Materials

PolSAR data and the test site

The data used in this experiment are a time series Radarsat-2 PolSAR (C-band) images acquired on May 23, August 3, and August 27, 2013, respectively. The acquired three images have the same sensor parameters such as the ascending orbit, the imaging mode of FQ18, the incident angle of 37.5°, and the azimuth and range resolution with 4.96 and 4.73 m, respectively. The study area is covered by the acquired is Shangkuli Farm (119°07′∼121°49′E, 50°01′∼53°26′N) between city Erguna and Genhe, Inner Mongolia. Part of the farmland region is selected as for our experiment. The selected farmland region was planted mainly with rape (Brassica napus L), wheat (Triticum aestivum L) and other crops. Fig. 1 shows the PolSAR image (PauliRGB) for the experiments. Due to the difference in factors such as height, moisture content, and appearance of the same crop at different crop growth stages, different backscattering coefficients of the same farmland parcel with same crop at different growth stages occurred in the time series images like in Fig. 1A, 1B & 1C. They show different color on multi-temporal PolSAR images.

Reference map for segmentation evaluation

Reference map for segmentation evaluation, which is generated based on ground campaigned data and expert knowledge, is shown here as Fig. 2. In this study, the segmentation evaluation reference map will be used to evaluate the accuracy, so as to verify the performance of the proposed multi-temporal MS-SGP segmentation algorithm. For the generation process of Fig. 2, readers are referred to the details in Zhao et al. (2015). There are mainly five types of land cover in this region, including rape, wheat, shrubs, bare soil and other types. Among them, bare soil shows three different scattering characteristics due to different factors such as roughness, ridge direction and water content, so it can be subdivided into three categories.

Multi-temporal polarimetric SAR segmentation method

According to the data characteristics of multi-temporal PolSAR images, a multi-temporal MS-SGP segmentation algorithm suitable for multi-temporal PolSAR images is proposed on the basis of single-temporal MS-SGP segmentation algorithm. The technical flow is shown in Fig. 3. Firstly, the PolSAR data is pre-processed. Secondly, MS algorithm is used to pre-segment the image to obtain the initial segmentation unit, and the edge extraction algorithm is used to provide segmentation clues for SGP. Then, the similarity measurement matrix is constructed based on the segmentation unit and segmentation clues, and then the normalized cut criterion is used to complete the segmentation of image. Finally, the segmentation results are evaluated in detail based on the reference segmentation map obtained from the ground survey data.

Pre-segmentation

• (1) MS method for single-temporal SAR image over-segmentation

• MS is an iterative algorithm for nonparametric kernel density estimation (Fukunaga & Hostetler, 1975). Firstly, the offset mean value of the current point is calculated in the feature space, and the point is moved according to its offset mean value. Then, taking the location of the above moved point as the input of the new starting point and repeating the procedure until it converges to the convergence point of probability density function. The offset mean value is calculated as follows:

(1) $$M_h(x)={\displaystyle \frac{\mathrm{\Sigma }{}_{i=1}^{n}G[(x_i-x)/h]w(x_i-x)}{\mathrm{\Sigma }{}_{i=1}^{n}G[(x_i-x)/h]w(x_i)}}$$where $h$ is the window size of the kernel function, $G$ is the kernel function, in this paper, Gaussian function is selected as kernel function. $w\left(x_i\right)\ge 0$ is weight function assigned to each sampling point $x_i$, $x=\left(x_r,x_s\right)$ where $x_s$ is a two-dimensional space vector, which include the coordinate information of each pixel, $x_r$ is the feature vector (He et al., 2008).Three polarimetric scattering components decomposed by PolSAR Pauli are used as the features vector of $x_r$. The kernel function is shown as Eq. (2).

(2) $$G_{h_s,h_r}={\displaystyle \frac{C}{h_s^2{h}_r^3}g\left(\parallel {{\displaystyle \frac{x_s}{h_s}}}^2\parallel \right)g\left(\parallel {{\displaystyle \frac{x_r}{h_r}}}^2\parallel \right)}$$where $h_s$ and $h_r$ are window sizes for space vector and feature vector of each pixel, respectively, C is normalized constant, $g(\cdot )$ is a Gaussian function (Zhao et al., 2015). The detailed steps and parameter setting principles of PolSAR image segmentation using MS algorithm can be found in the literature He et al. (2008) and Zou et al. (2009).

