# Effects of Different Parameter Settings for 3D Data Smoothing and Mesh Simplification on Near Real-Time 3D Reconstruction of High Resolution Bioceramic Bone Void Filling Medical Images

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## Abstract

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## 1. Introduction

- To compare Marching Cubes and Marching Tetrahedra in terms of reconstruction accuracy for large image dataset;
- To optimize the better surface rendering technique towards near real-time rendering and higher reconstruction accuracy, lower reconstruction and rendering time, and a lower number of vertices and faces by experimenting on different parameter value combinations;
- To study the effects of the improvements’ different parameter values on the reconstruction accuracy, reconstruction time, rendering time, and the number of vertices and faces.

## 2. Materials and Methods

## 3. Results

#### 3.1. Marching Cubes vs. Marching Tetrahedra

#### 3.2. Proposed Improved Marching Cubes with Different Parameter Value Combinations

#### 3.2.1. Effect of Convolution Kernel Size and Reduction Factor on Reconstruction Accuracy

#### 3.2.2. Effect of Convolution Kernel Size and Reduction Factor on Reconstruction Time

#### 3.2.3. Effect of Convolution Kernel Size and Reduction Factor on Rendering Time

#### 3.2.4. Effect of Convolution Kernel Size and Reduction Factor on Number of Vertices and Faces

#### 3.3. Marching Cubes vs. Wang et al. vs. Wi et al. vs. Proposed Enhancement

## 4. Discussion

- Image downsampling or downsizing before reconstruction;
- Stronger GPU and CPU with more cores;
- Experimenting with more convolution kernel sizes;
- Different mesh simplification approaches;
- Testing with more medical image datasets that can be processed at the same time;
- Implementing with languages like C++;
- Different metrics to evaluate the reconstruction accuracy;
- Different code optimization approaches;
- Support different GPU products like GPU from AMD.

## 5. Conclusions

- The larger the convolution kernel size, the higher the reconstruction accuracy;
- The reduction factor does not affect the reconstruction accuracy;
- The larger the convolution kernel size, the higher the reconstruction time;
- The reduction factor has an effect on the reconstruction time but no specific growth pattern can be deduced from the graphs; thus, the effect is random;
- The larger the convolution kernel size, the lower the rendering time;
- The higher the reduction factor, the higher the rendering time, up until the reduction factor of 0.7 where it stopped increasing;
- The larger the convolution kernel size, the lower the number of vertices and faces;
- The higher the reduction factor, the higher the number of vertices and faces, up until the reduction factor of 0.7 where it stopped increasing;
- Different convolution kernels do not affect the result of the reconstruction qualitatively and quantitatively, except for the reconstruction time.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## Appendix A

**Table A1.**SSIM, MS-SSIM, reconstruction time, rendering time, and number of vertices and faces for Marching Cubes and proposed improved Marching Cubes with different parameter combinations.

Reconstruction Method | SSIM (%) | MS-SSIM (%) | Reconstruction Time (s) | Rendering Time (s) | Vertices | Faces |
---|---|---|---|---|---|---|

