# Making Historical Gyroscopes Alive—2D and 3D Preservations by Sensor Fusion and Open Data Access

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## Abstract

**:**

## 1. Introduction

## 2. Merging 2.5D and 3D Data and Texturing—Making 3D Models Alive

**X**=

**X**+ µ

_{o}**Rx**

**X**is the (3 × 1)

_{u}vector of the target coordinates of u control points,

**X**is the (3 × 1)

_{o}_{u}vector of the three translation parameters (X

_{o}, Y

_{o}, Z

_{o}), µ is the scale,

**R**is the (3 × 3)

_{u}rotation matrix depending on the unknown rotation angles α, β, γ, and

**x**is the (3 × 1)

_{u}vector of the local u control point coordinates. This non-linear transformation is linearized considering only differential changes in the three translations, three rotations, and one scale, and therefore replaces Equation (1) by,

**dx**=

**S**

**dt**

**S**is the (3 × 7)

_{u}similarity transformation matrix resulting from the linearization process of Equation (1), and,

**dt’**= [dx

_{o}, dy

_{o}, dz

_{o}, dα, dβ, dγ, dµ]

**B**=

**S**, leading to,

**Av**+

**Bx**+

**w**=

**0**, and 2nd order: D(

**v**) = σ

^{2}

**P**

^{−1}**v**,

**x,**and the Lagrangian

**λ**, we use Gaussian error propagation for getting the desired dispersion matrices. With D(

**w**) = σ

^{2}

**AP**’ the precision of the registration parameters is propagated to,

^{−1}A**x**) = σ

^{2}[

**B’**(

**AP**)

^{−1}A’^{−1}

**B**]

^{−1}

**x**) contains the variances and covariances along its main diagonal and off-diagonals, which can be used to propagate any precision of the individual in-situ data collection method and finally assess the quality of the registration.

_{CT}= 0.10 mm, and the estimated precision of CV/Photogrammetry σ

_{CV}= 0.08mm, and for u = 10 these results are σ = 1.07, σ

_{CT}= 0.08 mm, and σ

_{CV}= 0.06 mm. The more control points that are used, the better the precision can be estimated. These figures demonstrate that CV/photogrammetry 3D point clouds are more precise than down-sampled CT 3D volume data, and efforts are to be made to reduce noise and artifacts in CT scans (see Section 5.1) in order for them to arrive at the same level of precision. The results of our combined models and their corresponding precision values are given in Section 6. It is noted here that the data fusion of CT and CV/photogrammetry can provide digital twins with a precision of 0.1 mm.

## 3. The University of Stuttgart’s Gyroscopes Collection—The Gyrolog Project

## 4. Two-Dimensional Data Collections and Postprocessing

## 5. Three-Dimensional Data Collections by Means of Computed Tomography, Computer Vision, and Endoscopy

#### 5.1. Computed Tomography 3D Data Collection

^{−2}with a total number of 50 iterations. In the cases considered, the MLEM algorithm required about 50 iterations to reconstruct all features of the reconstructed volume. If the signal-to-noise ratio of the projections is low, the number of iterations should exceed 50. However, the MLEM algorithm has a computing time of more than 300 h on a powerful computer with 8 GPUs for the resolution of the detector used here for the projection images of 2300 × 3200 pixels. This is due to the large number of forward and backward projections. In order to reduce the computing time for the reconstruction significantly by a factor of 50 and still achieve high-quality volume data sets with noise reduction, denoised X-ray projections using the CNN architecture of Figure 10 were reconstructed using the FBP. For the CNN network training, a ground truth of the original high-dose X-ray images and reconstructed 3D volume data sets were generated using FBP. A denoised projection is shown in Figure 11. As can be seen from Figure 12, the results obtained from the MLEM reconstruction of the noise projections and the FBP of high-dose projections are similar, and in some regions MLEM produces better results, although it is very time consuming. Denoising images with the CNN algorithm helps to remove shot noise for high photon counts.

#### 5.2. Geometric Computer Vision and Photogrammetric 3D Data Collection

_{1}and p

_{2}are measured. With additional camera orientation information for O

_{1}and O

_{2}(image poses) the 3D corresponding point P can be calculated by the forward intersection.

**R**. With regards to camera distortion, various models are based on either the mathematical principle, the physical principle, or the mixed principle. Among many, the classical Brown model and its variants are most widely used [37]. It classifies the distortion into radial distortion ∆

_{r}and tangential distortion ∆

_{t}.

_{1}, K

_{2}, and K

_{3}, and P

_{1}and P

_{2}are tangential distortion parameters. Furthermore, $r=\sqrt{{u}^{2}+{v}^{2}}$:

^{®}Calibration Toolbox, which uses a planar chessboard.

#### 5.3. Endoscopy in 3D

## 6. Results for Digital Twins of the Gyroscope Collection

#### 6.1. The Machine of Bohnenberger—The Very First Gyroscope

#### 6.2. Directional Gyro LKu4

#### 6.3. Gyro G200 of Inertial Platform LN3

#### 6.4. Two more Examples of Gyrolog 3D Digital Twins

^{3}m

^{3}with very complex structures, such as metal sheets, wires, electrical drives, and servos, etc. The view into the TH object can be accomplished without any difficulties using OS libraries, e.g., CloudCompare, MeshLab, PCL, etc.

