# Multi-Temporal Sentinel-1 Backscatter and Coherence for Rainforest Mapping

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Background

#### 2.1. Temporal Decorrelation Model

#### 2.2. Texture Features

- Average (AVE), that describes the mean co-occurrence frequencies:$$\mathrm{AVE}=\frac{1}{2}\sum _{i=1}^{{N}_{g}}\phantom{\rule{4pt}{0ex}}i\xb7{\widehat{P}}_{s}\left(i\right).$$
- Cluster prominence (CLP), that expresses the tailedness of the image in terms of kurtosis:$$\mathrm{CLP}=\sum _{i=1}^{{N}_{g}}\phantom{\rule{4pt}{0ex}}{(i-2\mu )}^{4}\xb7{\widehat{P}}_{s}\left(i\right).$$
- Cluster shade (CLS), that observes the asymmetry of the image in terms of skewness:$$\mathrm{CLS}=\sum _{i=1}^{{N}_{g}}\phantom{\rule{4pt}{0ex}}{(i-2\mu )}^{3}\xb7{\widehat{P}}_{s}\left(i\right).$$
- Contrast (CON), that corresponds to a statistical image stretching:$$\mathrm{CON}=\sum _{j=1}^{{N}_{g}}\phantom{\rule{4pt}{0ex}}{j}^{2}\xb7{\widehat{P}}_{d}{\left(j\right)}^{2}.$$
- Correlation (COR), that explains the linear dependency of gray level values:$$\mathrm{COR}=\frac{1}{2}\xb7\sum _{i=1}^{{N}_{g}}\phantom{\rule{4pt}{0ex}}{(i-2\mu )}^{2}\xb7{\widehat{P}}_{s}\left(i\right)-\frac{1}{2}\xb7\sum _{j=1}^{{N}_{g}}\phantom{\rule{4pt}{0ex}}{j}^{2}\xb7{\widehat{P}}_{d}\left(j\right).$$
- Energy (ENE), that describes the uniformity of a texture:$$\mathrm{ENE}=\sum _{i=1}^{{N}_{g}}\phantom{\rule{4pt}{0ex}}{\widehat{P}}_{s}{\left(i\right)}^{2}\xb7\sum _{j=1}^{{N}_{g}}\phantom{\rule{4pt}{0ex}}{\widehat{P}}_{d}{\left(j\right)}^{2}.$$
- Entropy (ENT), that characterizes the degree of disorder in the image:$$\mathrm{ENT}=-\sum _{i=1}^{{N}_{g}}\phantom{\rule{4pt}{0ex}}{\widehat{P}}_{s}\left(i\right)\xb7lo{g}_{2}\left({\widehat{P}}_{s}\left(i\right)\right)-\sum _{j=1}^{{N}_{g}}\phantom{\rule{4pt}{0ex}}{\widehat{P}}_{d}\left(j\right)\xb7lo{g}_{2}\left({\widehat{P}}_{d}\left(j\right)\right).$$
- Homogeneity (HOM), that represents the degree of similarity among gray tones within an image:$$\mathrm{HOM}=\sum _{j=1}^{{N}_{g}}\phantom{\rule{4pt}{0ex}}\frac{1}{1+{j}^{2}}\xb7{\widehat{P}}_{d}\left(j\right).$$
- Variance (VAR), that defines the dispersion of shades of gray around the mean value $\mu $:$$\mathrm{VAR}=\frac{1}{2}\xb7\sum _{i=1}^{{N}_{g}}\phantom{\rule{4pt}{0ex}}{(i-2\mu )}^{2}\xb7{\widehat{P}}_{s}\left(i\right)+\frac{1}{2}\xb7\sum _{j=1}^{{N}_{g}}\phantom{\rule{4pt}{0ex}}{j}^{2}\xb7{\widehat{P}}_{d}\left(j\right).$$

## 3. Method

- the resolution of S-1 IW mode along azimuth and ground range, 14 m × 3.7 m respectively,
- the common goal of having a window centered in the current estimated pixel.

- case (ORIG): $\widehat{{\gamma}^{0}}$, $\widehat{\tau}$, ${\widehat{\rho}}_{\mathrm{LT}}$, and ${\theta}_{\mathrm{inc}}$,
- case (SADH): $\widehat{{\gamma}^{0}}$, $\widehat{\tau}$, ${\widehat{\rho}}_{\mathrm{LT}}$, ${\theta}_{\mathrm{inc}}$, $SAD{H}_{(1,0)}$, and $SAD{H}_{(0,1)}$.