MC | 87.68 | 82.32 | 373.62 | 20.87 | 2,550,055 | 5,108,402 |

MC Box S 3 RF 0.1 | 87.67 | 82.32 | 117.14 | 2.05 | 369,786 | 740,229 |

MC Box S 5 RF 0.1 | 87.69 | 82.35 | 120.43 | 1.64 | 342,443 | 683,804 |

MC Box S 11 RF 0.1 | 87.77 | 82.48 | 159.81 | 1.52 | 315,490 | 629,003 |

MC Gaussian S 3 RF 0.1 | 87.67 | 82.32 | 115.37 | 1.82 | 369,786 | 740,229 |

MC Gaussian S 5 RF 0.1 | 87.69 | 82.35 | 117.45 | 1.66 | 342,443 | 683,804 |

MC Gaussian S 11 RF 0.1 | 87.77 | 82.48 | 146.73 | 1.53 | 315,490 | 629,003 |

MC Box S 3 RF 0.2 | 87.66 | 82.31 | 114.69 | 3.76 | 738,421 | 1,480,457 |

MC Box S 5 RF 0.2 | 87.69 | 82.34 | 114.72 | 3.34 | 683,832 | 1,367,611 |

MC Box S 11 RF 0.2 | 87.77 | 82.47 | 144.22 | 3.07 | 630,077 | 1,258,006 |

MC Gaussian S 3 RF 0.2 | 87.66 | 82.31 | 115.91 | 3.68 | 738,421 | 1,480,457 |

MC Gaussian S 5 RF 0.2 | 87.69 | 82.34 | 125.07 | 3.45 | 683,832 | 1,367,611 |

MC Gaussian S 11 RF 0.2 | 87.77 | 82.47 | 149.84 | 3.06 | 630,077 | 1,258,006 |

MC Box S 3 RF 0.3 | 87.66 | 82.31 | 114.37 | 5.63 | 1,108,621 | 2,220,687 |

MC Gaussian S 5 RF 0.3 | 87.69 | 82.33 | 127.39 | 5.05 | 1,025,215 | 2,051,416 |

MC Gaussian S 11 RF 0.3 | 87.77 | 82.47 | 147.25 | 4.58 | 944,575 | 1,887,008 |

MC Box S 3 RF 0.4 | 87.66 | 82.31 | 111.94 | 7.56 | 1,478,169 | 2,960,916 |

MC Box S 5 RF 0.4 | 87.69 | 82.34 | 116.59 | 6.96 | 1,366,705 | 2,735,223 |

MC Box S 11 RF 0.4 | 87.77 | 82.47 | 150.07 | 6.2 | 1,259,023 | 2,516,012 |

MC Gaussian S 3 RF 0.4 | 87.66 | 82.31 | 124.41 | 7.39 | 1,478,169 | 2,960,916 |

MC Gaussian S 5 RF 0.4 | 87.69 | 82.34 | 121.19 | 6.83 | 1,366,705 | 2,735,223 |

MC Gaussian S 11 RF 0.4 | 87.77 | 82.47 | 147.41 | 6.11 | 1,259,023 | 2,516,012 |

MC Box S 3 RF 0.5 | 87.67 | 81.31 | 109.07 | 9.29 | 1,847,830 | 3,701,144 |

MC Box S 5 RF 0.5 | 87.69 | 82.34 | 118.32 | 8.36 | 1,708,398 | 3,419,029 |

MC Box S 11 RF 0.5 | 87.77 | 82.47 | 148.62 | 7.63 | 1,573,546 | 3,145,015 |

MC Gaussian S 3 RF 0.5 | 87.67 | 81.31 | 117.18 | 9.28 | 1,847,830 | 3,701,144 |

MC Gaussian S 5 RF 0.5 | 87.69 | 82.34 | 122.75 | 8.54 | 1,708,398 | 3,419,029 |

MC Gaussian S 11 RF 0.5 | 87.77 | 82.47 | 149.38 | 7.67 | 1,573,546 | 3,145,015 |

MC Box S 3 RF 0.6 | 87.67 | 81.31 | 99.41 | 11.13 | 2,217,200 | 4,441,374 |

MC Box S 5 RF 0.6 | 87.69 | 82.34 | 108.28 | 10.14 | 2,049,797 | 4,102,833 |

MC Box S 11 RF 0.6 | 87.77 | 82.47 | 128.75 | 9.29 | 1,887,987 | 3,774,019 |

MC Gaussian S 3 RF 0.6 | 87.67 | 81.31 | 111.83 | 10.98 | 2,217,200 | 4,441,374 |

MC Gaussian S 5 RF 0.6 | 87.69 | 82.34 | 116.61 | 9.95 | 2,049,797 | 4,102,833 |

MC Gaussian S 11 RF 0.6 | 87.77 | 82.47 | 136.32 | 9.21 | 1,887,987 | 3,774,019 |

MC Box S 3 RF 0.7 | 87.67 | 81.31 | 108.81 | 11.94 | 2,394,652 | 4,798,599 |

MC Box S 5 RF 0.7 | 87.69 | 82.34 | 120.53 | 11.08 | 2,275,927 | 4,556,820 |

MC Box S 11 RF 0.7 | 87.77 | 82.47 | 126.8 | 10.32 | 2,154,966 | 4,308,705 |

MC Gaussian S 3 RF 0.7 | 87.67 | 81.31 | 115.68 | 11.78 | 2,394,652 | 4,798,599 |

MC Gaussian S 5 RF 0.7 | 87.69 | 82.34 | 116.06 | 11.04 | 2,275,927 | 4,556,820 |

MC Gaussian S 11 RF 0.7 | 87.77 | 82.47 | 138.83 | 10.5 | 2,154,966 | 4,308,705 |

MC Box S 3 RF 0.8 | 87.67 | 81.31 | 99.71 | 11.8 | 2,394,652 | 4,798,599 |

MC Box S 5 RF 0.8 | 87.69 | 82.34 | 106.33 | 11.11 | 2,275,927 | 4,556,820 |

MC Box S 11 RF 0.8 | 87.77 | 82.47 | 128.9 | 10.57 | 2,154,966 | 4,308,705 |

MC Gaussian S 3 RF 0.8 | 87.67 | 81.31 | 111.12 | 11.99 | 2,394,652 | 4,798,599 |

