# Point Cloud Coding Solutions, Subjective Assessment and Objective Measures: A Case Study

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## Abstract

**:**

## 1. Introduction

## 2. Point Cloud Coding Solutions

## 3. Subjective Assessment of Point Cloud Quality

#### 3.1. Point Cloud Datasets

#### 3.2. Subjective Evaluation of Point Clouds

## 4. Objective Measures of Point Cloud Quality

- Full-reference (FR) measures: The full original and degraded visual data are used.
- Reduced-reference (RR) measures: Only some features from the original visual data information and degraded visual data information are used.
- No-reference (NR) measures: Only degraded visual data information are used.

- measures based on point cloud projections computed on the 2D spaces onto which the points are projected; and
- geometry- and/or attribute-based measures computed on the original 3D space in which the point cloud information is represented.

#### 4.1. Measures Based on Point Cloud Projections

#### 4.2. Geometry- and/or Attribute-Based Measures

- Firstly, for each point ${a}_{j}$ in the first point cloud, corresponding point ${b}_{i}$ in the second point cloud is identified (e.g., by the nearest neighbor algorithm).
- Error vector ${E}_{i,j}$ is defined (similarly as for the p2p measure) as the difference vector between the arbitrary point in the first point cloud ${a}_{j}$ to the corresponding nearest point in the second point cloud ${b}_{i}$.
- Unit normal vector ${N}_{j}$ is calculated for each point ${a}_{j}$ in the first point cloud.
- The error vector is projected onto unit normal vector, by calculating the dot product between error vector ${E}_{i,j}$ and normal vector ${N}_{j}$, obtaining projected error vector.
- Point-to-plane measure is calculated as the mean of the squared magnitudes of all projected error vectors.

_{p2pl}is presented in Equation (4), RMSE

_{p2pl}in Equation (5), and Hausdorff

_{p2pl}in Equation (6).

## 5. Common Methods for the Analysis and Presentation of the Results from Subjective Assessment

## 6. Point Cloud Subjective and Objective Quality Evaluation—A Case Study

#### 6.1. Inter-Laboratory Correlation Results

#### 6.2. Objective Quality Measures and Correlation with MOS Scores

_{1}((10)), C

_{2}((11)), and C

_{3}((12)) functions. The RMSE

_{p2p}measure was used as square root of MSE (Equation (3)), while Hausdorff

_{p2p}distance used (1). RMSE

_{p2pl}was calculated as Equation (5) and Hausdorff

_{p2pl}as Equation (6). PSNR values were calculated similarly to Equation (7), but with ${p}^{2}$ in numerator and p value being defined as the largest diagonal distance of a bounding box of the point cloud, as defined in [40]. From the results in Table 4 and Table 5 and Figure 9, it can be seen that the best performing objective measure is RMSE

_{p2pl}, in both UC and UNIN laboratories. The second best measure is RMSE

_{p2p}, also in both tested laboratories (Table 4 and Table 5 and Figure 10). Other objective measures have lower correlation scores.

_{1}as fitting function for PCC calculation, in both UC and UNIN laboratories. The second best is C

_{2}, also in both laboratories, being only slightly lower than case with C

_{1}. When comparing RMSE

_{p2p}with PSNR

_{RMSE,p2p}and RMSE

_{p2pl}with PSNR

_{RMSE,p2pl}, it can be noticed that PSNR obtained lower correlation than RMSE. PSNR was calculated using p value defined as the largest diagonal distance of a bounding box of the point cloud.

_{1}between PSNR

_{RMSE,p2pl}and MOS is around 0.94 and PCC_C

_{1}between PSNR

_{RMSE,p2p}and MOS is around 0.87, in both UC and UNIN laboratories. In addition, best results were obtained using C

_{1}as fitting function for PCC calculation, in both UC and UNIN laboratories, while C

_{2}produces slightly lower PCC correlation between PSNR and MOS.

## 7. Conclusions

_{p2pl}measure, in both laboratories, while second best was RMSE

_{p2p}measure, also for both laboratories subjective scores sets.