_{0}. As stated below, all 3D digital twins could be reconstructed within a precision in the range of 0.1 mm, which is quite sufficient for our applications.

## 7. Curation of Gyrolog and Open Access

## 8. Conclusions and Outlook

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## Abbreviations

CH | Cultural Heritage |

TH | Technological Heritage; Tech Heritage |

MRI | Magnetic Resonance Imaging |

MRT | Magnetic Resonance Tomography |

PET | Positron Emission Tomography |

CT | Computed Tomography |

CV | Computer Vision |

SGM | Semi-global Matching |

tSGM | Tube-based Semi-global Matching |

SURE | Surface Reconstruction (from imagery) |

DIM | Dense Image Matching |

MVS | Multi-view Stereo |

AR | Augmented Reality |

VR | Virtual Reality |

OA | Open Access |

OS | Open Source |

CSG | Constructive Solid Geometry |

ICP | Iterative Closest Point (algorithm) |

CP | Control Point |

2D | Two-dimensional array of numbers |

2.5D | Three-dimensional points meshed by 2D topology (triangles, grids) |

3D | Three-dimensional array—3D points meshed by 3D topology |

SfM | Structure-from-Motion, Bundle Block Adjustment |

PCL | Open-source library of algorithms for point cloud processing |

Open3D | Open-source library dealing with 3D data |

V(O) | Set of 3D voxels—a voxel cloud |

P(O) | Set of 3D points—a point cloud |

GSD; OSD | Ground Sampling Distance; Object Sampling Distance |

P rate gyro | Gyroscope measuring angular rate along input axis |

I rate gyro | Gyroscope measuring integrated angular rate along input axis |

LGW | Luftfahrtgerätewerk Hakenfelde (Berlin) |

FoV | Field-of-View |

CC | Creative Commons |

CC BY-SA | License to share OA contents with other users who respect copyright |

Goobi | Open-source web-based software |

DT | Digital Twin |

FBP | Filtered Back Projection |

MLEM | Maximum-Likelihood Expectation-Maximization |

CNN | Convolutional Neural Network |

ReLU | Rectified Linear Unit (of neural networks) |

GPU | Graphics Processing Unit |

DSLR | Digital Single Lens Reflex (camera) |

MEMS | Micro-Electro-Mechanical Systems |

LKu4 | Directional Gyro of Type “Siemens LKu4” |

LN3 | Inertial Platform of Type “Litton LN-3” |

G200 | Type of the Gyroscopes of the “Litton LN-3” |

glTF | Graphics Language Transmission Format, standard file format for 3D models |

obj | Open file format for 3D data storage and handling |

Draco | Open-source library for compressing/decompressing 3D meshes |

CIDOC | International Committee for Documentation |

CIDOC CRM | CIDOC Conceptual Reference Model |

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**Figure 2.**The very first gyroscope of 1810—the Machine of Bohnenberger, Tuebingen, Germany. (

**a**) Original drawing; (

**b**) Photo; and (

**c**) 2.5D digital twin by CV/photogrammetry.

**Figure 4.**Voxel-to-point cloud transformation: (

**a**) Step 1: find surface voxels; (

**b**) Step 2: voxel-to-point cloud transformation.

**Figure 5.**Example of the co-registration of CT Scans with CV/photogrammetry point clouds—the 3D digital twin of the Gyro200 (see Section 6.3): (

**a**) iso-surface of a denoised filtered back projection (FBP) CT scan; (

**b**) the convex hull generated by CV/photogrammetry; and (

**c**) a cross-section of the integrated CT and CV/photogrammetry 3D reconstruction.

**Figure 6.**Examples of the University of Stuttgart’s gyroscope collection (Photos: B. Miklautsch, Photography Lab, University of Stuttgart, 2010): (

**a**) pneumatically driven direction gyro, Ternstedt Manufacturing Div, GM Corp, Detroit, USA; (

**b**) electrical direction gyro by Siemens-LGW, Berlin, Germany; (

**c**) direction gyro S.F.I.M by BEZU, France; (

**d**) gyro compass of Anschuetz, Germany; (

**e**) artificial Horizon, manufacturer not known; and (

**f**) electrical turning pointer by Apparatebau Gauting, Germany.

**Figure 7.**(

**a**) Characteristic view of the artificial horizon with a caging device (inventory number KH22-10, Gyrolog, CC-BY-SA). (

**b**) Difficult definition of a front view of a ship gyro compass manufactured by Anschuetz (inventory number GO05/01-10, Gyrolog, CC-BY-SA).

