# Active Contour Model Using Fast Fourier Transformation for Salient Object Detection

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## Abstract

**:**

## 1. Introduction

- A new hybrid active contour model using FFT comprising efficient features of the local region-based and global region-based fitting energies for salient object detection is proposed.
- Frequency domain has a property that can be used for discovering the salient object.
- Fourier force function is used to distinguish saliency objects from background for the active contour.
- Evaluating the proposed fast Fourier active contour model through a set of experiments using medical and synthetic images.

- The fast Fourier transform (FFT) is an effective process to design the discreate Fourier transform (DFT) time of series. The series takes advantages of the information that DFT coefficients can furnish iteratively to save considerable computational time.
- FFT not only set the computational problem, but also significantly reduces the associated round of errors computations.
- Frequency-based formulation provides simple characterization of the processing kernel.
- Automated smooth fitted curve during initialization time.
- Avoids re-initialization and re-iteration.
- Immediately draws curve on object boundary.
- Calculates accurate salient object with minimum complexity.
- Fast execution offers significant computational savings.

## 2. Related Work

#### 2.1. Active Contour (Snake) Formulations

#### 2.2. Chan-Vese Model

#### 2.3. Active Contour with Selective Local and Global Segmentation Model

## 3. Solution Implementing Fast Fourier Transformation

#### 3.1. Fourier Solution for Region Based Model

#### 3.2. The Local Force from the Gradient

#### 3.3. Fourier Force Function

## 4. Experimental Results and Discussion

Algorithm 1. The pseudo-code for the proposed algorithm. |

Input: the input image I, the initial level set function ${\varphi}^{0}$. |

Initialization: |

1: Initialization the Fourier level set function according to Equation (20). |

2: Initialize the related parameters: $\sigma =4,\tau =0.02$. |

Repeat: |

3: For 1 to T do |

4: Compute Magnitude using Fourier external function with Equation (21). |

5: Compute Fourier force function on Equation (22). |

6: Update the level set function according to Equation (23). |

7: end for |

8: If converge |

9: end |

10: Output: The resultant salient object $\varphi ={\varphi}^{T}$. |

#### 4.1. Robustness to Initial Curves

#### 4.2. Qualitative Analysis

#### 4.3. Quantitative Analysis

#### 4.4. Robustness to Noisy Images

## 5. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 2.**(

**a**) Consisting three original synthetic images, comparing results of the proposed model with DRLSE model [58], CV model [41], LIF model [22] on the basis of initial contour; (

**b**) comparing results of the proposed model with the DRLSE model [58], CV model [41], and LIF model [22] on the basis of final contour.

**Figure 8.**Comparison based on computation cost (image per second) between different state-of-the-arts algorithm and the proposed algorithm on 11 to 19 synthetic and medical images.

**Figure 9.**Comparison based on computation cost (iteration) between different state-of-the-arts algorithm and the proposed algorithm on 11 to 19 synthetic and medical images.

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**MDPI and ACS Style**

Khan, U.S.; Zhang, X.; Su, Y.
Active Contour Model Using Fast Fourier Transformation for Salient Object Detection. *Electronics* **2021**, *10*, 192.
https://doi.org/10.3390/electronics10020192

**AMA Style**

Khan US, Zhang X, Su Y.
Active Contour Model Using Fast Fourier Transformation for Salient Object Detection. *Electronics*. 2021; 10(2):192.
https://doi.org/10.3390/electronics10020192

**Chicago/Turabian Style**

Khan, Umer Sadiq, Xingjun Zhang, and Yuanqi Su.
2021. "Active Contour Model Using Fast Fourier Transformation for Salient Object Detection" *Electronics* 10, no. 2: 192.
https://doi.org/10.3390/electronics10020192