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 2.**Dragon point cloud: (

**a**) octree subdivision, five levels; and (

**b**) equirectangular projection, 1024 × 1024 pixels and 16 bit depth.

**Figure 3.**Point clouds from described datasets: (

**a**) Longdress (857,966 points); (

**b**) Phil (356,258 points); (

**c**) APR C1 002 (37,243,844 points); (

**d**) Biplane (about 106 million points); (

**e**) Arco Valentino (1,530,939 points); (

**f**) Ipanema (15,028,108 points); and (

**g**) Würzburg marketplace (approximately 135 million points).

**Figure 4.**Different types of objective measures: (

**a**) Full-Reference (FR); (

**b**) Reduced-Reference (RR); and (

**c**) No-Reference (NR).

**Figure 5.**Original point cloud visualization: (

**a**) Longdress; (

**b**) Loot; (

**c**) Redandblack; (

**d**) Ricardo10; (

**e**) Sarah9 and (

**f**) Soldier.

**Figure 6.**MOS results with CI values for six point clouds, UC laboratory: (

**a**) Longdress; (

**b**) Loot; (

**c**) Redandblack; (

**d**) Ricardo10; (

**e**) Sarah9 and (

**f**) Soldier.

**Figure 7.**MOS results with CI values for six point clouds, UNIN laboratory: (

**a**) Longdress; (

**b**) Loot; (

**c**) Redandblack; (

**d**) Ricardo10; (

**e**) Sarah9 and (

**f**) Soldier.

UC | UNIN | |
---|---|---|

Monitor | Sony KD-49X8005C | Sony KD-55X8505C |

Screen Diagonal | 49″ | 55″ |

Resolution | 3840 × 2160 pixels | 3840 × 2160 pixels |

Viewing distance | 1.8 m ± 30 cm | 1.5 m ± 15 cm |

Male Observers | 7 | 10 |

Female Observers | 8 | 5 |

Overall | 15 | 15 |

Age range (years) | 18–54 | 19–59 |

Average age (years) | 28 | 29 |

Number of outliers | 0 | 0 |

C_{1} | C_{2} | C_{3} | C_{4} | No Fit | |
---|---|---|---|---|---|

PCC | 0.9892 | 0.9886 | 0.9886 | 0.9864 | 0.9864 |

SROCC | 0.9823 | 0.9823 | 0.9823 | 0.9823 | 0.9823 |

KROCC | 0.8992 | 0.8992 | 0.8992 | 0.8992 | 0.8992 |

RMSE | 0.1832 | 0.1883 | 0.1886 | 0.2057 | 0.2186 |

OR | 0.0938 | 0.0417 | 0.0729 | 0.0625 | 0.0729 |

C_{1} | C_{2} | C_{3} | C_{4} | No Fit | |
---|---|---|---|---|---|

PCC | 0.9878 | 0.9868 | 0.9870 | 0.9864 | 0.9864 |

SROCC | 0.9831 | 0.9823 | 0.9823 | 0.9823 | 0.9823 |

KROCC | 0.9032 | 0.8992 | 0.8992 | 0.8992 | 0.8992 |

RMSE | 0.2001 | 0.2079 | 0.2062 | 0.2111 | 0.2186 |

OR | 0.1042 | 0.0833 | 0.0938 | 0.0833 | 0.0729 |

**Table 4.**PCC, SROCC, KROCC, RMSE and OR between UC and different objective measures (best values are bolded).

RMSE_{p2p} | PSNR_{RMSE,p2p} | RMSE_{p2pl} | PSNR_{RMSE,p2pl} | Haus_{p2p} | PSNR_{Haus,p2p} | Haus_{p2pl} | PSNR_{Haus,p2pl} | |
---|---|---|---|---|---|---|---|---|

