# Accurate Localization of Oil Tanks in Remote Sensing Images via FGMRST-Based CNN

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## Abstract

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## 1. Introduction

**object localization**is to determine the position of the object in a single object image, and

**object detection**is to identify all the objects and determine their positions in an image in which the type and number of objects are not fixed. In recent years, object localization in remote sensing images has been widely used in the investigation of agriculture and forestry, urban surveying, marine monitoring, and military reconnaissance [1,2]. The circle is a basic shape of objects in 2D images. Its localization technology is an important task in computer vision and pattern recognition, and it is also a hot research topic at home and abroad. The floating roof oil tank in remote a sensing image, as a representative of a man-fabricated object with the circular feature, plays an important role in both military and civil fields [3].

## 2. Methods

#### 2.1. CNN-Based Localization Method of the Oil Tank

- The main feature of an object with a circular structure such as the oil tank is on the circumference, but not in the circle (as shown in Figure 1). However, at present, the neural networks need to traverse all the pixels (as shown in Figure 2a), which leads to a large increase in unnecessary computation and a low processing efficiency.
- Due to the limitation of the receptive field, CNN gradually increases the receptive field and aggregates the spatial features by cascading networks (as shown in Figure 3a). Therefore, the larger the object size is, the deeper the network structure is required, which leads to a large number of parameters and computation.
- It depends on the abundance and quantity of training samples, which does not exist in the traditional parameterized feature extraction method.

#### 2.2. FGMRST-Based Localization Method of the Oil Tank

#### 2.2.1. Introduction of FRST Theory

**N**, where

**N**is the set of radii of the radially symmetric features to be detected. The value of the transform at the radius n indicates the contribution to radial symmetry of the gradients a distance n away from each point.

**g**(p) is pointing to, a distance n away from p, and the negatively affected pixel is the pixel a distance n away that the gradient is pointing directly away from.

**O**and a magnitude projection image

_{n}**M**are formed. For each pair of affected pixels, the corresponding point

_{n}**p**in the orientation projection image

_{+ve}**O**and magnitude projection image

_{n}**M**is incremented by 1 and ||

_{n}**g**(p)||, respectively, while the point corresponding to

**p**is decremented by these same quantities in each image (the orientation and magnitude projection images are initially zero). That is:

_{−ve}_{n}is a two-dimensional Gaussian, α is the radial strictness parameter, and k

_{n}is a scaling factor that normalizes

**M**and

_{n}**O**across different radii.

_{n}#### 2.2.2. An Improved FRST Algorithm Based on the Characteristics of Oil Tank Images—FGMRST

- When the floating roof of the oil tank is lower than the tank wall, there will be two areas that are brighter and darker in the image (as shown in Figure 7a), which makes positively affected pixels and negatively affected pixels at the boundary of the floating roof offset each other during transformation. Thus, the distribution of pixel values of orientation projection image and magnitude projection image is affected, and the final transformation result is affected. The solution to this problem in this study is to change the processing object of FRST from pixel to gradient modulus of pixel and cancel the positively affected pixel. Since the positively and negatively affected pixels play decisive roles in aggregating “black circle” (circle whose contour is darker than the background) and “white circle” (circle whose contour is brighter than the background), respectively, the coexistence of these two pixels makes FRST have the function of aggregating both “black circle” and “white circle” on an image. However, when the circle in the image is not a complete “black circle” or “white circle”, the coexistence of the positively and negatively affected pixels will interfere with each other, thus affecting the aggregation effect of circles. After all the pixels are processed into a gradient modulus, all circles in the image will become “white circles”, and then only negatively affected pixels need to be retained (because positively affected pixels have little effect on aggregating “white circles”), which solves the problem that some positively and negatively affected pixels offset each other during transformation.
- In the transformation results, almost only one aggregation area can be seen (see Figure 7b,c), and it is impossible to distinguish the center of the tank roof from the center of the circular-arc-shaped shadow cast by the sun on the floating roof. Therefore, FRST cannot complete the accurate localization task of the oil tank in this study. In view of the fact that the positions of the two circle centers are close, and the blur effect of the 3 × 3 Sobel operator used in FRST to calculate the gradient will have an adverse effect on accurate localizing, a simple first-order difference is used to calculate the gradient instead in this study.
- The effect of the transformation is greatly limited by the range of the input radius, and the wider the range, the worse the effect, which leads to the transformation being extremely dependent on the priori knowledge of radius. It can be inferred that the parameters related to the radius in FRST are particularly important to the result. The value of scaling factor k
_{n}is 9.9 by default when the radius is not 1, but this value is an empirical value given in an experiment with a radius range of 2–30. However, in this study and practice, the radius may exceed 30. Therefore, in this study, M_{n}and O_{n}are normalized by dividing all pixels in M_{n}and O_{n}by the maximum value of pixels in M_{n}and O_{n}respectively instead of k_{n}.

