Introduction

The basis of quantitative remote sensing is acquiring accurate reflectance (Jin et al. 1986). Although reflectance measured by ground hyperspectrometer has higher precision (Du et al. 2011; Lee et al. 2004; Maire et al. 2004; Wei et al. 2017), it is only discrete single point data. We need accurate reflectance for spatially continuous regions. Unmanned Aerial Vehicle (UAV) remote sensing is widely used in agricultural quantitative remote sensing monitoring for spatially continuous regions. Because it is important to acquire accurate reflectance for UAV remote sensing, the UAV sensor reflectance accuracy needs improvement.

Decomposition of mixed pixels is a vital method for improving the accuracy of reflectance. Endmember is an important component of spectral mixture model. At present, endmember extraction algorithms mainly include minimum noise fraction method, pure pixel index method, principal component transformation method, field measurement method, model simulation method and so on (Adams et al. 1995; De Asis and Omasa 2007; Dennison and Roberts 2003; Hu et al. 2004; Townshend et al. 2000; Zhu 2005). Many studies applied Multiple Endmember Spectral Mixture Analysis (MESMA) on remote sensing images, and allowed a linear combination of endmembers to vary in number and type on each pixel to explore the optimal endmember combination (Degerickx et al. 2019; Dennison and Roberts 2003; Fan 2015; Fernández-Manso et al. 2012; Quintano et al. 2013; Thorp et al. 2013). Some researchers (Cai 2010; Gu et al. 2007) extracted endmember spectrum of remote sensing images by Minimum Noise Fraction-Pure Pixel Index (MNF-PPI) method. Shanmugam et al. (2006) used endmember extraction algorithm to obtain endmember spectral characteristics of three kinds of ground objects after classification of ground objects from Indian remote sensing satellite IRS image and Landsat 5 TM image, including vegetation, soil and water. Bian et al. (2014) derived each endmember from HJ satellite images by an adaptive selection endmember method.

Previous studies have extracted the spectral reflectance of the endmember from the satellite remote sensing images, or used the spectral mixture models to integrate the ground and satellite remote sensing data (Wang et al. 2012, 2013). However, the ground measured data was not used to integrate the UAV remote sensing data for reflectance inversion.

We chose the apple orchard as the research district, as apple cultivation is widespread in China (An et al. 2019; Fang et al. 2019; Han et al. 2019). We explored a better method for improving the inversion accuracy of apple tree canopy reflectance by comparing Minimum Noise Fraction-Pure Pixel Index-Linear Spectral Mixture Model (MNF-PPI-LSMM) and Ground-Unmanned Aerial Vehicle-Linear Spectral Mixture Model (G-UAV-LSMM), which were the two representative methods of mixed pixel decomposition with G-UAV integrated remote sensing data and only UAV remote sensing data.

Materials and methods

Study area

The study was executed outdoors in an apple orchard in Yedian town, Mengyin county, Linyi city, Shandong Province (Fig. 1) in eastern China on 10th, June 2019. Mengyin county is located in the central and southern of Shandong. The geographical scope is 117°45′—118°15′ E, 35°27′ —36°02′ N, belonging to a temperate continental monsoon climate.

Fig. 1
figure 1

Location of the study area. a Location of Linyi City in Shandong Province. b Location of study area in Yedian Town, Mengyin County. c Image of study area acquired by UAV. The green dots represent the sampling points

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Experimental design

The data sources of the research were ground hyperspectral data and UAV multispectral data. The acquiring processing for the data is the following.

(1) Radiometric calibration was performed on the calibration board (whose reflectance is 1) of Sequoia sensor before flying. Low-altitude UAV was used for aerial photography, and four control points were set at four corners of the sampling area.

(2) 15 sample squares of 5 m × 5 m were arranged in the sampling area (50 m × 50 m) randomly. We located the coordinates of the center points of the sample squares. The multispectral images were taken with mosaic and radiometric calibration. Then the image was geometrically corrected using GPS coordinates of the four control points. The 15 sample squares were located on the UAV image to obtain multispectral reflectance.

