# Study of Three-Dimensional Image Brightness Loss in Stereoscopy

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## Abstract

**:**

## 1. Introduction

## 2. Three-Dimensional Image and Brightness Loss

#### 2.1. Theory of Stereo Vision

#### 2.2. Three-Dimensional Display and Three-Dimensional Glasses

**Figure 3.**Classification by color-code: (

**a**) red and cyan and (

**b**) red and green anaglyph 3D glasses used to create 3D stereo images.

#### 2.3. Three-Dimensional Image Brightness Loss

## 3. Experiment Design for Brightness Loss Measurement

Aperture | EV | Shutter Speed (s) | ISO | Scene Recording Brightness (lx) |
---|---|---|---|---|

F4 | −2–+2 | 1/50–1/3200 | 400 | 3200 and 7500 |

F5.6 | −2–+2 | 1/6–1/500 | 400 | 3200 and 7500 |

F7.1 | −2–+2 | 1/6–1/500 | 400 | 3200 and 7500 |

F9 | −2–+2 | 3–1/500 | 400 | 3200 and 7500 |

F10 | −2–+2 | 4–1/500 | 400 | 3200 and 7500 |

**Figure 6.**Schematic of darkroom for display brightness measurement [13].

Vendor | Model | 3D Glasses | Used Time (h) | Year |
---|---|---|---|---|

Vizio | VL320M 32-inch | Polarized Glasses | 50 | 2012 |

Vizio | M420KD 42-inch | Polarized Glasses | 45 | 2012 |

Sony | KDL-52XBR7 52-inch | Flash Glasses | 70 | 2011 |

- The camera was turned to M mode and images were recorded at the given shutter value, ensuring that the EV was 0.
- The images were recorded within the EV −2 and EV +2 ranges. As a result, each group had 19 datasets.
- The obtained images were presented on the television screen, and the image brightness was measured in the 2D and 3D modes.
- The data was collected for analysis using statistical product and service solutions (SPSS) software (IBM, Chicago, IL, USA).

## 4. Experimental Results

- ■
- Dependent variable (Y): Screen image brightness;
- ■
- Independent variables (X):
- (1)
- Screen size;
- (2)
- Screen recording brightness;
- (3)
- Mode (2D or 3D);
- (4)
- Photographic equipment EV;
- (5)
- Interactions between variables, as shown in Table 3.

Variable Type | Name | Values |
---|---|---|

Dependent Variable (Y) | Screen Image Brightness | Because of the nature of the luminance variables, there is no normal distribution, so a Box-Cox transform is used to convert the variable (λ = 0.3), so that ε (Note 1) has a normal distribution. |

Independent Variables (X) | (1) Screen Size | 32, 47, and 52 inch |

(2) Field Brightness | 3200 and 7500 lx | |

(3) 2D or 3D mode | 2D and 3D modes | |

(4) Photographic Equipment EV | Converted using the camera’s shutter aperture combination.
Conversion Formula: EV = log _{2} (N^{2}/t), where N is the aperture (F value), and t is the shutter speed (s). | |

(5) Interactions between Variables | The interactions between each variable. |

^{2}is used to illustrate the explanatory power of the entire pattern. However, this measure tends to overestimate phenomena depending on the sample size; the smaller the sample, the more prone the model is towards overestimation. Therefore, the majority of researchers use ${\overline{R}}^{2}$, which is the error variance and variable (Y) divided by the degree of freedom.

Brightness Regression Model | Correlation Coefficient (R) | Coefficient of Determination (R^{2}) | Adjusted Coefficient of Determination (${\overline{R}}^{2}$) |

0.995 | 0.990 | 0.990 |

Source | Sum of Squares | Degrees of Freedom | Mean Square | F Value |
---|---|---|---|---|

Return | 5382.379 | 10 | 538.238 | 10200.217 |

Residual | 55.617 | 1054 | 0.053 | |

Total | 5437.996 | 1064 |

Brightness Regression Variables | Non-Standardized Coefficients | Standardized Coefficients | T | |
---|---|---|---|---|

B | Standard Error | β | ||

(A) Constant | 21.259 | 0.115 | 184.892 | |

(1) Screen Size 1 | 1.905 | 0.145 | 0.399 | 13.180 |

(2) Screen Size 2 | 0.707 | 0.145 | 0.147 | 4.890 |

(B) Shooting Scene Brightness | 0.690 | 0.020 | 0.153 | 35.235 |

(C) 2D or 3D Mode | −5.749 | 0.119 | −1.270 | −48.340 |

(D) Photographic Equipment EV | −1.342 | 0.008 | −1.037 | −169.750 |

(E) Interaction Value of Variables | ||||

(1) and (C) | −0.314 | 0.030 | −0.051 | −10.499 |

(1) and (D) | −0.096 | 0.010 | −0.293 | −9.753 |

(2) and (D) | −0.045 | 0.010 | −0.137 | −4.549 |

(B) and (C) | −0.137 | 0.029 | −0.026 | −4.809 |

(C) and (D) | 0.311 | 0.008 | 0.991 | 37.541 |

_{i}is a random variable, X

_{i}is a known fixed constant, ε

_{i}is an unobservable, and i = 1, … , n

_{x}(i-th test; Y

_{i}is the reaction value corresponding to X

_{i}). Expressing the main variables in the experimental linear model formula yields

_{1}is the size of screen 1, X

_{2}is the size of screen 2, X

_{B}is the scene recording brightness, X

_{C}indicates the mode (2D or 3D), X

_{D}is the photographic equipment EV, and μ is the interaction value of the variables.

Shutter Speed (s) | 2D Mode Brightness Value (lx) | RGB Values | 3D Mode Brightness Value (lx) |
---|---|---|---|

1/125 | 6.6 | R:125, G:131, B:126 | 2.2 |

1/250 | 2.2 | R:74, G:79, B:74 | 0.7 |

Shutter Speed (s) | 2D Mode Brightness Value (lx) | RGB Values | 3D Mode Brightness Value (lx) |
---|---|---|---|

1/20 | 19.8 | R:193, G:198, B:194 | 6.6 |

1/40 | 9.4 | R:138, G:144, B:139 | 3.2 |

1/50 | 6.6 | R:117, G:123, B:117 | 2.2 |

1/80 | 3.2 | R:81, G:87, B:82 | 1.1 |

Experimental Item | Values |
---|---|

3D Image Brightness Degradation | 60.8% |

3D Image Brightness Degradation within 95% Confidence Level | 52.4%–69.2% |

## 5. Conclusions

## Acknowledgments

## Author Contributions

## Conflicts of Interest

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**MDPI and ACS Style**

Yu, H.-C.; Tsai, X.-H.; Luo, A.-C.; Wu, M.; Chen, S.-W. Study of Three-Dimensional Image Brightness Loss in Stereoscopy. *Appl. Sci.* **2015**, *5*, 926-941.
https://doi.org/10.3390/app5040926

**AMA Style**

Yu H-C, Tsai X-H, Luo A-C, Wu M, Chen S-W. Study of Three-Dimensional Image Brightness Loss in Stereoscopy. *Applied Sciences*. 2015; 5(4):926-941.
https://doi.org/10.3390/app5040926

**Chicago/Turabian Style**

Yu, Hsing-Cheng, Xie-Hong Tsai, An-Chun Luo, Ming Wu, and Sei-Wang Chen. 2015. "Study of Three-Dimensional Image Brightness Loss in Stereoscopy" *Applied Sciences* 5, no. 4: 926-941.
https://doi.org/10.3390/app5040926