^{2}with the increase of the partial least squares (PLS) component number (

**A**) and the PLS regression model when the component number was 60 (

**B**).

**Figure 9.**The gradient-boosting regression model with PLS components for the estimation of OC contents.

**Table 1.**Pearson correlation coefficients between soil properties and fractal dimensions calculated by rodogram, madogram and variogram estimators.

Rodogram | Madogram | Variogram | |
---|---|---|---|

SOC | −0.40 | −0.47 | −0.54 |

N | −0.38 | −0.43 | −0.50 |

pH | −0.12 | −0.13 | −0.12 |

**Table 2.**Best Performance step–window pairs for soil properties estimation using fractal-based feature extraction and comparison with PCA. R

^{2}: coefficient of determination.

Method | Step Size/nm | Window Size/nm | Dimension | R^{2} | |
---|---|---|---|---|---|

SOC | PCA | - | - | 28 | 0.813 |

Rodogram | 2.5 | 80 | 769 | 0.847 | |

Madogram | 2.5 | 90 | 765 | 0.847 | |

Variogram | 2.5 | 105 | 759 | 0.851 | |

N | PCA | - | - | 34 | 0.735 |

Rodogram | 2.5 | 50 | 781 | 0.756 | |

Madogram | 2.5 | 90 | 765 | 0.767 | |

Variogram | 2.5 | 65 | 775 | 0.776 | |

pH | PCA | - | - | 34 | 0.814 |

Rodogram | 5 | 55 | 390 | 0.806 | |

Madogram | 2.5 | 100 | 761 | 0.818 | |

Variogram | 7.5 | 45 | 261 | 0.821 |

Features | Modelling | OC (R^{2}) | N (R^{2}) | pH (R^{2}) | |
---|---|---|---|---|---|

Method A | PLS components | Linear regression | 0.834 | 0.743 | 0.87 |

Method B | PLS components | Gradient-boosting regression | 0.846 | 0.759 | 0.823 |

Method C | Fractal features | Gradient-boosting regression | 0.851 | 0.776 | 0.821 |

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Liu, L.; Ji, M.; Dong, Y.; Zhang, R.; Buchroithner, M.
Quantitative Retrieval of Organic Soil Properties from Visible Near-Infrared Shortwave Infrared (Vis-NIR-SWIR) Spectroscopy Using Fractal-Based Feature Extraction. *Remote Sens.* **2016**, *8*, 1035.
https://doi.org/10.3390/rs8121035

**AMA Style**

Liu L, Ji M, Dong Y, Zhang R, Buchroithner M.
Quantitative Retrieval of Organic Soil Properties from Visible Near-Infrared Shortwave Infrared (Vis-NIR-SWIR) Spectroscopy Using Fractal-Based Feature Extraction. *Remote Sensing*. 2016; 8(12):1035.
https://doi.org/10.3390/rs8121035

**Chicago/Turabian Style**

Liu, Lanfa, Min Ji, Yunyun Dong, Rongchung Zhang, and Manfred Buchroithner.
2016. "Quantitative Retrieval of Organic Soil Properties from Visible Near-Infrared Shortwave Infrared (Vis-NIR-SWIR) Spectroscopy Using Fractal-Based Feature Extraction" *Remote Sensing* 8, no. 12: 1035.
https://doi.org/10.3390/rs8121035