## 4. Materials

## 5. Results

#### 5.1. Large-Scale Classification

#### 5.2. Analysis of Single Patches

## 6. Discussion

## 7. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## Appendix A

**Table A1.**Ancillary information about the Sentinel-1 acquisitions selected for the 12 short-time-series.

List of Acquisitions | |||||||||
---|---|---|---|---|---|---|---|---|---|

Name | ${\mathit{TS}}_{\mathbf{0}}$ | ${\mathit{TS}}_{\mathbf{1}}$ | ${\mathit{TS}}_{\mathbf{2}}$ | ${\mathit{TS}}_{\mathbf{3}}$ | |||||

Orbit | Date | Sensor | Mode | Type | Level | ID | ID | ID | ID |

2019.04.25 | S1B | IW | SLC | 1 | 432C | 4D3E | 416E | A798 | |

2019.05.01 | S1A | IW | SLC | 1 | 7E8C | 93EC | F1D1 | 744F | |

010 | 2019.05.07 | S1B | IW | SLC | 1 | E44A | F86E | E876 | EBCE |

2019.05.13 | S1A | IW | SLC | 1 | 5D14 | 7F74 | 1105 | CD19 | |

2019.05.19 | S1B | IW | SLC | 1 | 5239 | F6E8 | D8E8 | 148C | |

Stack | 1 | 2 | 3 | 4 | |||||

Name | ${\mathit{TS}}_{\mathbf{0}}$ | ||||||||

Orbit | Date | Sensor | Mode | Type | Level | ID | ID | ID | ID |

2019.04.28 | S1B | IW | SLC | 1 | 1E1A | ||||

2019.05.04 | S1A | IW | SLC | 1 | 036E | ||||

054 | 2019.05.10 | S1B | IW | SLC | 1 | E759 | |||

2019.05.16 | S1A | IW | SLC | 1 | 4387 | ||||

2019.05.22 | S1B | IW | SLC | 1 | 6425 | ||||

Stack | 5 | ||||||||

Name | ${\mathit{TS}}_{\mathbf{0}}$ | ${\mathit{TS}}_{\mathbf{1}}$ | ${\mathit{TS}}_{\mathbf{2}}$ | ${\mathit{TS}}_{\mathbf{3}}$ | |||||

Orbit | Date | Sensor | Mode | Type | Level | ID | ID | ID | ID |

2019.04.24 | S1A | IW | SLC | 1 | 3540 | D975 | 4377 | 16C4 | |

2019.04.30 | S1B | IW | SLC | 1 | 15A6 | C128 | DB79 | F212 | |

083 | 2019.05.06 | S1A | IW | SLC | 1 | 7107 | FEBF | 19E1 | 1048 |

2019.05.12 | S1B | IW | SLC | 1 | 1564 | 24AE | E331 | 430E | |

2019.05.18 | S1A | IW | SLC | 1 | 8EBB | 93C1 | 6547 | A78A | |

Stack | 6 | 7 | 8 | 9 | |||||

Name | ${\mathit{TS}}_{\mathbf{0}}$ | ${\mathit{TS}}_{\mathbf{1}}$ | ${\mathit{TS}}_{\mathbf{2}}$ | ||||||

Orbit | Date | Sensor | Mode | Type | Level | ID | ID | ID | ID |

2019.04.29 | S1A | IW | SLC | 1 | 831D | F0E2 | F0E2 | ||

2019.05.05 | S1B | IW | SLC | 1 | 2C50 | 2C50 | 5973 | ||

156 | 2019.05.11 | S1A | IW | SLC | 1 | B4E4 | 1AE8 | 1AE8 | |

2019.05.17 | S1B | IW | SLC | 1 | AEED | AEED | 8239 | ||

2019.05.23 | S1A | IW | SLC | 1 | E7BE | 0B54 | 0B54 | ||

Stack | 10 | 11 | 12 |

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**Figure 1.**Developed processing chain for short-time-series, based on the architecture presented in [7], with the integration of Sum and Difference Histograms (SADH) textures.

**Figure 2.**Sentinel-1 acquisition times description. A dot represents the master image, while the arrows represent the date of the slave images. The acquisitions centroid represents the average date among all the master acquisitions.

**Figure 3.**Finer Resolution Observation and Monitoring of Global Land Cover (FROM-GLC, 2017) reference map chosen for the training and validation stages. Black: invalid pixels (INV), blue: artificial surfaces (ART), green: forests (FOR), red: non-forested areas (NFR). The white numbers identify the corresponding stack, described in Table 2, while the numbers at the bottom show the orbits associated to the different swaths.