PCC_C_{1} | 0.8705 | 0.6047 | 0.9426 | 0.6666 | 0.6038 | 0.5148 | 0.6215 | 0.4907 |

PCC_C_{2} | 0.8694 | 0.5722 | 0.9418 | 0.6016 | 0.5723 | 0.4844 | 0.5722 | 0.4699 |

PCC_C_{3} | 0.8400 | 0.5599 | 0.9218 | 0.5832 | 0.4604 | 0.4918 | 0.5573 | 0.4717 |

SROCC | 0.8207 | 0.5522 | 0.9172 | 0.5752 | 0.4532 | 0.4491 | 0.5391 | 0.4314 |

KROCC | 0.6265 | 0.3933 | 0.7379 | 0.4281 | 0.3268 | 0.3220 | 0.3896 | 0.3153 |

RMSE_C_{1} | 0.5684 | 0.9197 | 0.3856 | 0.8608 | 0.9204 | 0.9899 | 0.9047 | 1.0061 |

OR_C_{1} | 0.0238 | 0.2143 | 0 | 0.1667 | 0.2024 | 0.1786 | 0.1905 | 0.2143 |

**Table 5.**PCC, SROCC, KROCC, RMSE and OR between UC and different objective measures (best values are bolded).

RMSE_{p2p} | PSNR_{RMSE,p2p} | RMSE_{p2pl} | PSNR_{RMSE,p2pl} | Haus_{p2p} | PSNR_{Haus,p2p} | Haus_{p2pl} | PSNR_{Haus,p2pl} | |
---|---|---|---|---|---|---|---|---|

PCC_C_{1} | 0.8803 | 0.6542 | 0.9423 | 0.7038 | 0.5721 | 0.5071 | 0.5923 | 0.5115 |

PCC_C_{2} | 0.8763 | 0.6181 | 0.9397 | 0.6424 | 0.5504 | 0.4782 | 0.5500 | 0.4989 |

PCC_C_{3} | 0.8446 | 0.6129 | 0.9225 | 0.6354 | 0.4161 | 0.4828 | 0.5262 | 0.4795 |

SROCC | 0.8212 | 0.5888 | 0.9194 | 0.6196 | 0.4187 | 0.4755 | 0.5379 | 0.4726 |

KROCC | 0.6205 | 0.4298 | 0.7451 | 0.4715 | 0.3055 | 0.3325 | 0.3954 | 0.3391 |

RMSE_C_{1} | 0.5683 | 0.9059 | 0.4011 | 0.8510 | 0.9824 | 1.0324 | 0.9651 | 1.0293 |

OR_C_{1} | 0.1429 | 0.2857 | 0.0714 | 0.2738 | 0.3333 | 0.3333 | 0.2976 | 0.3452 |

UC | UNIN | |||
---|---|---|---|---|

PSNR_{RMSE,p2p} | PSNR_{RMSE,p2pl} | PSNR_{RMSE,p2p} | PSNR_{RMSE,p2pl} | |

PCC_C_{1} | 0.8712 | 0.9440 | 0.8802 | 0.9426 |

PCC_C_{2} | 0.8693 | 0.9439 | 0.8768 | 0.9421 |

PCC_C_{3} | 0.8421 | 0.9279 | 0.8478 | 0.9290 |

SROCC | 0.8207 | 0.9172 | 0.8212 | 0.9194 |

KROCC | 0.6265 | 0.7379 | 0.6205 | 0.7451 |

RMSE_C_{1} | 0.5669 | 0.3810 | 0.5684 | 0.4000 |

OR_C_{1} | 0.0238 | 0 | 0.1429 | 0.0714 |

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Dumic, E.; da Silva Cruz, L.A.
Point Cloud Coding Solutions, Subjective Assessment and Objective Measures: A Case Study. *Symmetry* **2020**, *12*, 1955.
https://doi.org/10.3390/sym12121955

**AMA Style**

Dumic E, da Silva Cruz LA.
Point Cloud Coding Solutions, Subjective Assessment and Objective Measures: A Case Study. *Symmetry*. 2020; 12(12):1955.
https://doi.org/10.3390/sym12121955

**Chicago/Turabian Style**

Dumic, Emil, and Luis A. da Silva Cruz.
2020. "Point Cloud Coding Solutions, Subjective Assessment and Objective Measures: A Case Study" *Symmetry* 12, no. 12: 1955.
https://doi.org/10.3390/sym12121955