• (2) Over-segmentation regions merging of multi-temporal images

• Over-segmentation regions of multi-temporal images are merged by the over-segmentation regions of each single-temporal PolSAR image. The merging strategy is shown in Fig. 4. Each square describes a pixel in images, the value of the square means the attribute of the object in the images. Different values or colors in the squares discriminate the different objects in the images.

• Even the over-segmentation result of the merged multi-temporal PolSAR image contains more regions than that of the single-temporal PolSAR image, the number of the regions in it is still less than the number of the pixels in the original image.

Edge information extraction

The construction of similarity measurement matrix needs to select appropriate features as segmentation clues, which is not only the core of transforming image segmentation problem into graph segmentation problem, but also the premise of segmentation. Edge information is very important information in image segmentation, especially when excellent segmentation results can’t be obtained by using information such as image gray level and color. For PolSAR images, the strong multiplicative noise makes the segmentation method based on pixel-based region growth unable to achieve application purpose, and relatively stable edge information is a excellent choice. Through the edge intensity information between pixels, the similarity between two pixels can be effectively measured. Therefore, the edge information of multi-temporal PolSAR images is used as the segmentation clue of SGP.

• (1) Edge information extraction of single-temporal

• In this paper, referring to the method proposed by Schou et al. (2003) and Zhao et al. (2015), edge detectors in four directions (0°, 45°, 90°, 135°) are set, as shown in Fig. 5. The window size can be determined according to the actual situation (3 $\times$ 3, 5 $\times$ 5, …).

Assuming that the central pixel of the edge detector is the edge, there should be a strong difference between the regions on both sides of the central pixel. Therefore, the Wishart test statistics suitable for PolSAR data is utilized to measure the difference between two regions. In the Wishart algorithm, the maximum likelihood-ratio function is utilized to test the equality of center covariance matrices of two regions. The hypothesis test equation is

(3) $$H_0:{\mathrm{\Sigma }}_i={\mathrm{\Sigma }}_{j}versus{H}_1:{\mathrm{\Sigma }}_i\ne {\mathrm{\Sigma }}_j$$where ${\mathrm{\Sigma }}_i$ and ${\mathrm{\Sigma }}_j$ are the center covariance matrices of the $i$th and $j$th regions, respectively. Let ${\mathrm{\Theta }}_i$ and ${\mathrm{\Theta }}_j$ be the sample covariance matrix data sets of the $i$th and $j$th regions, respectively. It is assumed that sample covariance matrices are spatially independent, therefore, the difference measure between the $i$th and $j$th regions can be derived from the likelihood ratio test. The test statistic equation is

(4) $$Q={\displaystyle \frac{L_{H_0}\left(\hat{\mathrm{\Sigma }}|{\mathrm{\Theta }}_i,{\mathrm{\Theta }}_j\right)}{L_{H_1}\left({\hat{\mathrm{\Sigma }}}_i,{\hat{\mathrm{\Sigma }}}_j|{\mathrm{\Theta }}_i,{\mathrm{\Theta }}_j\right)}={\displaystyle \frac{{\left|{\hat{\mathrm{\Sigma }}}_i\right|}^{n{N}_i}|{\hat{\mathrm{\Sigma }}}_j{|}^{n{N}_j}}{{\left|\hat{\mathrm{\Sigma }}\right|}^{n\left(N_i+N_j\right)}}}}$$where $L_{H_0}(\cdot )$ and $L_{H_1}(\cdot )$ are likelihood functions under different assumptions, respectively. $\mathrm{\Sigma }$ is the center covariance matrices of the whole region. $\hat{\mathrm{\Sigma }}$, ${\hat{\mathrm{\Sigma }}}_i$ and ${\hat{\mathrm{\Sigma }}}_j$ are maximum likelihood estimators of $\mathrm{\Sigma }$, ${\mathrm{\Sigma }}_i$ and ${\mathrm{\Sigma }}_j$, respectively. $N_i$ and $N_j$ are the numbers of samples in the $i$th and $j$th regions, respectively. $n$ is the number of looks. If the value of $Q$ is too low, the null hypothesis $H_0$ is rejected. Thus, the difference measure between the $i$th and $j$th regions can be defined as