MC Gaussian S 5 RF 0.8 | 87.69 | 82.34 | 128.52 | 11.11 | 2,275,927 | 4,556,820 |

MC Gaussian S 11 RF 0.8 | 87.77 | 82.47 | 148.97 | 10.47 | 2,154,966 | 4,308,705 |

MC Box S 3 RF 0.9 | 87.67 | 81.31 | 99.59 | 11.97 | 2,394,652 | 4,798,599 |

MC Box S 5 RF 0.9 | 87.69 | 82.34 | 107.82 | 11.01 | 2,275,927 | 4,556,820 |

MC Box S 11 RF 0.9 | 87.77 | 82.47 | 131.88 | 10.41 | 2,154,966 | 4,308,705 |

MC Gaussian S 3 RF 0.9 | 87.67 | 81.31 | 116.47 | 12.08 | 2,394,652 | 4,798,599 |

MC Gaussian S 5 RF 0.9 | 87.69 | 82.34 | 120.75 | 11.25 | 2,275,927 | 4,556,820 |

MC Gaussian S 11 RF 0.9 | 87.77 | 82.47 | 148.69 | 10.38 | 2,154,966 | 4,308,705 |

## Appendix B

Reduction Factor | Box Size 3 | Box Size 5 | Box Size 11 | Gaussian Size 3 | Gaussian Size 5 | Gaussian Size 11 |
---|---|---|---|---|---|---|

0.1 | −0.0051 | 0.2939 | 0.2659 | −0.0036 | 0.2962 | 0.2758 |

0.2 | −0.3190 | 0.2835 | 0.2642 | −0.3199 | 0.2756 | 0.2599 |

0.3 | −0.3347 | 0.2624 | 0.2482 | −0.3434 | 0.2592 | 0.2484 |

0.4 | −0.3488 | 0.2526 | 0.2327 | −0.3582 | 0.2492 | 0.2348 |

0.5 | −0.3625 | 0.2368 | 0.2204 | −0.3686 | 0.2333 | 0.2198 |

0.6 | −0.3710 | 0.2297 | 0.2219 | −0.3803 | 0.2235 | 0.2162 |

0.7 | −0.3857 | 0.2108 | 0.2122 | −0.3909 | 0.2142 | 0.2029 |

0.8 | −0.3787 | 0.2216 | 0.2104 | −0.3875 | 0.2047 | 0.1952 |

0.9 | −0.3788 | 0.2205 | 0.2082 | −0.3917 | 0.2105 | 0.1955 |

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**Figure 2.**3D models reconstructed with proposed improvement of different parameter value combinations.

**Figure 9.**Graph of reconstruction time against convolution kernel size for convolution kernel Gaussian.

Reconstruction Method | SSIM (%) | MS-SSIM (%) |
---|---|---|

Marching Cubes | 87.68 | 82.32 |

Marching Tetrahedra | 87.66 | 82.27 |

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## Share and Cite

**MDPI and ACS Style**

Chin, D.J.Y.; Mohamed, A.S.A.; Shariff, K.A.; Ab Wahab, M.N.; Ishikawa, K.
Effects of Different Parameter Settings for 3D Data Smoothing and Mesh Simplification on Near Real-Time 3D Reconstruction of High Resolution Bioceramic Bone Void Filling Medical Images. *Sensors* **2021**, *21*, 7955.
https://doi.org/10.3390/s21237955

**AMA Style**

Chin DJY, Mohamed ASA, Shariff KA, Ab Wahab MN, Ishikawa K.
Effects of Different Parameter Settings for 3D Data Smoothing and Mesh Simplification on Near Real-Time 3D Reconstruction of High Resolution Bioceramic Bone Void Filling Medical Images. *Sensors*. 2021; 21(23):7955.
https://doi.org/10.3390/s21237955

**Chicago/Turabian Style**

Chin, Daniel Jie Yuan, Ahmad Sufril Azlan Mohamed, Khairul Anuar Shariff, Mohd Nadhir Ab Wahab, and Kunio Ishikawa.
2021. "Effects of Different Parameter Settings for 3D Data Smoothing and Mesh Simplification on Near Real-Time 3D Reconstruction of High Resolution Bioceramic Bone Void Filling Medical Images" *Sensors* 21, no. 23: 7955.
https://doi.org/10.3390/s21237955