# Semi-Automatic Algorithms for Estimation and Tracking of AP-Diameter of the IVC in Ultrasound Images

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## Abstract

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## 1. Introduction

## 2. Background and Related Work

## 3. Proposed Algorithms

#### 3.1. Active Ellipse Model

#### 3.2. Active Rectangle Model

## 4. Results

#### Tracking Performance

## 5. Discussion

#### 5.1. The Performance of the Proposed Algorithms

#### 5.2. Complexity Comparison

## 6. Conclusions

## Author Contributions

## Conflicts of Interest

## Abbreviations

AP | Anterior–posterior |

IVC | Inferior vena cava |

CSA | Cross sectional area. |

## References

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**Figure 1.**Flowchart for the proposed active ellipse algorithm for estimation and tracking of the IVC AP-diameter from ultrasound videos.

**Figure 3.**Flowchart for the proposed active rectangle algorithm for estimation and tracking of the IVC AP-diameter from ultrasound videos.

**Figure 6.**AP-diameter for the first video depicted in Figure 5, as measured by the manual measurement (red line), active circle algorithm (black line), active ellipse algorithm (green line) and active rectangle algorithm (blue line).

**Figure 7.**AP-diameter for the second video depicted in Figure 5, as measured by the manual measurement (red line), active circle algorithm (black line), active ellipse algorithm (green line) and active rectangle algorithm (blue line).

**Figure 8.**AP-diameter for the third sample video depicted in Figure 5, as measured by the manual measurement (red line), active circle algorithm (black line), active ellipse algorithm (green line) and active rectangle algorithm (blue line).

**Figure 9.**PDF of the AP-diameter estimation error w.r.t. manual measurement for the first sample video depicted in Figure 5, as measured by active circle algorithm (black line), active ellipse algorithm (red line) and active rectangle algorithm (green line).

**Figure 10.**PDF of the AP-diameter estimation error w.r.t. manual measurement for the second sample video depicted in Figure 5, as measured by active circle algorithm (black line), active ellipse algorithm (red line) and active rectangle algorithm (green line).

**Figure 11.**PDF of the AP-diameter estimation error w.r.t. manual measurement for the third sample video depicted in Figure 5, as measured by active circle algorithm (black line), active ellipse algorithm (red line) and active rectangle algorithm (green line).

Subject No. | (1) | (2) | (3) | (4) | (5) | (6) | (7) | (8) | Ave. | |
---|---|---|---|---|---|---|---|---|---|---|

Method | ||||||||||

Circle model | 0.10 | 0.16 | 0.16 | 0.25 | 0.25 | 0.10 | 0.11 | 0.26 | 0.17 | |

Ellipse model | 0.21 | 0.19 | 0.14 | 0.26 | 0.18 | 0.11 | 0.11 | 0.20 | 0.35 | |

Rectangle model | 0.08 | 0.11 | 0.12 | 0.23 | 0.14 | 0.10 | 0.10 | 0.18 | 0.12 |

Subject No. | (1) | (2) | (3) | (4) | (5) | (6) | (7) | (8) | |
---|---|---|---|---|---|---|---|---|---|

Method | |||||||||

Circle model | 0.06 | 0.29 | 0.48 | 0.57 | 0.75 | 0.41 | 0.44 | 0.43 | |

Ellipse model | 0.11 | 0.32 | 0.35 | 0.59 | 0.48 | 0.54 | 0.47 | 0.38 | |

Rectangle model | 0.05 | 0.18 | 0.19 | 0.42 | 0.28 | 0.37 | 0.39 | 0.29 |

**Table 3.**Correlation between the AP-diameters estimated by the three shape-based algorithms and manual measurement.

Subject No. | (1) | (2) | (3) | (4) | (5) | (6) | (7) | (8) | |
---|---|---|---|---|---|---|---|---|---|

Method | |||||||||

Circle model | 0.9987 | 0.9987 | 0.9652 | 0.7971 | 0.9985 | 0.9986 | 0.9988 | 0.9958 | |

Ellipse model | 0.9974 | 0.9985 | 0.9945 | 0.9981 | 0.9986 | 0.9985 | 0.9991 | 0.9850 | |

Rectangle model | 0.9993 | 0.9994 | 0.9949 | 0.9991 | 0.9992 | 0.9991 | 0.9994 | 0.9985 |

**Table 4.**The average position error for the three shape-based algorithms w.r.t. the manual measurement.

Subject No. | (1) | (2) | (3) | (4) | (5) | (6) | (7) | (8) | Ave. | |
---|---|---|---|---|---|---|---|---|---|---|

Method | ||||||||||

Circle model | 0.41 | 0.39 | 0.63 | 0.65 | 0.36 | 0.49 | 0.55 | 0.64 | 0.51 | |

Ellipse model | 0.42 | 0.43 | 0.31 | 0.47 | 0.44 | 0.49 | 0.54 | 0.56 | 0.45 | |

Rectangle model | 0.37 | 0.33 | 0.27 | 0.28 | 0.29 | 0.47 | 0.54 | 0.55 | 0.39 |

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**MDPI and ACS Style**

Karami, E.; Shehata, M.S.; Smith, A.
Semi-Automatic Algorithms for Estimation and Tracking of AP-Diameter of the IVC in Ultrasound Images. *J. Imaging* **2019**, *5*, 12.
https://doi.org/10.3390/jimaging5010012

**AMA Style**

Karami E, Shehata MS, Smith A.
Semi-Automatic Algorithms for Estimation and Tracking of AP-Diameter of the IVC in Ultrasound Images. *Journal of Imaging*. 2019; 5(1):12.
https://doi.org/10.3390/jimaging5010012

**Chicago/Turabian Style**

Karami, Ebrahim, Mohamed S. Shehata, and Andrew Smith.
2019. "Semi-Automatic Algorithms for Estimation and Tracking of AP-Diameter of the IVC in Ultrasound Images" *Journal of Imaging* 5, no. 1: 12.
https://doi.org/10.3390/jimaging5010012