(3) For each sample square, the apple tree canopy near the central point was selected to collect the canopy spectrum on the ground. The four spectrums of bare soil on the ground were measured at the north, south, west and east of the apple tree canopy. The average reflectance of 15 apple tree canopy samples and the 60 bare soil samples were taken as the endmember of apple tree canopy and bare soil. The reflectance of 15 apple tree canopy samples were used to validate the inversion reflectance.

UAV remote sensing data acquisition and preprocessing

We used the Dajiang Matrice 600 Pro UAV to carry the sensor, and a Parrot Sequoia Multispectral Camera, for aerial photography. There were four multispectral bands, including green band (GRE: 530–570 nm), red band (RED: 640–680 nm), red edge band (REG: 730–740 nm) and near-infrared band (NIR: 770–810 nm). The four center wavelengths of the bands were 550, 660, 735 and 790 nm. The flying altitude was 50 m. The multispectral remote sensing image was of the coordinates of WGS-84. The ground spatial resolution of the multispectral image was 5 cm. A total of 292 multispectral images of the aerial photography area were obtained. Pix4D software was used to take mosaic and radiate the multispectral images to obtain multispectral images with surface mixed reflectance data.

Acquisition of ground hyperspectral data

During UAV aerial photography, the spectral collection of apple tree canopy was conducted by FieldSpec4 (ASD Inc., USA). The spectral range of FieldSpec 4 is 350–2500 nm. Between 350 and 1000 nm, the spectral sampling interval is 1.4 nm and the spectral resolution is 3 nm. Between 1000 and 2500 nm, the sampling interval is 2 nm and spectral resolution is 8 nm.

The determination time was 10:00–12:00. The weather was clear and cloudless. We optimized the reflectance of the UAV images with a standard whiteboard (a reference with the reflectance of 1). During the canopy spectral measurement, the measuring probe was aligned downward vertically, so that the probe center was above the canopy directly, where the vertical height was 1.5 m from the top of canopy. According to the appropriate adjustment of canopy size, the field of view was 25°. We carried out the spectral data acquisition 5 times at each canopy sample (5 m × 5 m) with its average as reflectance of the canopy sample. When determining the spectrum of bare soil, we ensured that the probe center was directly above the target at 1.5 m. According to the target size, the field of view was also 25°. We collected five times at each bare soil sample for spectral data, with its average as the reflectance of the bare soil sample.

Mixed pixel decomposition method

Mixed pixel decomposition is the process where we research the composition and proportion of mixed pixels by remote sensing images, including endmember extraction and abundance inversion. Endmember extraction refers to determining the basic features that make up the mixed pixel, and abundance inversion refers to calculating the proportion of each basic feature in the mixed pixel (De Asis and Omasa 2007). The inversion reflectance can be defined as the product of the spectral reflectance of different endmember components and their abundance (Wang et al. 2012). G-UAV-LSMM took the measured hyperspectral data of canopy and bare soil as the endmember, and then we used LSMM for abundance inversion to obtain the G-UAV-LSMM canopy inversion reflectance. MNF-PPI-LSMM can distinguish canopy and bare soil by visual interpretation. The endmember reflectance of the canopy and bare soil, whose PPI values are the maximum value, can be extracted by MNF-PPI method, respectively. Then, we used the LSMM for abundance inversion to obtain MNF-PPI-LSMM canopy inversion reflectance.

G-UAV-LSMM

To unify the hyperspectral data obtained by the ground spectrometer with the multi-spectral image data of the low-altitude UAV, we selected the measured hyperspectral data at wavelengths of 550, 660, 735 and 790 nm. We took the linear mixed pixel decomposition for the average surface mixed reflectance (\(\rho_{a}\)) of each band at every sample square by the measured canopy and bare soil endmember reflectance at these wavelengths. G-UAV-LSMM canopy inversion reflectance (\(\rho_{b}\)) was obtained with the multiple of the abundance and the canopy endmember spectrum. The formula of LSMM (Liu and Yao 2009) is:

$$r_{i} = \sum\limits_{j = 1}^{m} {\alpha_{ij} e_{j} +\upvarepsilon _{j} }$$
(1)