(5) $$D\left(S_i,S_j\right)=-{\displaystyle \frac{1}{n}lnQ=\left(N_i+N_j\right)\mathrm{l}\mathrm{n}\left|\hat{\mathrm{\Sigma }}\right|-N_{i}ln\left|{\hat{\mathrm{\Sigma }}}_i\right|-N_{j}ln\left|{\hat{\mathrm{\Sigma }}}_j\right|}$$where $S_i$ and $S_{\mathrm{j}}$ represent the $i$th and $j$th regions, respectively. The difference measure D is symmetric. If $i=j$, $D\left(S_i,S_j\right)$ has a minimum value equaling to zero. If the $i$th and $j$th regions are more dissimilar, the value of $D\left(S_i,S_j\right)$ is higher. Details of the derivation of edge extraction algorithm can be found in, Cao et al. (2007) and Liu et al. (2013).

The Eq. (5) is used to calculate the $D\left(S_i,S_j\right)$ in four directions of each pixel, that is, the edge intensity values in different directions, and retain the maximum edge intensity value $D_{max}$ and its edge direction θ*. After edge extraction, the polarimetric information of PolSAR image is transformed into edge information.

• (2) Multi-temporal edge information fusion

• First, it is necessary to further optimize the edge extraction results of the single-temporal PolSAR image to determine the boundary elements and avoid positioning deviations. For any pixel $x$ on the image, the maximum edge intensity value $D_{max}\left(x\right)$ and edge direction ${\theta }^{\ast }\left(x\right)$ orientation have been determined. Compare the edge intensity values of the pixels on both sides perpendicular to the edge direction ${\theta }^{\ast }\left(x\right)$. If the maximum edge intensity value $D_{max}\left(x\right)$ of pixel $x$ is greater than or equal to the edge intensity value of pixels on both sides, then keep the value, otherwise, set to zero. For example, as shown in Figs. 6A and 6B, assuming that ${\theta }^{\ast }\left(x\right)$ is 0°, $D_{max}\left(x\right)$ can be preserved only if it is greater than or equal to the edge intensity values of the upper and lower pixels. Similarly, if the ${\theta }^{\ast }\left(x\right)$ is 90°, the $D_{max}\left(x\right)$ can be retained only if it is greater than or equal to the edge intensity values of the left and right pixels. Then, based on the edge optimization results of different time temporal, the edge intensity values of pixels in the same position are compared, and the maximum value is taken as the multi-temporal edge value, that is, the edge information fusion of multi-temporal PolSAR images is completed. The fusion result is shown in Fig. 6C. The result of multi-temporal edge information fusion will provide segmentation clues for subsequent SGP of multi-temporal PolSAR images.

Construction of similarity measurement matrix

On the basis of dividing the original pixels of the multi-temporal PolSAR image into many over-segmentation region units with similar statistical characteristics, it is necessary to find a pixel that can represent the spatial position of the entire over-segmentation region. The calculation method is shown in Fig. 7.

In the Fig. 7, p is the internal pixel of an over-segmentation region S, L(α) is the distance from the pixel p to the boundary of the region when the azimuth angle is α, when the value of α is determined, the extensibility of the pixel p in the over-segmentation region S can be expressed as:

(6) $$E(p\in S)=\prod _{i=1}^{n}L(\alpha \times i),n=2\pi /\alpha$$where the pixel corresponding to $max\left\{E(p\in S)\right\}$ is the pixel representing the S space position of the entire over-segmentation region. If the over-segmentation region is a regular shape (such as a rectangle, a circle, etc.), the pixel corresponding to $max\left\{E(p\in S)\right\}$ is the geometric centre of the region.

