# A Weighted Fourier and Wavelet-Like Shape Descriptor Based on IDSC for Object Recognition

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## Abstract

**:**

## 1. Introduction

## 2. The Weighted Fourier and Wavelet-Like Descriptor Based on IDSC

#### 2.1. Inner-Distance Shape Context

#### 2.2. Weighted Fourier and Wavelet-Like Descriptor IDSC-wFW

#### 2.2.1. Weighted Fourier Descriptor IDSC-wF

#### 2.2.2. Weight Wavelet-Like Descriptor IDSC-wW

#### 2.2.3. Weighted Fourier and Wavelet-Like Descriptor

#### 2.3. Invariance of IDSC-wFW

#### 2.4. Shape Dissimilarity Measure

## 3. Computational Complexity

## 4. Experiments

#### 4.1. Experimental Results on the MPEG-7 CE-1 Part B Shape Database

#### 4.2. Experimental Results on the Articulated Database

#### 4.3. Experimental Results on the 270 Plant Leaf Database

#### 4.4. Experimental Results on Sensitivity to Noise

## 5. Discussion

## 6. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**Seventy examples of all the categories in MPEG-7 CE1 Part B shape database, respectively, are on the left side of this figure. All of the various shapes of the class “Chicken” are on the right side of this figure.

**Figure 6.**The retrieval results of IDSC and IDSC-wFW on four queries. The odd columns are of IDSC-wFW and the even columns are of IDSC. The first row are the queries and the second row to the eleventh row are the second to the eleventh most similar shapes to queries.

IDSC-wFW (ours) | IDSC+DP | SC+DP | Shape Tree |
---|---|---|---|

$O(KlogN)$ | $O\left(K{N}^{2}\right)$ | $O\left(K{N}^{2}\right)$ | $O\left({N}^{4}\right)$ |

M | 2 | 4 | 6 | 8 | 10 | 12 | 14 | 16 |
---|---|---|---|---|---|---|---|---|

Retrieval Rate (%) | 73.02 | 78.23 | 80.55 | 81.45 | 81.53 | 81.64 | 81.61 | 81.60 |

J | 1 | 2 | 3 | 4 | 5 | 6 |
---|---|---|---|---|---|---|

Retrieval Rate (%) | 67.81 | 71.87 | 71.83 | 70.91 | 70.27 | 68.44 |

**Table 4.**Retrieval results on MPEG-7 CE-1 Part B shape database of IDSC-wFW with different M and J values.

M, J | 10, 2 | 12, 2 | 14, 2 | 16, 2 | 10, 3 | 12, 3 | 14, 3 | 16, 3 |
---|---|---|---|---|---|---|---|---|

Retrieval Rate (%) | 81.52 | 81.65 | 81.67 | 81.64 | 82.12 | 82.34 | 82.33 | 82.31 |

Method | Retrieval Rate (%) | Matching Time (ms) |
---|---|---|

IDSC-wFW (ours) | 82.34 | 11.4 |

IDSC+DP [3] | 85.40 | 6120.2 |

DIR [16] | 77.69 | 6.7 |

MDM [13] | 70.46 | 44.2 |

ASD&CCD [20] | 76.85 | 27,037.9 |

FD [12] | 68.14 | 4.1 |

FPD [11] | 65.52 | 3.3 |

Methods | 1st (%) | 2nd (%) | 3rd (%) | Average Accuracy (%) | Matching Time ($\mathsf{\mu}\mathit{s}$) |
---|---|---|---|---|---|

IDSC-wFW (ours) | 95.0 | 85.0 | 75.0 | 85.00 | 279.3 |

IDSC+DP [3] | 97.5 | 87.5 | 67.5 | 84.17 | 149,774.1 |

DIR [16] | 82.5 | 57.5 | 45.0 | 61.67 | 158.4 |

ASD&CCD [20] | 80.0 | 50.0 | 32.5 | 54.16 | 735,390.9 |

FD [12] | 77.5 | 37.5 | 42.5 | 52.50 | 105.6 |

FPD [11] | 70.0 | 50.0 | 32.5 | 50.83 | 75.7 |

MDM [13] | 62.5 | 30.0 | 27.5 | 40.00 | 1187.0 |

SC+DP [10] | 50.0 | 25.0 | 27.5 | 34.17 | 146,203.5 |

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**MDPI and ACS Style**

Zheng, Y.; Guo, B.; Li, C.; Yan, Y.
A Weighted Fourier and Wavelet-Like Shape Descriptor Based on IDSC for Object Recognition. *Symmetry* **2019**, *11*, 693.
https://doi.org/10.3390/sym11050693

**AMA Style**

Zheng Y, Guo B, Li C, Yan Y.
A Weighted Fourier and Wavelet-Like Shape Descriptor Based on IDSC for Object Recognition. *Symmetry*. 2019; 11(5):693.
https://doi.org/10.3390/sym11050693

**Chicago/Turabian Style**

Zheng, Yan, Baolong Guo, Cheng Li, and Yunyi Yan.
2019. "A Weighted Fourier and Wavelet-Like Shape Descriptor Based on IDSC for Object Recognition" *Symmetry* 11, no. 5: 693.
https://doi.org/10.3390/sym11050693