**Figure 4.**Comparison between the REF reference (

**left**), with in yellow the clearcuts (CUT) marked by PRODES between 2017 and 2019, and the final result of the Random Forests algorithm using SADH textures (

**right**). The white square identifies a region of interest in which the maps are clearly different. Such an area corresponds to the Pacaás Novos National Park and is separately analyzed in Figure 9.

**Figure 5.**Classification map of the stack number 7 summarized in Table 2. Black: invalid pixels (INV), blue: artificial surfaces (ART), green: forests (FOR), red: non-forested areas (NFR). White polygons delimit four patches of $512\times 512$ pixels used for the classification accuracy analysis. They are named (a), (b), (c), and (d).

**Figure 6.**Four analyzed patches of $512\times 512$ pixels are placed along the rows. They are indicated as (

**a**–

**d**), selected from the classification results over the stack number 7 defined in Table 2. Each column addresses to a different quantity: (REF) is the modified FROM-GLC reference with the clearcuts marked by PRODES between 2017 and 2019 as invalids (INV), (S-1, ORIG) is the Random Forests classification map using the input parameters from [7] only, (S-1, SADH) is the Random Forests result adding the SADH textures to the original parameters, (S-2, RGB) and (S-2, NDVI) are the optical True Color and NDVI maps, respectively, of Sentinel-2 acquisitions from the considered month. (REF), (S-1, ORIG), and (S-1, SADH) maps follow the legend described in Figure 5, while (S-2, NDVI) map comprises three classes: missing data (MDA) in black, forests (FOR) in green, and other structures (OTH) in white.

**Figure 7.**Confusion matrices for the whole test dataset, considering the two analyzed cases, (ORIG) and (SADH). The sum of all the elements along each column correspond to the total number of pixels associated to each class. The elements along the diagonal of the confusion matrix correspond to the correctly predicted pixels, class-by-class. The color associated to each element corresponds to the percentage obtained by normalizing the current element for the total number of samples for each specific class.

**Figure 8.**Feature importance for the two analyzed cases, (

**a**) ORIG and (

**b**) SADH; in particular, pie chart (

**c**) shows the distribution of importance for the SADH textures only.

**Figure 9.**Comparison between, from left to right, the selected reference (REF), the final result of the Random Forests algorithm (S-1, SADH) and the True Color (S-2, RGB) and NDVI (S-2, NDVI) map extracted from the best Sentinel-2 acquisition within the same observation month. The analyzed $1024\times 1024$ pixels patch corresponds to an area located around the mount Tracoa, in the Pacaás Novos National Park, Rondonia State, Brazil.

**Table 1.**List of the 22 features considered in Section 5. Column $ORIG$ shows the parameters used in [7], while columns $SAD{H}_{(1,0)}$ and $SAD{H}_{(0,1)}$ explain the textures extracted by using displacement vectors along both the azimuth $d=(1,0)$ and the slant-range $d=(0,1)$ directions, respectively, whose mathematical formulation is presented in Equations (4)–(12).

$\mathit{ORIG}$ | ${\mathit{SADH}}_{(\mathbf{1},\mathbf{0})}$ | ${\mathit{SADH}}_{(\mathbf{0},\mathbf{1})}$ |
---|---|---|

$\widehat{{\gamma}^{0}}$ | $AV{E}_{(1,0)}$ | $AV{E}_{(0,1)}$ |

$\widehat{\tau}$ | $CL{P}_{(1,0)}$ | $CL{P}_{(0,1)}$ |

${\widehat{\rho}}_{\mathrm{LT}}$ | $CL{S}_{(1,0)}$ | $CL{S}_{(0,1)}$ |

${\theta}_{\mathrm{inc}}$ | $CO{N}_{(1,0)}$ | $CO{N}_{(0,1)}$ |

$CO{R}_{(1,0)}$ | $CO{R}_{(0,1)}$ | |

$EN{E}_{(1,0)}$ | $EN{E}_{(0,1)}$ | |

$EN{T}_{(1,0)}$ | $EN{T}_{(0,1)}$ | |

$HO{M}_{(1,0)}$ | $HO{M}_{(0,1)}$ | |

$VA{R}_{(1,0)}$ | $VA{R}_{(0,1)}$ |

**Table 2.**Sentinel-1 stacks description. From left to right: stack number, relative orbit number, name of the time-series associated to the orbit number, corner coordinates in latitude (Lat. min and Lat. max) and longitude (Lon. min and Lon. max). The stacks marked with an asterisk are chosen for the validation, while the others are used for training the Random Forests algorithm.