After obtaining the representative central pixel of the over-segmentation region of the multi-temporal PolSAR image, then, the edge fusion information of the multi-temporal PolSAR image can be used to measure the degree of similarity between the regions. The basic idea is shown in Fig. 8.

Figure 8A shows the Pauli RGB display of the PolSAR image, Fig. 8B is the local region, $S_1$, $S_2$ and $S_3$ are three segmentation regions. $p_1$, $p_2$ and $p_3$ are the corresponding spatial representative pixels. The similarity measure between the two regions can be represented by the maximum edge intensity value on the line between the representative pixels, as shown in Fig. 8C. There are obvious edges between pixels $p_1$ and $p_3$, and the similarity will be lower. Correspondingly, the similarity between pixel $p_1$ and $p_2$ is higher.

Therefore, based on multi-temporal edge fusion information, the difference between any two pixels $x$, $y$ can be defined $D_c(x,y)$. As shown in the following equation (Leung & Malik, 1998; Ersahin, Cumming & Ward, 2010; Ersahin, Cumming & Ward, 2014).

(7) $$D_c(x,y)=D^{\ast }\left(z^{\ast }\right),z^{\ast }=\arg {max}_{z\in l}{D}^{\ast }(z)$$where $D^{\ast }(\cdot )$ denotes the strength of edge maps after the oriented nonmaximal suppression, $l$ is the line joining $x$ and $y$, and $z^{\ast }$ is the location where the strength of edge maps after the oriented nonmaximal suppression is maximum along $l$. Then, the pairwise affinity is defined using a gaussian kernel (Shi & Malik, 2000; Ersahin, Cumming & Ward, 2010; Ersahin, Cumming & Ward, 2014).

(8) $$W(x,y)=\exp \left\{{\displaystyle \frac{-D_C^2(x,y)}{2{\sigma }_C^2}}\right\}$$where ${\sigma }_C$ is the scaling parameter for the kernel. Based on this, the construction of the similarity measurement matrix between the over-segmentation regions of the multi-temporal PolSAR image can be completed.

Method of segmentation evaluation

At present, there are many methods of segmentation evaluation, each of which has different advantages, disadvantages and applicable objects. In this paper, the improved method of maximum overlapping area proposed in reference Zhao et al. (2015) is used to evaluate the results of image segmentation. The segmentation accuracy calculated by this method reflects the degree of over-segmentation and under-segmentation of the image. The basic principle is shown in Fig. 9.

Firstly, for a reference segmentation region $SS$, there may be multiple segmentation regions to be evaluated ( $A,B,C\dots$) overlapping with it. Assuming that the overlapping region of the segmented region to be evaluated $A$ and $SS$ is the largest, the overlapping region is recorded as $A_{SS}$, then $(1-A_{SS}/\phantom{A_{SS}A}A)$ is defined as the under segmentation ratio (USR). Then, the percentage of correctly segmented pixels can be calculated by limiting the value of USR. That is, only the pixels with the largest overlap region and the under-segmentation ratio not greater than USR will be counted as the number of pixels for correct segmentation. For example, as shown in Fig. 9, if we set USR = 0.3, then $(1-A_{SS}/\phantom{A_{SS}A}A)$ = (1 $-$9/16) = 0.44 > 0.3, it can be considered that the $A_{SS}$ region is a wrongly segmented. At this time, there is no correctly segmented pixel for the reference region $SS$, and its segmentation accuracy is 0. When setting USR = 0.5, $(1-A_{SS}/\phantom{A_{SS}A}A)$ = (1 $-$9/16) < 0.5, the $A_{SS}$ region can be considered as the correct segmented pixel. For the reference region $SS$, the segmentation accuracy is the ratio of the number of pixels in the region $A_{SS}$ to the number of pixels in the region $SS$. Finally, the segmentation accuracy of the whole image is the average of the segmentation accuracy of all reference segmentation regions.

