# Minimal Required Resolution to Capture the 3D Shape of the Human Back—A Practical Approach

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

## 3. Results

**Approach A—Frequency analysis of the ground-truth 3D representation**

^{−1}, corresponding to the capturing limit of the Photoneo MotionCam-3D. The most power (magnitude of frequencies) is contained in frequencies smaller than 0.1 mm

^{−1}, resulting in a wavelength of 10 mm. According to the Nyquist criteria, in theory, a sampling frequency of 0.2 mm

^{−1}is sufficient to capture the relevant frequencies contained in the signal. This translates to one sampling point every 5 mm. The Nyquist criteria, however, is only valid for a perfect signal without noise, and thus, in practice, oversampling must be used.

^{−1}, which translates to one sampling point every millimeter (oversampling of at least five times leads to a frequency that is ten times higher). The resulting frequency of 0.1 mm

^{−1}is used as the initial cut-off frequency for approaches B and C.

**Approach B—Comparison of the shape of the reduced-quality 3D representation with the ground-truth shape**

^{−1}from approach A, the error (MAE) is small (0.04 mm). With a cut-off frequency of 0.05 mm

^{−1}, the error remains small (0.13 mm). Applying a five-times oversampling to this cut-off frequency results in a required sampling point every 2 mm. With a cut-off frequency of 0.02 mm

^{−1}, the error starts to increase exponentially (1.33 mm). Applying a five-fold oversampling to this cut-off frequency results in a required sampling point every 5 mm. Therefore, the slope breakpoint is between 0.05 mm

^{−1}and 0.02 mm

^{−1}.

**Approach C—Comparison of the symmetry line of the reduced-quality 3D representation with its benchmark**

^{−1}and lower. The largest cut-off frequency of 0.1 mm

^{−1}was used as a reference, and thus the error (MAE between symmetry lines) is 0 mm. With a cut-off frequency of 0.05 mm

^{−1}, the error is small (2.1 mm). Applying a five-times oversampling to this cut-off frequency requires a sampling point every 2 mm. With a cut-off frequency of 0.02 mm

^{−1}, the error starts to increase exponentially (6.6 mm). Applying a five-fold oversampling to this cut-off frequency requires a sampling point every 5 mm. Therefore, the slope breakpoint is between 0.05 mm

^{−1}and 0.02 mm

^{−1}.

**Minimal spatial resolution**

**Minimal camera resolution**

## 4. Discussion

^{−1}). Depending on the acceptable error, both Orbbec Astra Mini and Intel D415 can be used to capture the human back, but the authors do not recommend using Intel D415. Astra Mini is also only recommended if the low price of the 3D capturing system is weighted higher than the quality of the results. The Photoneo MotionCam-3D and SL/AS with THE TIDA-00254 projector and HIKROBOT cameras are all valid options for capturing the human back.

^{−1}, the MAE is 6.6 mm; however, the individual error can be as large as 30 mm. In this uncertainty quantification, we could also include models for camera noise, especially for approach A, using a transfer function for the camera, which could improve the result.

## 5. Conclusions

## Supplementary Materials

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**Three-dimensional back shape captures from (

**a**) Photoneo MotionCam-3D; (

**b**) structured light with TIDA-00254; (

**c**) active stereo with BoofCV; (

**d**) Orbbec Astra Mini; (

**e**) Intel D415.

**Figure 3.**Process to calculate the horizontal slices from the ground-truth 3D representation: (

**left**) ground-truth 3D representation; (

**right**) horizontal slice.

**Figure 5.**Example of shape quality reduction for a horizontal slice using a Butterworth low-pass filter.

**Figure 7.**Process for calculating the symmetry line from the ground-truth 3D representation: (

**left**) symmetry map, e.g., evaluation of symmetry function for each horizontal slice (Figure 3); (

**right**) resulting symmetry line (red).

**Figure 10.**Error from the shape of a reduced-quality 3D representation compared to the ground-truth shape.

**Figure 11.**Error from symmetry line of reduced-quality 3D representation compared to its benchmark symmetry line.

Method | MATLAB Method | Description |
---|---|---|

Downsampling | pcdownsample | Random downsampling |

Reduction in spatial frequencies | Butter/filtfilt | Filtering with a low-pass filter |

Limiting depth resolution | round | Rounding to the next allowed value |

Adding random spatial noise | rand | Adding random spatial noise |

Adding sinusoidal spatial noise | Sin | Adding spatial noise in sinusoidal form |

System | Resolution | Accuracy |
---|---|---|

Photoneo MotionCam-3D M+ | 1680 × 1200 resp. 1120 × 800 | error < 0.3 mm at 0.9 m |

SL/AS with TIDA and HIKROBOT | 912 × 1140 resp. 1920 × 1200 | error ~1 mm at 1 m |

Intel D415 | 1280 × 720 | error < 2% up to 2 m |

Orbbec Astra Mini | 640 × 480 | error < 3 mm at 1 m |

Used Oversampling | Corresponding Frequency Factor | Resulting Minimal Required Spatial Resolution |
---|---|---|

1× (Nyquist limit) | 2× | 10 mm–25 mm |

5× | 10× | 2 mm–5 mm |

10× | 20× | 1 mm–2.5 mm |

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**MDPI and ACS Style**

Kaiser, M.; Brusa, T.; Wyss, M.; Ćuković, S.; Bertsch, M.; Taylor, W.R.; Koch, V.M.
Minimal Required Resolution to Capture the 3D Shape of the Human Back—A Practical Approach. *Sensors* **2023**, *23*, 7808.
https://doi.org/10.3390/s23187808

**AMA Style**

Kaiser M, Brusa T, Wyss M, Ćuković S, Bertsch M, Taylor WR, Koch VM.
Minimal Required Resolution to Capture the 3D Shape of the Human Back—A Practical Approach. *Sensors*. 2023; 23(18):7808.
https://doi.org/10.3390/s23187808

**Chicago/Turabian Style**

Kaiser, Mirko, Tobia Brusa, Marco Wyss, Saša Ćuković, Martin Bertsch, William R. Taylor, and Volker M. Koch.
2023. "Minimal Required Resolution to Capture the 3D Shape of the Human Back—A Practical Approach" *Sensors* 23, no. 18: 7808.
https://doi.org/10.3390/s23187808