# Efficient Fiducial Point Detection of ECG QRS Complex Based on Polygonal Approximation

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## Abstract

**:**

## 1. Introduction

## 2. Composition of ECG Signal

- Power line interference: various high frequency noise according to country.
- Baseline wander: a low-frequency noise (0.15 up to 0.3 Hz). This noise results from the patient breathing and leads to a baseline shift in the signals.
- Electrode contract noise, electrode motion artifacts, muscle contractions, electrosurgical noise, instrumentation noise, and so on.

## 3. Polygonal Approximation of ECG Signal

- Separate the R-R section of the input signal. In this paper, we detect the R-peak by Pan’s method.
- After calculating the curvature for the separated R-R section, the curvature-based polygonal approximation technique is applied to select the initial vertices. Equation (1) represents the set of initial vertices.$${V}^{I}=\{{v}_{1}^{I},{v}_{2}^{I},\cdots ,{v}_{S}^{I}\}$$
- We apply the sequential polygonal approximation method to the interval between each initial vertex to select additional vertices. Equation (2) represents a set of ${N}_{{V}_{i}}-1$ additional vertices between the i-th initial vertex and the $i+1$-th initial vertex, and both end vertices coincide with the two initial vertices.$$\begin{array}{c}{V}_{i}=\{{v}_{i,0},\cdots ,{v}_{i,{N}_{{V}_{i}}}\}\phantom{\rule{5.69046pt}{0ex}}\\ {v}_{i,0}={v}_{i}^{I},\phantom{\rule{14.22636pt}{0ex}}{v}_{i,{N}_{{V}_{i}}}={v}_{i+1}^{I}\end{array}$$
- Dynamic programming is applied to the additional vertices to optimize their position. Equation (3) is a set of corrected vertices for the additional vertex set ${V}_{i}$.$$\begin{array}{c}{V}_{i}^{Opt}=\{{v}_{i,0}^{Opt},\cdots ,{v}_{i,{N}_{{V}_{i}}}^{Opt}\}\phantom{\rule{5.69046pt}{0ex}}\\ {v}_{i,0}^{Opt}={v}_{i,0}={v}_{i}^{I},\phantom{\rule{14.22636pt}{0ex}}{v}_{i,{N}_{{V}_{i}}}^{Opt}={v}_{i,{N}_{{V}_{i}}}={v}_{i+1}^{I}\end{array}$$
- Repeat steps 2–4 to proceed with polygonal approximation for the entire input signal. Equation (4) represents the set of ${N}_{V}$ vertices as the result of vertex selection.$$V=\{{v}_{1},\cdots ,{v}_{{N}_{V}}\},{v}_{i}=({v}_{{x}_{i}},{v}_{{y}_{i}})$$

## 4. Fiducial Point Detection Based on Polygonal Approximation

#### 4.1. Generate the Cumulative Signal

#### 4.2. Algorithm of Fiducial Point Detection

#### 4.2.1. Amplitude Difference between R-Peak and Vertex

#### 4.2.2. Time Difference between Reference Point and Vertex

#### 4.2.3. Angles with Neighbor Vertices

#### 4.2.4. Detecting the Fiducial Point

## 5. Experiment and Analysis of Results

#### 5.1. Experiment in QT-DB

#### 5.2. Experiment in MIT-BIH ADB

## 6. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## Abbreviations

ECG | Electrocardiogram |

PVC | Premature Ventricular Contraction |

PAC | Premature Atrial Contraction |

SVP | Supraventricular premature |

LBBB | Left Bundle Branch Block |

RBBB | Right Bundle Branch Block |

PM | PaceMaker |

MLII | Modified Lead II |

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Method | Ref | QRS Onset (ms) | QRS Offset (ms) |
---|---|---|---|

This work | - | −4.02 ± 7.99 | −5.45 ± 8.04 |

Yazdani and Vesin | [36] | 6.16 ± 8.3 | 1.5 ± 4.2 |

Martinez et al. | [20] | −0.2 ± 7.2 | 2.5 ± 8.9 |

Ghaffari et al. | [37] | −0.6 ± 8.0 | 0.3 ± 8.8 |

Manriquez and Zhang | [21] | −2.6 ± 7.1 | 0.7 ± 8.0 |

Manriquez and Zhang | [38] | 0.58 ± 7.18 | −0.95 ± 8.25 |

Dumont et al. | [39] | 0.3 ± 6.6 | −1.9 ± 8.3 |

Martinez et al. | [10] | 4.6 ± 7.7 | 0.8 ± 8.7 |

Jane et al. | [40] | −7.82 ± 10.86 | −3.64 ± 10.74 |

Laguna et al. | [23] | −3.6 ± 8.6 | −1.1 ± 8.3 |

Tolerance | [35] | 6.5 | 11.6 |

**Table 2.**Detailed results for stable data in Figure 12.

Record of PAC | ♯ of Beat | $\mathit{\sigma}$ of Onset (ms) | $\mathit{\sigma}$ of Offset (ms) | Record of PVC | ♯ of Beat | $\mathit{\sigma}$ of Onset (ms) | $\mathit{\sigma}$ of Offset (ms) |
---|---|---|---|---|---|---|---|

100 | 33 | 2.45 | 1.59 | 114 | 43 | 12.64 | 10.48 |

207 | 106 | 7.89 | 14.60 | 116 | 109 | 13.04 | 9.29 |

209 | 383 | 7.50 | 11.61 | 119 | 444 | 3.21 | 15.14 |

220 | 94 | 10.85 | 1.28 | 201 | 198 | 7.09 | 12.23 |

222 | 212 | 15.28 | 16.78 | 208 | 992 | 11.02 | 14.96 |

232 | 1381 | 8.66 | 24.80 | 221 | 396 | 10.31 | 10.45 |

Average | 8.77 | 11.78 | Average | 9.55 | 12.09 |

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**MDPI and ACS Style**

Lee, S.; Jeong, Y.; Park, D.; Yun, B.-J.; Park, K.H. Efficient Fiducial Point Detection of ECG QRS Complex Based on Polygonal Approximation. *Sensors* **2018**, *18*, 4502.
https://doi.org/10.3390/s18124502

**AMA Style**

Lee S, Jeong Y, Park D, Yun B-J, Park KH. Efficient Fiducial Point Detection of ECG QRS Complex Based on Polygonal Approximation. *Sensors*. 2018; 18(12):4502.
https://doi.org/10.3390/s18124502

**Chicago/Turabian Style**

Lee, Seungmin, Yoosoo Jeong, Daejin Park, Byoung-Ju Yun, and Kil Houm Park. 2018. "Efficient Fiducial Point Detection of ECG QRS Complex Based on Polygonal Approximation" *Sensors* 18, no. 12: 4502.
https://doi.org/10.3390/s18124502