**N**, where

**N**is the set of radii of the radially symmetric features to be detected. The gradient modulus of pixel p is calculated to obtain ||

**g**(p)||. For the convenience of subsequent expression, let:

**g**(q) is pointing directly away from, a distance n away from q. The coordinates of the negatively affected pixel are given by:

**O**and a magnitude projection image

_{n}**M**are formed. For each affected pixel, the corresponding point

_{n}**q**in the orientation projection image

_{−ve}**O**and magnitude projection image

_{n}**M**is decremented by 1 and ||

_{n}**g**(q)|| (the orientation and magnitude projection images are initially zero). That is:

_{n}is a two-dimensional Gaussian, α is the radial strictness parameter.

#### 2.3. FGMRST-Based CNN Localization Method of the Oil Tank

#### 2.3.1. Overview of Methods

#### 2.3.2. Flow of Methods

- 1.
- Data set preparation

- 2.
- Pre-processing

- 3.
- Define CNN

- 4.
- Training network

- 5.
- Testing network on the test set

## 3. Experiments and Results

#### 3.1. Training Details

#### 3.2. Data sets

#### 3.3. Experimental Process and Results

- When the number of additional convolution layers is 0, the number of parameters and computation (params and MAC) of the two methods are the same, but the prediction error of the dual-channel method is less than that of the ordinary CNN method.
- The prediction error of adding 4 layers in the dual-channel method is close to that of adding 15 layers in the ordinary CNN method, but the amount of parameters (params) of the latter is 1.6 times that of the former, and the amount of computation (MAC) of the latter is 3.2 times that of the former.
- The number of parameters and computation (params and MAC) of the two methods increases with the increase in the number of network layers, but the dual-channel method grows more slowly. Therefore, the dual-channel method effectively reduces the number of parameters and computation, that is, improves the computational efficiency.

## 4. Conclusions

- In the FGMRST-based CNN method, the average prediction error of the dual-channel method is reduced by 14.64% compared with the ordinary CNN method, which effectively improves the accuracy.
- In the shallowest network (net_conv2), the average prediction error of the dual-channel method is reduced by 19.66% compared with the ordinary CNN method. In the deeper network (net_conv3), the average prediction error is reduced by 15.73%. In the deepest network (net_alex), the average prediction error is reduced by 8.54%. It shows that the proposed method is still better than the method using only CNN when the number of network layers increases.
- In the FGMRST-based CNN method, the dual-channel method significantly improves the computational efficiency compared with the ordinary CNN method.

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

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**Figure 1.**Structural diagram of floating roof oil tank. (

**a**) Original image; (

**b**) top of oil tank and circle of circular arc on the floating roof; (

**c**) three-dimensional structure of floating roof oil tank.

**Figure 2.**Comparison of the number of pixels traversed by CNN and FRST to process circular objects. (

**a**) Comparison of the number of pixels traversed by CNN in processing circular objects; (

**b**) comparison of the number of pixels traversed by FRST in processing circular objects

**Figure 3.**Schematic diagram of CNN, FGMRST/FRST, and dual-channel method applied to circular objects. (

**a**) CNN applied to circular objects; (

**b**) FGMRST/FRST applied to circular objects; (

**c**) dual-channel method applied to circular objects.

**Figure 7.**Comparison of results. (

**a**) Original image; (

**b**) when the radius is 23.5; (

**c**) when the radius range is [20,27]; (

**d**) when the radius range is [1,34].

**Figure 10.**Comparison of results. (

**a**) Original image; (

**b**) when the radius is 23.5; (

**c**) when the radius range is [20,27]; (

**d**) when the radius range is [1,34].

Calculation Location | Whether the Features at the Circumference Can Be Processed | ||
---|---|---|---|

