# Image Interpolation via Scanning Line Algorithm and Discontinuous B-Spline

^{1}

^{2}

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## Abstract

**:**

## 1. Introduction

#### 1.1. PSF-Based Interpolation

#### 1.2. Learning-Based Interpolation

#### 1.3. Edge-Directed Interpolation

#### 1.4. Geometry-Based Method

#### 1.5. Polynomial-Based Interpolation

## 2. ${\mathit{C}}^{-\mathbf{1}}$ Interpolation

## 3. Algorithm and Experiment Results

## 4. Conclusions

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## References

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**Figure 1.**B-Spline interpolation with two discontinuous points. (

**a**) is the traditional B-spline; (

**b**) is the discontinuous B-spline.

**Figure 2.**Results of image interpolation. From left to right are: (

**a**) original image; (

**b**) bi-linear interpolation; (

**c**) new edge directed interpolation (NEDI) interpolation; (

**d**) fast upsampling interpolation; (

**e**) ${C}^{-1}$ interpolation.

**Figure 3.**$4\times 4$ enlargement results of our image interpolation. (

**a**) $4\times 4$ enlargement result of Kodim05; (

**b**) $4\times 4$ enlargement result of Kodim23.

Bilinear | NEDI | Upsampling | ${\mathit{C}}^{\mathbf{-}\mathbf{1}}$ Interpolation | |
---|---|---|---|---|

baboon | 24.684 | 24.072 | 24.576 | 25.168 |

kodim05 | 23.817 | 23.545 | 23.878 | 24.269 |

kodim23 | 31.334 | 30.828 | 31.039 | 32.234 |

Bilinear | NEDI | Upsampling | ${\mathit{C}}^{\mathbf{-}\mathbf{1}}$ Interpolation | |
---|---|---|---|---|

baboon | 0.7245 | 0.7041 | 0.7448 | 0.7670 |

kodim05 | 0.7370 | 0.7281 | 0.7534 | 0.7689 |

kodim23 | 0.9249 | 0.9207 | 0.9185 | 0.9335 |

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**MDPI and ACS Style**

Liu, C.-m.; Wang, Z.-k.; Pang, H.-b.; Xue, J.-x.
Image Interpolation via Scanning Line Algorithm and Discontinuous B-Spline. *Math. Comput. Appl.* **2017**, *22*, 34.
https://doi.org/10.3390/mca22020034

**AMA Style**

Liu C-m, Wang Z-k, Pang H-b, Xue J-x.
Image Interpolation via Scanning Line Algorithm and Discontinuous B-Spline. *Mathematical and Computational Applications*. 2017; 22(2):34.
https://doi.org/10.3390/mca22020034

**Chicago/Turabian Style**

Liu, Cheng-ming, Ze-kun Wang, Hai-bo Pang, and Jun-xiao Xue.
2017. "Image Interpolation via Scanning Line Algorithm and Discontinuous B-Spline" *Mathematical and Computational Applications* 22, no. 2: 34.
https://doi.org/10.3390/mca22020034