In formula (1), \(r_{i}\) is the surface mixed reflectance. \(\alpha_{ij}\) is the weight of \(e_{j}\) in \(r_{i}\), which is called abundance. \(e_{j}\) is the endmember spectral reflectance. \(\upvarepsilon _{j}\) is the error term, which reflects the random noise of the data. The physical meaning of \(\alpha_{ij}\) is the area ratio of the \(j^{th}\) endmember in the \(i^{th}\) pixel. m is the total number of endmembers. Therefore, the constraint conditions should be followed, as shown in formula (2–3):

$$\alpha_{ij} \ge 0,\forall i,j$$
(2)
$$\sum\limits_{j = 1}^{m} {\alpha_{ij} = 1,i = 1,2,...,n}$$
(3)

MNF-PPI-LSMM

Each wavelength of UAV multispectral remote sensing image was taken with the MNF-PPI processing, and the canopy and bare soil endmember spectral reflectance was obtained. We took the linear mixed pixel decomposition for the surface mixed reflectance of each band at every sample square using these canopy and bare soil spectral reflectance, then we got the canopy abundance value of every sample square. The canopy abundance value multiplied by canopy endmember spectral reflectance of each sample square was MNF-PPI-LSMM canopy inversion reflectance (\(\rho_{c}\)).

The researchers (Green et al. 1988; Lee et al. 1990) took MNF conversion and then modified it. The high-pass filter template is used to filter the whole image data block with the same quality, and the noise covariance matrix \(C_{N}\) is obtained, which is diagonally transformed into the matrix \(D_{N}\).

$$D_{N} = U^{T} C_{N} U$$
(4)

In formula (4), \(D_{N}\) is the diagonal matrix whose eigenvalues of \(C_{N}\) are arranged in descending order. U is an orthogonal matrix of eigenvectors.

$$I = P^{T} C_{N} P$$
(5)
$$P = UD_{N}^{ - 1/2}$$
(6)

In formula (5–6), \(I\) is the identity matrix. \(P\) is the transformation matrix. When \(P\) is applied to the image \(X\), the original image is projected into the new space through \(Y = PX\) transformation. The noise has unit variance and is not correlated among the bands in the generated transformation data. Standard principal component transformation is performed on noise data.

$$C_{D - adj} = P^{T} C_{D} P$$
(7)

In formula (7), \(C_{D}\) is the covariance matrix of image. \(C_{D - adj}\) is the matrix after \(P\) transformation, which is further diagonalized to the matrix \(D_{D - adj}\).

$$D_{D - adj} = V^{T} C_{D - adj} V$$
(8)

In formula (8), \(D_{D - adj}\) is the diagonal matrix whose eigenvalues are arranged in descending order by \(C_{D - adj}\). \(V\) is an orthogonal matrix of eigenvectors. Through the above two steps, the transformation matrix \(T_{MNF}\) is obtained, \(T_{MNF} = PV\).

The reflectance of apple tree canopy and bare soil pixel with the highest PPI values in various quadrates was used to represent the reflectance of canopy and bare soil endmember through MNF processing. Then the LSMM was used to inverse the abundance. The formula and constraint conditions of LSMM are the same as formulas (1–3).

Inversion accuracy evaluation

The determination coefficient (R2), Root Mean Square Error (RMSE) and Residual Prediction Deviation (RPD) are used to evaluate the reflectance accuracy of canopy inversion. R2 is the measure of the degree of correlation between variables, which determines the degree of correlation. The larger R2 is, the closer the predicted value is to the measured value. RMSE is used to measure the deviation between the predicted value and the measured value. The less the RMSE is, the better the prediction effect is. RPD is an effective indicator to judge the prediction effect of the model. SD is standard deviation. When RPD > 2, it indicates that the model has a good effect and can be used for quantitative analysis. When 1.8 < RPD < 2.0, it indicates that the model is effective and can be used for quantitative estimation. When 1.4 < RPD < 1.8, it indicates that the model can roughly estimate the sample. When RPD < 1.4, the model is less effective (Gaston et al. 2010). Formula (9–12) is the calculation formula of each indicator:

$$R^{2} = \frac{{(\sum\limits_{i = 1}^{N} {(y_{i} - \overline{y})} (x_{i} - \overline{x}))^{2} }}{{\sum\limits_{i = 1}^{N} {(y_{i} - \overline{y})^{2} \sum\limits_{i = 1}^{N} {(x_{i} - \overline{x})^{2} } } }}$$
(9)
$$RMSE = \sqrt {\frac{1}{N}\sum\limits_{i = 1}^{N} {(y_{i} - x_{i} )^{2} } }$$
(10)
$$RPD = \frac{SD}{{RMSE}}$$
(11)
$$SD = \sqrt {\frac{1}{N - 1}\sum\limits_{i = 1}^{N} {(x_{i} - \overline{x})^{2} } }$$
(12)

In the formula (9–12), x is the measured canopy reflectance. \(\overline{x}\) is the average measured canopy reflectance. y is the inversion reflectance.\(\overline{y}\) is the average inversion reflectance. N is the amount of samples. i is the number of the samples.

Results

Figure 2 refers to the average ground hyperspectral and UAV multispectral curves of the 15 canopy samples, which reflect their spectral characteristics. As can be seen from Fig. 2, the hyperspectral curve has an absorption valley at 690 nm, and the reflectance increases at 735 nm sharply, while it is relatively stable at 760—790 nm. The multispectral curve shows a trend of decline from 550 to 660 nm. The reflectance rises gradually from 660 to 735 nm. There is an obvious absorption valley at 660 nm because of the strong absorption to the red band. The curve presents an increasing tendency from 735 to 790 nm, owing to the strong reflection of the near infrared band. Through the comparison for the hyperspectral and multispectral curves, it is found that the hyperspectral curve can reflect the continuous spectral characteristics, and the multispectral curve is a line connected by discrete points.

Fig. 2
figure 2

Apple tree canopy average hyperspectral and multispectral curves

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Splicing and radiometric calibration of the multispectral image were both completed in Pix4D software. Then \(\rho_{a}\) was obtained directly, and we used \(\rho_{a}\) to inverse reflectance based on G-UAV-LSMM and MNF-PPI-LSMM. We obtained the measured canopy and bare soil endmember spectral reflectance by the ground spectrometer. They were selected at the central wavelengths of 550, 660, 735 and 790 nm. Figure 3a shows the canopy abundance of each pixel obtained by the G-UAV-LSMM method. The results show that the canopy abundance value is higher at the top of the tree canopy, while the canopy abundance value is lower at the edge of the tree canopy, which is caused by the greater influence of bare soil spectrum on the edge. The G-UAV-LSMM canopy inversion reflectance is the measured hyperspectral reflectance selected at the central wavelengths of the UAV multispectral data multiplied by the abundance \(\alpha\).

Fig. 3
figure 3

Canopy abundance based on a G-UAV-LSMM and b MNF-PPI-LSMM

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We used the MNF-PPI method to obtain the canopy and bare soil endmember spectral reflectance from the multispectral image. Figure 3b shows the canopy abundance values of each pixel obtained by MNF-PPI-LSMM method. The results show that the canopy abundance value at the top of the canopy was higher, but the canopy abundance value at the edge of the canopy was lower, which was caused by the great influence of bare soil spectrum on the edge. It is consistent with the law of the canopy abundance value obtained by the G-UAV-LSMM method. The MNF-PPI-LSMM canopy inversion reflectance is canopy abundance \(\alpha\) multiplied by \(e_{j}\), of which PPI is the highest.