Convolution | FGMRST | Convolution + FGMRST | |

Circumference | √ | × | √ |

Circle center | × | √ | √ |

Experimental Types | Way | Network Structures |
---|---|---|

Control group 1: original image→shallow CNN | Only using CNN | net_conv2 |

Control group 2: original image→deeper CNN | net_conv3 | |

Control group 3: original image→modified AlexNet | net_alex | |

Experimental group 1: FGMRST→shallow CNN | Tandem method | net_conv2 |

Experimental group 2: FGMRST→deeper CNN | net_conv3 | |

Experimental group 3: FGMRST→modified AlexNet | net_alex | |

Experimental group 4: original image + FGMRST→shallow CNN | Dual-channel method | net_conv2 |

Experimental group 5: original image + FGMRST→deeper CNN | net_conv3 | |

Experimental group 6: original image + FGMRST→modified AlexNet | net_alex |

Random Seed | Experimental Types | Way | Network Structures | Learning Rate | Average Prediction Errors (Unit: Pixel) |
---|---|---|---|---|---|

0 | Control group 1 | Only using CNN | net_conv2 | 0.0025 | 1.5509 |

Control group 2 | net_conv3 | 0.0025 | 1.2725 | ||

Control group 3 | net_alex | 0.00125 | 1.1822 | ||

Experimental group 1 | Tandem method | net_conv2 | 0.00125 | 1.6869 | |

Experimental group 2 | net_conv3 | 0.00125 | 1.5640 | ||

Experimental group 3 | net_alex | 0.00125 | 1.6629 | ||

Experimental group 4 | Dual-channel method | net_conv2 | 0.0025 | 1.2901 | |

Experimental group 5 | net_conv3 | 0.0025 | 1.1287 | ||

Experimental group 6 | net_alex | 0.00125 | 1.0355 ^{1} | ||

1 | Control group 1 | Only using CNN | net_conv2 | 0.0025 | 1.6793 |

Control group 2 | net_conv3 | 0.0025 | 1.4085 | ||

Control group 3 | net_alex | 0.00125 | 1.1198 | ||

Experimental group 1 | Tandem method | net_conv2 | 0.00125 | 1.7540 | |

Experimental group 2 | net_conv3 | 0.00125 | 1.7258 | ||

Experimental group 3 | net_alex | 0.00125 | 1.7109 | ||

Experimental group 4 | Dual-channel method | net_conv2 | 0.0025 | 1.3022 | |

Experimental group 5 | net_conv3 | 0.0025 | 1.1245 | ||

Experimental group 6 | net_alex | 0.00125 | 1.0675 |

^{1}Bold font is the best value under each random seed.

Way | Parameter | Additional Convolution Layers Added on net_conv3 | ||
---|---|---|---|---|

0 | 5 | 15 | ||

Only using CNN | Params(e+00M) | 2.357 | 3.095 | 4.571 |

MAC(e+00M) | 30.42 | 174.9 | 463.9 | |

Prediction errors (Unit: pixel) | 1.21 | 1.07 | 0.95 | |

Way | Parameter | Additional Convolution Layers Added on net_conv3 | ||

0 | 4 | 8 | ||

Dual-channel method | Params(e+00M) | 2.357 | 2.933 | 3.527 |

MAC(e+00M) | 30.42 | 145.1 | 260.8 | |

Prediction errors (Unit: pixel) | 1.16 | 0.96 | 0.88 |

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**MDPI and ACS Style**

Jiang, H.; Zhang, Y.; Guo, J.; Li, F.; Hu, Y.; Lei, B.; Ding, C.
Accurate Localization of Oil Tanks in Remote Sensing Images via FGMRST-Based CNN. *Remote Sens.* **2021**, *13*, 4646.
https://doi.org/10.3390/rs13224646

**AMA Style**

Jiang H, Zhang Y, Guo J, Li F, Hu Y, Lei B, Ding C.
Accurate Localization of Oil Tanks in Remote Sensing Images via FGMRST-Based CNN. *Remote Sensing*. 2021; 13(22):4646.
https://doi.org/10.3390/rs13224646

**Chicago/Turabian Style**

Jiang, Han, Yueting Zhang, Jiayi Guo, Fangfang Li, Yuxin Hu, Bin Lei, and Chibiao Ding.
2021. "Accurate Localization of Oil Tanks in Remote Sensing Images via FGMRST-Based CNN" *Remote Sensing* 13, no. 22: 4646.
https://doi.org/10.3390/rs13224646