# An Automatic Car Counting System Using OverFeat Framework

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## Abstract

**:**

## 1. Introduction

## 2. Related Work

## 3. Methodology

#### 3.1. Background Subtraction Method

#### 3.1.1. Gaussian Mixture Model (GMM)

- model the values of a particular pixel as a mixture of Gaussians;
- determine which Gaussians may correspond to background colors-based on the persistence and the variance of each of the Gaussians;
- pixel values that do not fit the background distributions are considered foreground until there is a Gaussian that includes them;
- update the Gaussians;
- pixel values that do not match one of the pixel’s “background” Gaussians are grouped using connected components.

- ${\mathsf{\omega}}_{i,t}$ is an estimate of the weight of ith Gaussian in the mixture at time t (the portion of data accounted for by this Gaussian). Initially, we considered that all the Gaussians have the same weights.
- ${\mathsf{\mu}}_{i,t}$ is the mean value of the ith Gaussian in the mixture at time t.
- ${\sum}_{i,t}$ is the covariance matrix of the ith Gaussian in the mixture at time t.

**Stage 1:**

- Every new pixel value, ${X}_{t}$ is checked against the existing k Gaussian distributions until a match is found.

**Stage 2—No match:**

- If none of the k distributions match the current pixel value, the least probable distribution is discarded.
- A new distribution with the current value as its mean value, and an initially high variance and low prior weight is entered.

**Stage 3:**

- The prior weights of the k distribution at time t are adjusted as follows:$${\mathsf{\omega}}_{k,t}=\left(1-\mathsf{\alpha}\right){\mathsf{\omega}}_{k,t-1}+\mathsf{\alpha}\left({M}_{k,t}\right),$$

**Stage 4:**

#### 3.1.2. Implementation of the Background Subtraction Method

#### 3.2. OverFeat Framework

#### 3.2.1. Convolution Neural Network (CNN)

- Convolution
- Nonlinearity (ReLu)
- Pooling
- Fully-connected layer (FC)

#### Convolution

#### Nonlinearity (ReLu)

#### Pooling

#### Fully-Connected Layer (FC)

#### 3.2.2. OverFeat Architecture

#### 3.2.3. Implementation of the OverFeat Framework

#### 3.3. Commercial Software (Placemeter)

#### 3.4. Manual Counting

## 4. Datasets

#### 4.1. Training Data

#### 4.2. Testing Data

## 5. Result and Discussion

## 6. Conclusions

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## References

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**Figure 3.**The filter on the left might activate strongest when it encounters a horizontal line; the one in the middle for a vertical line and the right one for ‘L’ shape line.

Layer | 1 | 2 | 3 | 4 | 5 | 6 | 7 | Output 8 |
---|---|---|---|---|---|---|---|---|

Stage | conv + max | conv + max | conv | conv | conv + max | full | full | full |

#channels | 96 | 256 | 512 | 1024 | 1024 | 3072 | 4096 | 1000 |

Filter size | 11 × 11 | 5 × 5 | 3 × 3 | 3 × 3 | 3 × 3 | - | - | - |

Conv. stride | 4 × 4 | 1 × 1 | 1 × 1 | 1 × 1 | 1 × 1 | - | - | - |

Pooling size | 2 × 2 | 2 × 2 | - | - | 2 × 2 | |||

Pooling stride | 2 × 2 | 2 × 2 | - | - | 2 × 2 | - | - | - |

Zero-Padding size | - | - | 1 × 1 × 1 × 1 | 1 × 1 × 1 × 1 | 1 × 1 × 1 × 1 | - | - | - |

Spatial input size | 231 × 231 | 24 × 24 | 12 × 12 | 12 × 12 | 12 × 12 | 6 × 6 | 1 × 1 | 1 × 1 |

Camera | Time Duration (Local Time) | Manual Counts | Placemeter | BSM | OverFeat |
---|---|---|---|---|---|

C34 | 10:00–11:00 | 879 | 582 (66.21%) | 597 (67.91%) | 910 (96.47%) |

18:00–19:00 | 2075 | 1467 (70.96%) | 1335 (64.33%) | 2120 (99.97%) | |

C35 | 07:00–08:00 | 1862 | 1332 (71.53%) | 2236 (79.91%) | 1902 (97.85%) |

C66 | 11:00–12:00 | 1978 | 1393 (70.42%) | 1674 (84.63%) | 1942 (98.17%) |

23:00–00:00 | 549 | 335 (61.02%) | 108 (19.67%) | 566 (99.96%) | |

C73 | 11:00–11:10 (for 10 min) | 270 | 156 (57.77%) | 151 (52.92%) | 255 (94.44%) |

C103 | 07:00–08:00 | 210 | 145 (69.04%) | 372 (22.85%) | 225 (92.85%) |

11:00–12:00 | 579 | 432 (74.61%) | 463 (79.96%) | 619 (93.09%) | |

Under the bridge | 09:00-09:01 (1 min) | 52 | - | 50 (96.15%) | 54 (96.15%) |

Average | - | - | 67.69% | 63.14% | 96.55% |

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**MDPI and ACS Style**

Biswas, D.; Su, H.; Wang, C.; Blankenship, J.; Stevanovic, A.
An Automatic Car Counting System Using OverFeat Framework. *Sensors* **2017**, *17*, 1535.
https://doi.org/10.3390/s17071535

**AMA Style**

Biswas D, Su H, Wang C, Blankenship J, Stevanovic A.
An Automatic Car Counting System Using OverFeat Framework. *Sensors*. 2017; 17(7):1535.
https://doi.org/10.3390/s17071535

**Chicago/Turabian Style**

Biswas, Debojit, Hongbo Su, Chengyi Wang, Jason Blankenship, and Aleksandar Stevanovic.
2017. "An Automatic Car Counting System Using OverFeat Framework" *Sensors* 17, no. 7: 1535.
https://doi.org/10.3390/s17071535