Figure 4a–d are 1:1 scatter plots between the measured and inversion reflectance values based on G-UAV-LSMM method at central wavelengths of 550, 660, 735 and 790 nm, respectively. The results show that the R2 of fitting equation composed by measured reflectance (\(\rho\)) and \(\rho_{b}\) are 0.845, 0.869, 0.861 and 0.871. The RMSE are 0.005, 0.007, 0.017 and 0.025. The RPD are 2.432, 1.891, 2.507 and 2.275 by the G-UAV-LSMM method, respectively.

Fig. 4
figure 4

1:1 scatter plots of measured and inversion reflectance based on G-UAV-LSMM at wavelengths of a 550 nm, b 660 nm, c 735 nm and d 790 nm

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Figure 5a–d are the 1:1 scatter plots of the measured and predicted canopy reflectance values based on MNF-PPI-LSMM method at the central wavelength of 550, 660, 735 and 790 nm respectively. The results show that the R2 of fitting equation composed by \(\rho\) and \(\rho_{c}\) are 0.709, 0.728, 0.760 and 0.794. The RMSE are 0.012, 0.010, 0.024 and 0.042. The RPD are 1.013, 1.324, 1.776 and 1.354 by the MNF-PPI-LSMM method. The comparison shows that G-UAV-LSMM can better inverse the canopy reflectance of apple trees.

Fig. 5
figure 5

1:1 scatter plots of measured and inversion reflectance based on MNF-PPI-LSMM at wavelengths of a 550 nm, b 660 nm, c 735 nm and d 790 nm

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Discussion

The surface mixed reflectance mentioned in this study was the reflectance of radiance values of multispectral image after radiometric calibration. Canopy inversion reflectance is the canopy reflectance obtained after mixed pixel decomposition (Wang et al. 2012, 2013), including the canopy inversion reflectivity obtained by MNF-PPI-LSMM and G-UAV-LSMM methods. In this study, the reflectance inversion methods were mixed pixel decomposition methods.

This research introduced the canopy reflectance inversion method, G-UAV-LSMM, which integrated the ground hyperspectral and UAV remote sensing data. Its accuracy was higher than that of MNF-PPI-LSMM, because it obtained the endmember spectrum through the ground hyperspectral data. The PPI algorithm used the spectral reflectance with maximum PPI as components. PPI algorithm accuracy depended on the endmember spectrum which was chosen (Zeng et al. 2009). The accuracy of PPI was affected by the phenomenon of the different spectrum in the same kind of item, which led to the lower accuracy of canopy inversion reflectance obtained by the MNF-PPI-LSMM method.

The accuracy of canopy inversion reflectance is affected by soil background (Liu et al. 2018). At the same time, the inversion of canopy reflectance taken by the G-UAV-LSMM method requires the support of the measured hyperspectral data on the ground. Because of the limitation of actual conditions, it is impossible to obtain the measured hyperspectral reflectance of all locations in the aerial photography area. Therefore, the most representative sites in the aerial photography area, such as the four corners and center point, are selected to obtain the measured average hyperspectral reflectance data of the canopy and bare soil as the endmember spectral reflectance of all pixels of the study area. Every time we get UAV multispectral images, we should obtain the measured ground reflectance data of the canopy and bare soil as the endmember spectrum on the most representative sites of the aerial photography area. The aim is to make sure that the endmember spectrum can represent the canopy and bare soil spectrum for each aerial photography area.

Our study also had some shortcomings. It did not consider the influence of the spectral resolution of UAV multispectral and ground measured hyperspectral data on the G-UAV-LSMM model. It ignored the influence of cloud, which needs further research to be incorporated to the model. Also, we need to study how the difference in spectral resolution and the sky condition affect the inversion accuracy. With the improvement of the related technologies and parameters, the inversion accuracy will be improved. More accurate canopy reflectance data will be obtained by G-UAV remote sensing data.

Conclusion

We explored the integrating method of ground and UAV remote sensing data to inverse the canopy reflectance. The accuracy of the canopy inversion reflectance obtained by G-UAV-LSMM was higher than that of MNF-PPI-LSMM at the central wavelengths of 550, 660, 735 and 790 nm. Therefore, G-UAV-LSMM had a better effect on the reflectance inversion for apple tree canopy.