Corner Coordinates [deg] | ||||||
---|---|---|---|---|---|---|

Stack | Orbit | Name | Lat. Min | Lat. Max | Lon. Min | Lon. Max |

1 | 010 | $T{S}_{0}$ | ${9}^{\circ}{40}^{\prime}{58.34}^{\u2033}\mathrm{S}$ | ${7}^{\circ}{42}^{\prime}{53.99}^{\u2033}\mathrm{S}$ | ${59}^{\circ}{52}^{\prime}{18.71}^{\u2033}\mathrm{W}$ | ${61}^{\circ}{44}^{\prime}{43.20}^{\u2033}\mathrm{W}$ |

2 | 010 | $T{S}_{1}$ | ${11}^{\circ}{16}^{\prime}{36.74}^{\u2033}\mathrm{S}$ | ${9}^{\circ}{15}^{\prime}{31.41}^{\u2033}\mathrm{S}$ | ${60}^{\circ}{12}^{\prime}{59.94}^{\u2033}\mathrm{W}$ | ${62}^{\circ}{5}^{\prime}{1.52}^{\u2033}\mathrm{W}$ |

3 | 010 | $T{S}_{2}$ | ${12}^{\circ}{45}^{\prime}{21.09}^{\u2033}\mathrm{S}$ | ${10}^{\circ}{43}^{\prime}{21.81}^{\u2033}\mathrm{S}$ | ${60}^{\circ}{33}^{\prime}{23.20}^{\u2033}\mathrm{W}$ | ${62}^{\circ}{26}^{\prime}{23.22}^{\u2033}\mathrm{W}$ |

4 | 010 | $T{S}_{3}$ | ${14}^{\circ}{10}^{\prime}{32.67}^{\u2033}\mathrm{S}$ | ${12}^{\circ}{12}^{\prime}{43.74}^{\u2033}\mathrm{S}$ | ${60}^{\circ}{53}^{\prime}{48.14}^{\u2033}\mathrm{W}$ | ${62}^{\circ}{46}^{\prime}{54.92}^{\u2033}\mathrm{W}$ |

5 | 054 | $T{S}_{0}$ | ${10}^{\circ}{12}^{\prime}{15.96}^{\u2033}\mathrm{S}$ | ${8}^{\circ}{4}^{\prime}{40.60}^{\u2033}\mathrm{S}$ | ${66}^{\circ}{8}^{\prime}{34.73}^{\u2033}\mathrm{W}$ | ${67}^{\circ}{59}^{\prime}{40.25}^{\u2033}\mathrm{W}$ |

6* | 083 | $T{S}_{0}$ | ${8}^{\circ}{51}^{\prime}{9.51}^{\u2033}\mathrm{S}$ | ${6}^{\circ}{50}^{\prime}{56.20}^{\u2033}\mathrm{S}$ | ${61}^{\circ}{42}^{\prime}{32.10}^{\u2033}\mathrm{W}$ | ${63}^{\circ}{36}^{\prime}{0.35}^{\u2033}\mathrm{W}$ |

7* | 083 | $T{S}_{1}$ | ${10}^{\circ}{22}^{\prime}{8.36}^{\u2033}\mathrm{S}$ | ${8}^{\circ}{32}^{\prime}{54.94}^{\u2033}\mathrm{S}$ | ${62}^{\circ}{4}^{\prime}{44.36}^{\u2033}\mathrm{W}$ | ${63}^{\circ}{37}^{\prime}{30.02}^{\u2033}\mathrm{W}$ |

8* | 083 | $T{S}_{2}$ | ${11}^{\circ}{51}^{\prime}{16.77}^{\u2033}\mathrm{S}$ | ${10}^{\circ}{2}^{\prime}{26.15}^{\u2033}\mathrm{S}$ | ${62}^{\circ}{25}^{\prime}{15.09}^{\u2033}\mathrm{W}$ | ${64}^{\circ}{19}^{\prime}{5.05}^{\u2033}\mathrm{W}$ |

9* | 083 | $T{S}_{3}$ | ${13}^{\circ}{24}^{\prime}{3.87}^{\u2033}\mathrm{S}$ | ${11}^{\circ}{32}^{\prime}{42.18}^{\u2033}\mathrm{S}$ | ${62}^{\circ}{44}^{\prime}{38.52}^{\u2033}\mathrm{W}$ | ${64}^{\circ}{40}^{\prime}{34.71}^{\u2033}\mathrm{W}$ |

10 | 156 | $T{S}_{0}$ | ${9}^{\circ}{24}^{\prime}{34.67}^{\u2033}\mathrm{S}$ | ${8}^{\circ}{4}^{\prime}{15.76}^{\u2033}\mathrm{S}$ | ${63}^{\circ}{53}^{\prime}{30.37}^{\u2033}\mathrm{W}$ | ${65}^{\circ}{56}^{\prime}{1.88}^{\u2033}\mathrm{W}$ |