Segmentation experiment

The PolSAR images of three temporal are pre-processed by radiometric calibration, image registration, multi-look, filter and geocode. First of all, the main purpose of radiometric calibration in PolSARpro6.0 software (https://earth.esa.int/web/polsarpro/home) is to determine the relationship between the grayscale of radar image and the standard backscatter coefficient. Secondly, the registration of multi-temporal images is carried out in Gamma software (https://www.gamma-rs.ch/). The detailed registration process can be found in the literature Wang (2013). The image after registration is processed with 2 × 2 window multi-look processing in PolSARpro6.0 software, the pixel sizes in azimuth and range of PolSAR image after multi-look are about 9.92 and 9.47 m respectively. In order to reduce the influence of speckle noise, this paper uses Mean-Shift filtering method to filter, and its window is set to 5 × 5. Finally, the digital elevation model (DEM) data of 30 m resolution in the study area is used for geocoding in Gamma software. The projection of Radarsat-2 image is transformed into “UTM_Zone_51N” projection under WGS84 coordinate system, and resampled to obtain PolSAR polarization covariance matrix data with a spatial resolution of 10 m.

Then, the single-temporal PolSAR images are over-segmented by MS. In this paper, based on the existing literature reference (He et al., 2008; Zou et al., 2009; Zhao et al., 2015). The kernel function window values $h_s$ and $h_r$ of pixel space vector and feature vector are set to 7 and 6.5. And the minimum segmentation region parameter M plays a role in controlling the size of the segmentation region. The setting of this parameter only needs to ensure the over-segmentation degree of the image, which has a large setting space. In this paper, considering the operation cost of SGP for multi-temporal PolSAR images, a certain degree of attempt and comparison is made according to experience, and the segmentation results are qualitatively evaluated based on visual evaluation. The parameter M which ensures that each of the three temporal PolSAR images can be over-segmented and has a small computational cost is determined as the optimal parameter selected in this paper. As shown in Figs. 10A–10C, the number of over-segmentation regions of MS for different temporal is 118, 102 and 111, respectively, under setting of different M (M: 235, 235, 192). Based on this, the over-segmentation results produced by the initial segmentation of three temporal PolSAR images are merged, and the number of over-segmentation regions after merging is 1411. The merging result of multi-temporal over-segmentation regions is shown in Fig. 10D, with the 20130803 Pauli RGB as the display image.

In addition, the central position of the over-segmentation region is calculated according to Eq. (6). That is, the pixels that can represent the spatial position of the over-segmentation region of the single-temporal and multi-temporal PolSAR images are obtained. The result is shown as the yellow point in Fig. 11. It can be seen that these points are in the relative center of the region.

While the over-segmentation of multi-temporal PolSAR images is carried out, the edge information of multi-temporal PolSAR images is also extracted to obtain the segmentation clues of SGP. Firstly, the edge information of the single-temporal PolSAR image is extracted based on the edge detector, and the window is set to 7 $\times$ 7. Then, edge optimization based on rough edge extraction. Based on the edge optimization results of different temporal, the edge intensity values of pixels in the same position are compared, and the maximum value is taken as the multi-temporal edge value. As shown in Fig. 12. Among them, the edge information of the farmland parcels in the yellow rectangle in Fig. 12A, the parcels in the green rectangle in Fig. 12B and the parcels in the red rectangle in Fig. 12C are clearer and more complete compared with the same position of the other two images. The edge information of the three temporal PolSAR images is fused, so that the result after the fusion Fig. 12D contains rich edge information of the multi-temporal PolSAR image. The edge fusion results are used as the segmentation clues for the subsequent SGP, which can achieve better segmentation results than single-temporal PolSAR images.

Through the above-mentioned pixel points representing the spatial position of the over-segmentation regions of the multi-temporal PolSAR image Fig. 11D and the edge fusion result of the multi-temporal PolSAR image Fig. 12D, the similarity measurement matrix can be constructed. Then, the segmentation of the multi-temporal PolSAR image is completed by the normalized cut criterion. In this step, the segmentation scale can be controlled by setting the number of final segmentation regions. After a certain degree of attempt and comparison according to the experience, and the qualitative evaluation of the segmentation results based on visual evaluation, it can be found that the optimal segmentation effect can be achieved when the number of segmentation regions is set to 47. At this time, the farmland parcels of different sizes are well segmented and become independent objects. In addition, the details of segmentation results are excellent, and the regional consistency is well maintained. The final segmentation result is shown in Fig. 13. In order to show the effect of the multi-temporal MS-SGP segmentation algorithm, the PauliRGB of three temporal PolSAR images are all used as the display image, respectively.

