# SCN: A Novel Shape Classification Algorithm Based on Convolutional Neural Network

^{*}

## Abstract

**:**

## 1. Introduction

- Performing the binary representation of object shapes in the image to obtain shape features;
- Calculating the similarity between two or more shapes according to certain measurement criteria;
- Matching and classifying shapes according to calculation results and premise tasks.

## 2. Related Work

#### 2.1. Traditional Algorithm

_{1}, p

_{2},…, p

_{n}}. The shape information of each point is represented by the relative vector set formed by all other points and represented by the histogram. The matching cost of point p

_{i}on the target P and point q

_{i}on the target Q is calculated, which is represented by C

_{i,j}:

_{i}(k) is the histogram of the shape of the point p

_{i}of the target P; and h

_{j}(k) is the histogram of the shape of point q

_{i}of target Q. The smaller the result is, the more similar they are. However, this descriptor has a poor matching result when there are too many backgrounds and noise points. Daliri [5] combined the shape context description method with strings of symbols to improve the result of shape matching. Ling [6,7] proposed an inner-distance shape context (IDSC) method using the inner distance between contour points, which achieved good results in shape retrieval, but the algorithm complexity was high. Thayananthan [8] combined shape context descriptors with chamfer matching and showed a good performance in object matching in complex scenes.

#### 2.2. Development of Deep Learning

## 3. Method

#### 3.1. Size of Convolution Kernel

#### 3.2. Fine-Tuning

#### 3.3. Addition of BN Layer

- Input data x
_{1}…x_{m}over a mini-batch B = {x_{1…m}} sequentially, which are the data ready to enter the activation function; - Find the data average by ${\mu}_{B}=\frac{1}{m}{\displaystyle \sum _{i=1}^{m}{x}_{i}}$;
- Using the formula ${\sigma}_{B}^{2}=\frac{1}{m}{\displaystyle \sum _{i=1}^{m}{({x}_{i}-{\mu}_{B})}^{2}}$ to obtain the variance of the input data;
- The data ire normalized by ${\widehat{x}}_{i}=\frac{{x}_{i}-{\mu}_{B}}{\sqrt{{\sigma}_{B}^{2}+\theta}}$, or referred to as normalization;
- The parameters $\gamma ,\beta $ are trained by the formula ${y}_{i}=\gamma {\widehat{x}}_{i}+\beta \equiv B{N}_{\gamma ,\beta}({x}_{i})$, and the output y value is obtained by linear transformation of $\gamma ,\beta $.

#### 3.4. Application of the Transposed Convolution Layer

#### 3.4.1. Transposed Convolution

#### 3.4.2. Checkerboard Effect

#### 3.5. Architecture

## 4. Experiment

#### 4.1. Performance on Animals Dataset

#### 4.2. Performance on Swedish Plant Leaf Dataset

#### 4.3. Performance on MPEG-7 CE-1 Part B DATASET

## 5. Application

## 6. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 4.**Perform convolution calculation on the 3 × 3 size image with padding = 1 and kernel size = 3 × 3.

**Figure 5.**The transposition of convolving a 3 × 3 kernel over a 4 × 4 input using unit strides (i.e., i = 4, k = 3, s = 1 and p = 0). It is equivalent to convolving a 3 × 3 kernel over a 2 × 2 input padded with a 2 × 2 border of zero using unit strides (i.e., i′ = 2, k′ = k, s′ = 1 and p′ = 2).

**Figure 7.**Perform transposed convolution calculation with (

**a**) stride = 2, kernel size = 5; (

**b**) stride = 2, kernel size = 4.

**Figure 17.**After getting adaptive binarization with saliency detection, it is input into the SCN network. Then, the binary image of the same class is obtained. Finally, the original image is obtained due to the corresponding labels, and the shape retrieval is completed.

Method | Classification Accuracy |
---|---|

FMSCCD [19] | 37.33% |

IDSC-WFW (a weighted Fourier and wavelet-like descriptor based on inner distance shape context) [34] | 49.36% |

DIR [17] | 46.45% |

AP & BAP [18] | 52.79% |

MDM [16] | 35.81% |

FPD (farthest point distance) [35] | 26.63% |

FD [15] | 27.97% |

FASD & FMSCCD (fast angle scale descriptor and FMSCCD) [19] | 37.85% |

FD-ASD (Fourier descriptor-angle scale descriptor) [36] | 27.44% |

ASD & CCD (angle scale descriptor and centroid contour distance) [36] | 39.30% |

SC + DP [14] | 67.27% |

IDSC + DP [13] | 70.99% |

HSC (Hierarchical string cuts) [37] | 56.80% |

SCN (ours) | 75.39% |

Method | Classification Accuracy |
---|---|

FMSCCD [19] | 87.98% |

IDSC-WFW [34] | 93.66% |

DIR [17] | 88.20% |

MDM [16] | 87.32% |

FPD [35] | 77.16% |

FD [15] | 82.40% |

FASD & FMSCCD [19] | 91.04% |

FDASD [36] | 87.32% |

ASD & CCD [36] | 85.14% |

MLBP (modified LBP) [38] | 96.83% |

SCN (ours) | 94.46% |

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**MDPI and ACS Style**

Zhang, C.; Zheng, Y.; Guo, B.; Li, C.; Liao, N.
SCN: A Novel Shape Classification Algorithm Based on Convolutional Neural Network. *Symmetry* **2021**, *13*, 499.
https://doi.org/10.3390/sym13030499

**AMA Style**

Zhang C, Zheng Y, Guo B, Li C, Liao N.
SCN: A Novel Shape Classification Algorithm Based on Convolutional Neural Network. *Symmetry*. 2021; 13(3):499.
https://doi.org/10.3390/sym13030499

**Chicago/Turabian Style**

Zhang, Chaoyan, Yan Zheng, Baolong Guo, Cheng Li, and Nannan Liao.
2021. "SCN: A Novel Shape Classification Algorithm Based on Convolutional Neural Network" *Symmetry* 13, no. 3: 499.
https://doi.org/10.3390/sym13030499