11 | 156 | $T{S}_{1}$ | ${10}^{\circ}{15}^{\prime}{7.76}^{\u2033}\mathrm{S}$ | ${8}^{\circ}{48}^{\prime}{35.78}^{\u2033}\mathrm{S}$ | ${64}^{\circ}{5}^{\prime}{7.05}^{\u2033}\mathrm{W}$ | ${66}^{\circ}{8}^{\prime}{22.17}^{\u2033}\mathrm{W}$ |

12 | 156 | $T{S}_{2}$ | ${10}^{\circ}{36}^{\prime}{21.14}^{\u2033}\mathrm{S}$ | ${9}^{\circ}{46}^{\prime}{22.31}^{\u2033}\mathrm{S}$ | ${64}^{\circ}{9}^{\prime}{39.68}^{\u2033}\mathrm{W}$ | ${66}^{\circ}{19}^{\prime}{6.56}^{\u2033}\mathrm{W}$ |

**Table 3.**Finer Resolution Observation and Monitoring of Global Land Cover (FROM-GLC) classes aggregation strategy: artificial surfaces (ART), forests (FOR), non-forested areas (NFR), and water bodies and unclassified or no data as invalids (INV).

FROM-GLC | Higher-Level Class |
---|---|

Unclassified | |

Water | INV |

Snow/Ice | |

Impervious surface | ART |

Forest | FOR |

Cropland | NFR |

Grassland | |

Shrubland | |

Wetland | |

Tundra | |

Bareland |

Class | Stack 6 | Stack 7 | Stack 8 | Stack 9 | |
---|---|---|---|---|---|

ART | 10060 | 34890 | 6009 | 1054 | |

pixels | FOR | 14626324 | 7846234 | 9822268 | 10087671 |

NFR | 1655335 | 6194973 | 4193972 | 4280135 | |

Case | Metric | Stack 6 | Stack 7 | Stack 8 | Stack 9 |

ORIG | OA | 88.48% | 82.50% | 85.03% | 84.84% |

AA | 61.05% | 81.64% | 80.50% | 71.95% | |

SADH | OA | 91.90% | 84.26% | 86.49% | 87.66% |

AA | 65.11% | 85.59% | 85.06% | 82.46% |

**Table 5.**Overall accuracy (OA) and average accuracy (AA) for the four patches in Figure 6: patch (

**a**) and patch (

**b**) are characterized by urban areas, while patch (

**c**) and patch (

**d**) contain clear-cuts. ${\Delta}_{\mathrm{OA}}$ and ${\Delta}_{\mathrm{AA}}$ represent the increment in (OA) and (AA), respectively, when including textures within the classification.

Class | Patch (a) | Patch (b) | Patch (c) | Patch (d) | |
---|---|---|---|---|---|

ART | 20419 | 7706 | 0 | 0 | |

pixels | FOR | 118922 | 86290 | 216741 | 141669 |

NFR | 100506 | 155408 | 42073 | 117044 | |

Case | Metric | Patch (a) | Patch (b) | Patch (c) | Patch (d) |

ORIG | OA | 72.31% | 80.71% | 94.63% | 85.88% |

AA | 75.94% | 79.96% | 93.04% | 85.79% | |

SADH | OA | 73.60% | 82.49% | 95.75% | 87.98% |

AA | 78.15% | 85.98% | 94.28% | 87.88% | |

${\Delta}_{\mathrm{OA}}$ | 1.29% | 1.78% | 1.12% | 2.10% | |

${\Delta}_{\mathrm{AA}}$ | 2.21% | 6.02% | 1.24% | 2.09% |

© 2020 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Pulella, A.; Aragão Santos, R.; Sica, F.; Posovszky, P.; Rizzoli, P. Multi-Temporal Sentinel-1 Backscatter and Coherence for Rainforest Mapping. *Remote Sens.* **2020**, *12*, 847.
https://doi.org/10.3390/rs12050847

**AMA Style**

Pulella A, Aragão Santos R, Sica F, Posovszky P, Rizzoli P. Multi-Temporal Sentinel-1 Backscatter and Coherence for Rainforest Mapping. *Remote Sensing*. 2020; 12(5):847.
https://doi.org/10.3390/rs12050847

**Chicago/Turabian Style**

Pulella, Andrea, Rodrigo Aragão Santos, Francescopaolo Sica, Philipp Posovszky, and Paola Rizzoli. 2020. "Multi-Temporal Sentinel-1 Backscatter and Coherence for Rainforest Mapping" *Remote Sensing* 12, no. 5: 847.
https://doi.org/10.3390/rs12050847