In terms of the operation cost of the algorithm, the experimental image consists of 374 rows and 205 columns, with a total of 76,670 pixels. If the traditional pixel-based SGP is adopted to complete the segmentation of multi-temporal PolSAR images, the similarity measurement matrix of 76,670 × 76,670 size needs to be established through $C_{76670}^2$ operations, while the proposed method only needs $C_{1411}^2$ operations to establish a similarity measurement matrix of 1,411 × 1,411 size. Thus, the requirements of computing space and time are reduced by about 3,000 times. It can be seen that the pre-segmentation with MS can reduce the operation cost of SGP to a certain extent, and the global optimization strategy of SGP also is used to achieve excellent segmentation effect.

Quantitative evaluation and analysis

In the previous section, multi-temporal MS-SGP segmentation algorithm is used to obtain the segmentation results of multi-temporal PolSAR images. In order to evaluate the segmentation algorithm more objectively, a quantitative method is used to evaluate the pros and cons of the segmentation results. Firstly, the accuracy of the segmentation results of multi-temporal PolSAR images are evaluated based on the obtained segmentation reference images (Fig. 2), as shown in Fig. 14. It is calculated that when USR = 0.3, the segmentation accuracy of multi-temporal PolSAR image is 86.5%. Fig. 14 is a distribution diagram of correctly segmentation pixels in multi-temporal PolSAR images. Among them, the yellow region is the pixel of correct segmentation, the indigo region is the pixel of wrong segmentation, and the blue region is the pixel that do not participate in segmentation evaluation. It can be seen that the multi-temporal MS-SGP segmentation algorithm proposed in this paper can achieve preferable segmentation results. The farmland parcel unit of the experimental region can be segmented relatively completely, making it an independent farmland parcel object. The regional consistency is excellent, which lays a good foundation for the next image interpretation.

In order to clarify the influence of the parameter setting of each link on the segmentation accuracy of the multi-temporal MS-SGP segmentation algorithm proposed in this paper, the variation of segmentation accuracy with the number of final segmentation regions and the number of MS over-segmentation regions is analyzed, as shown in Figs. 15 and 16. Finally, in order to further discuss the influence of the choice of temporal on the segmentation accuracy, the segmentation accuracy of different combinations of single-temporal and multi-temporal is compared, as shown in Fig. 17. Based on the above analysis, users can fully understand the performance of the algorithm.

The trend of the segmentation accuracy of the multi-temporal MS-SGP segmentation algorithm with the number of final segmentation regions is shown in Fig. 15. Except for the different settings of the final number of segmentation regions, the other parameter settings are consistent with those in Fig. 10. It can be seen that when the number of regions is in the range of 20–40, the segmentation accuracy shows an increasing trend with the increase of the number of regions. Then it reached a peak and stabilized in the range of 40–120 regions, and then showed a downward trend. It can be seen that the segmentation effect is the best and stable when the number of regions in the map is in the range of 40–120, which is the segmentation scale that users can choose. In addition, Fig. 15 also verifies that the segmentation evaluation index used in this article can reflect both over-segmentation and under-segmentation. Whether the number of regions is too small or too many, the segmentation accuracy will be low.

The trend of the segmentation accuracy of the multi-temporal MS-SGP segmentation algorithm with the number of merged MS over-segmentation regions is shown in Fig. 16. Except for the different number of merged MS over-segmentation regions, the other parameter settings are the same as those in Fig. 13. It can be seen that the segmentation accuracy exhibits a fluctuating growth trend with the increase of the number of regions and stabilizes after reaching a peak. It shows that the number of regions in the over-segmentation stage of MS should not be too small, and it is necessary to avoid the impact of under-segmentation on the subsequent segmentation effect. The specific parameter setting should firstly ensure the realization of over-segmentation, and secondly consider the influence of the number of regions on the operation cost.

