# Efficient Vehicle Detection and Distance Estimation Based on Aggregated Channel Features and Inverse Perspective Mapping from a Single Camera

## Abstract

**:**

## 1. Introduction

#### 1.1. Related Works

#### 1.2. Definition of Problems

## 2. Proposed Methods

## 3. Vehicle Detection

#### 3.1. ROI Selection

#### 3.2. Extraction of Aggregated Channel Features

_{n}, Y

_{n}, and Z

_{n}are white color information. Figure 4 shows a flowchart of the vehicle detector processing based on ACF.

#### 3.3. Object Detection

## 4. Vehicle Tracking

## 5. Vehicle Distance Estimation

#### 5.1. Camera Parameters Extraction

#### 5.2. Inverse Perspective Transformation

## 6. Experimental Results

#### 6.1. Results of Vehicle Detection

#### 6.2. Results of Vehicle Distance Estimation

## 7. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 7.**Results of vehicle tracking: (

**a**) pixel-matching region for vehicle tracking in the detected vehicle region; (

**b**) pixel-matching process [47].

**Figure 8.**Results of the camera 3D position and pattern board images for extracting the camera parameters: (

**a**) camera parameter estimation using pattern boards; (

**b**) camera parameter estimation errors; (

**c**) position of pattern boards in the 3D space.

**Figure 12.**Results of vehicle average detection rate (

**a**) and log average detection error rate according to vehicle verification step (

**b**).

Step 1. Define learning data: m objects of interest (+1) and n non-objects of interest (−1): |

$\left({x}_{1},{y}_{1}\right),\dots ,\left({x}_{i},{y}_{i}\right),i=1,\dots ,N,N=m+n$ ${x}_{i}\in \left\{trainingsamples\right\},{y}_{i}\in \left\{1,-1\right\}$ |

Step 2. Initialization of the weight value of i-th weak classifier (h): |

$weigt{h}_{i}^{1}=\{\begin{array}{c}\frac{1}{m},{y}_{i}=-1\\ \frac{1}{n},{y}_{i}=+1\end{array}$ |

Step 3. Training step (repeat for t = 1, …, C, t++) |

(1) Normalization of the weight value of the i-th learning sample of the t-th weak classifier: |

$weigt{h}_{i}^{t}=\frac{weigh{t}_{i}^{t}}{{{\displaystyle \sum}}_{i=1}^{N}weigh{t}_{i}^{i}}$ |

(2) Calculation of error rate (${\epsilon}_{t}$) of t-th weak classifier: |

${\epsilon}_{t}={\displaystyle {\displaystyle \sum}_{i=1}^{N}}weigh{t}_{i}^{t}\left|{h}_{t}\left({x}_{i}\right)-{y}_{i}\right|$ |

(3) Selection of a weak classifier (h) with a minimum error rate. |

(4) Updating weight values: |

$weigt{h}_{i}^{t+1}=weigt{h}_{i}^{t}\times \{\begin{array}{c}{e}^{-{\alpha}_{t}},if{h}_{t}\left({x}_{i}\right)={y}_{i}\\ {e}^{{\alpha}_{t}},if{h}_{t}\left({x}_{i}\right)\ne {y}_{i}\end{array}$ ${\alpha}_{t}=log\frac{1}{{\beta}_{t}},{\beta}_{t}=\frac{{\epsilon}_{t}}{1-{\epsilon}_{t}}$ |

Step 4. Creation of a strong classifier (H(x)) as a linear combination of weak classifiers (h): |

$H\left(x\right)=sign\left({\displaystyle {\displaystyle \sum}_{n=1}^{C}}{\alpha}_{n}{h}_{n}\left(x\right)\right)$ |

Criteria | Method |
---|---|

position (x, y, width, height) | position = [25, 101, 846, 267] |

aspect ratio (width/height) | 0.6939 <= ratio <= 13.1700 |

brightness Ratio (avrIntensity) | 0.3563 <= avrIntensity <= 3.7889 |

vehicle template | template >= 0.7 |

**Table 3.**Experimental results for an average vehicle detection accuracy, error rate, and learning time requirements according to the vehicle detector setting parameters (T: learning cycle, S: non-vehicle area sampling factor).

Measures | Average Precision | Log Average Error Rate | Training Time (s) | |
---|---|---|---|---|

Parameters | ||||

T = 2, S = 2 | 0.7847 | 0.4917 | 283.57 | |

T = 2, S = 4 | 0.5791 | 0.6387 | 432.47 | |

T = 4, S = 2 | 0.8755 | 0.3017 | 592.30 | |

T = 4, S = 4 | 0.8422 | 0.2947 | 680.04 | |

T = 5, S = 2 | 0.8428 | 0.2901 | 751.25 | |

T = 5, S = 4 | 0.8433 | 0.2908 | 821.34 | |

T = 6, S = 2 | 0.8292 | 0.3161 | 1257.56 | |

T = 6, S = 4 | 0.8375 | 0.2906 | 1503.33 |

Measures | Average Precision | Recall (R) | Average Processing Time, (s) | |
---|---|---|---|---|

Features | ||||

Haar | 0.7310 | 0.4941 | 0.135 | |

LBP | 0.7641 | 0.5634 | 0.126 | |

HOG | 0.8375 | 0.4775 | 0.149 | |

Our methods | 0.8755 | 0.3017 | 0.121 |

Measure | Average Distance Estimation (m) | Accuracy (%) | |
---|---|---|---|

Distance | |||

10 m | 9.8 | 98.0 | |

20 m | 21.7 | 92.2 | |

30 m | 32.7 | 91.7 | |

40 m | 43.8 | 91.3 | |

50 m | 54.8 | 91.2 |

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**MDPI and ACS Style**

Kim, J.B.
Efficient Vehicle Detection and Distance Estimation Based on Aggregated Channel Features and Inverse Perspective Mapping from a Single Camera. *Symmetry* **2019**, *11*, 1205.
https://doi.org/10.3390/sym11101205

**AMA Style**

Kim JB.
Efficient Vehicle Detection and Distance Estimation Based on Aggregated Channel Features and Inverse Perspective Mapping from a Single Camera. *Symmetry*. 2019; 11(10):1205.
https://doi.org/10.3390/sym11101205

**Chicago/Turabian Style**

Kim, Jong Bae.
2019. "Efficient Vehicle Detection and Distance Estimation Based on Aggregated Channel Features and Inverse Perspective Mapping from a Single Camera" *Symmetry* 11, no. 10: 1205.
https://doi.org/10.3390/sym11101205