The variation trend of segmentation accuracy in the combination of temporal is shown in Fig. 17. The temporal data are three images acquired on May 23, August 3, and August 27, 2013. Except for the different temporal combination, the other parameter settings are the same as those in Figs. 10 and 13. It can be seen that the segmentation accuracy of the two-date combination is greater than that of the single-temporal, but is less than the segmentation accuracy of the three temporal combination. This shows that the addition of multi-temporal information can effectively improve the segmentation accuracy and obtain the ideal segmentation effect.

Comparison and analysis of single-temporal segmentation results

In order to further verify the effectiveness of the proposed method, the single-temporal MS-SGP segmentation algorithm is used to segment three temporal PolSAR images. Furthermore, the segmentation results of multi-temporal MS-SGP segmentation algorithm and single-temporal MS-SGP segmentation algorithm are compared and analyzed. For the single-temporal PolSAR image, the representative pixels of spatial position of over-segmentation region (Figs. 11A–11C) and edge information (Figs. 12A–12C) of three temporal were used as input of SGP. The number of segmentation regions in the final SGP is consistent with that in Fig. 13, which is 47. The results are shown in Fig. 18.

Figure 18A shows the segmentation results of the first temporal (20130523) PolSAR image. Due to the most crops had just been sown when the images were obtained in this period, the backscattering in this region was mainly soil surface scattering. Therefore, it is easy to be segmented when the difference of soil backscattering coefficient between different farmland parcels is large. As shown by the farmland parcel in the black rectangle, it has different color representations from the surrounding field parcels, and the difference is obvious. At this time, the farmland parcel has been well segmented and has become an independent object. However, the farmland parcels at the same location in the two temporal images of Figs. 18B and 18C are not segmented. The reason is that the rape in the two images is in the filling stage and mature stage respectively, growing well and the vegetation structure is similar. A large region of rape planting farmland parcels have similar backscattering coefficients and have the same color representation on images. However, the ridge that actually distinguishes the boundary of the farmland parcels can’t be reflected in the image due to its limited width (about 0.5 m) (Zou, Li & Tian, 2014). Therefore, it is not possible to effectively segment different field parcel units based on single-temporal PolSAR images.

Although the region in the yellow rectangle in Fig. 18A contains two types of ground targets, rape and shrubs. However, due to the small difference of backscattering coefficient and similar color representation of soil surface in this area, its separability is poor and it can’t be effectively segmented. On the other hand, the rape and shrub in the same region of the two images of Figs. 18B and 18C were well segmented, because that rape grows vigorously in these two images, and its backscattering is stronger, which is obviously higher than other ground targets. At this time, the backscattering coefficients of ground targets and their color representations in images are quite different between rape and shrub, so rape and shrub can be well separated.

Based on the obtained segmentation reference images (Fig. 2), the accuracy of segmentation results of single-temporal PolSAR images is evaluated, as shown in Fig. 19. It is calculated that when USR = 0.3, the segmentation accuracy of single-temporal PolSAR image are 42.4%, 43.8% and 21.8%, respectively. It can be seen that the segmentation results of single-temporal PolSAR images show a large area of wrong segmentation, and the final segmentation accuracy is poor. It can be seen that the segmentation effect of the multi-temporal MS-SGP segmentation algorithm proposed in this paper (Fig. 14) is better than that of the single-temporal MS-SGP segmentation algorithm.

It is not difficult to see from Figs. 18 and 19. In each period of images, the difference of surface scattering, secondary scattering and volume scattering between two types of objects or multiple types of objects is small, so it is difficult to effectively identify all objects by using single-temporal PolSAR images (Deng et al., 2014). Through the segmentation of multi-temporal PolSAR images, it is found that the backscattering coefficients of some two types of objects may be close in one period of images, but quite different in the other period of images. Therefore, it is beneficial to improve the segmentation accuracy to try to combine multi-stage images and make comprehensive use of the characteristics of images in different periods for multi-temporal MS-SGP segmentation. At the same time, it can distinguish the planting time sequence information and the growth status information of the ground targets which cannot be identified in the traditional algorithm, which is of great significance for the monitoring of crops.