**Figure 8.**Measurement setup in CT: (

**a**) X-Ray tube; (

**b**) object to be scanned; (

**c**) rotation table; and (

**d**) flat panel detector.

**Figure 10.**CNN architecture according to [32].

**Figure 11.**Result of the denoising of KH-09-09 using the CNN of Figure 10.

**Figure 12.**Region of volume KH-09-09 reconstructed: (

**a**) FBP of high-dose projections; (

**b**) FBP of denoised projection by CNN architecture of Figure 10; (

**c**) FBP of noisy projections; and (

**d**) MLEM of noisy projections.

**Figure 13.**Two views of the iso-surface of G200 from the 3D volume data set reconstructed by the FBP.

**Figure 14.**Two views of the iso-surface of the G200 calculated from the 3D volume data set reconstructed by the FBP from the denoised projections.

**Figure 15.**Comparison of two iso-surfaces calculated from the reconstructed volumes in the regions-of-interest (ROIs): (

**a**) from original projections; and (

**b**) from denoised projections.

**Figure 16.**The Machine of Bohnenberger and CT scans: (

**a**) photo; (

**b**) cross-sectional view of the CT scan of the inner rod; and (

**c**) gimbal iso-surface of the CT scan.

**Figure 18.**Data acquisition in the Gyrolog project: (

**a**) workflow of CV/photogrammetry; and (

**b**) Gyrolog Lab facility used for photo collections.

**Figure 19.**Gaussian fitting experiment results of the calibrated focal length in x direction for the Sony α7R II.

**Figure 20.**Gaussian fitting standard deviations for the calibrated focal length of four camera systems: (

**a**) Sony α7R II focal length; (

**b**) Leica Q focal length; (

**c**) Samsung Galaxy Note 8 focal length; and (

**d**) Apple iPhone 7Plus focal length.

**Figure 23.**An endoscopy 3D mesh aligned with RealityCapture: (

**a**) alignment; (

**b**) meshed point cloud; and (

**c**) meshed point cloud by CV/photogrammetry.

**Figure 24.**The 3D digital twin of the Machine of Bohnenberger: (

**a**) meshed point cloud of CV/photogrammetry; (

**b**) iso-surface of the gimbal CT scan; and (

**c**) split view of the CT/CV integrated model.

**Figure 25.**The LKu4 by Siemens: (

**a**) mounted in a Junkers JU 88 A-1 cockpit; (

**b**) a Siemens advert from the early 1940s; and (

**c**) front view of the Gyrolog asset.

**Figure 26.**A 3D digital twin of the LKu4: (

**a**) CT scan; (

**b**) CV/photogrammetry point cloud mesh with normal and sprayed images; and (

**c**) the CT/CV integrated model.

**Figure 27.**The Gyro G200 of the LN3 Inertial Platform: (

**a**) Gyro G200; and (

**b**) G200 transportation box.

**Figure 28.**The 3D digital twin of the DM-LN3-G200 gyro: (

**a**) iso-surface of a denoised FBP CT scan; (

**b**) meshed point cloud of CV/photogrammetry; and (

**c**) split view of the CT/CV integrated model.

**Figure 29.**Two more 3D digital twins of the Stuttgart gyroscope collection—the Ternstedt direction gyro (

**a**–

**c**), and the Siemens direction gyro (

**d**–

**f**): (

**a**,

**d**) iso-surfaces of the denoised FBP CT scans; (

**b**,

**e**) meshed point clouds of CV/photogrammetry; and (

**c**,

**f**) split views of the CT/CV integrated models.

X-ray tube voltage (kV) | 180 |

Current (µA) | 400 |

Exposure (s) | 1 |

Filter material (mm) | Copper (2.5) |

Number of projections | 1150 |

X-ray tube voltage (kV) | 170 |

Current (µA) | 740 |

Exposure (s) | 1.4 |

Filter material | Copper (4.5) |

Number of projections | 1256 |

**Table 3.**Tracing the gyroscope manufacturers [45].

Inventory Number | Manufacturer |
---|---|

KK02-09 | Luftfahrtgerätewerk Hakenfelde GmbH, Berlin |

KK09-09 | Siemens App. u. Masch. GmbH, Berlin |

KK12-09 | Luftfahrtgerätewerk Hakenfelde, Berlin |

KK34-20 | hdc Luftfahrtgerätewerk Hakenfelde, Berlin |

Object | #CPs | σ_{0} | σ_{CT} | σ_{CV} | CT Resolution | CV Resolution | File Size CV/Photogr. | Integrated File Size |
---|---|---|---|---|---|---|---|---|

G200 | 4 | 1.38 | 0.10 mm | 0.08 mm | 0.22 mm | 0.05 mm | 425 MB | 1.05 GB |

10 | 1.07 | 0.08 mm | 0.06 mm | |||||

Machine of B. | 4 | 1.36 | 0.12 mm | 0.15 mm | 0.035 mm | 0.03 mm | 157 MB | 378 MB |

10 | 1.02 | 0.09 mm | 0.11 mm | |||||

Ternstedt Gyro | 4 | 1.24 | 0.11 mm | 0.14 mm | 0.035 mm | 0.03 mm | 152 MB | 1.46 GB |

10 | 1.09 | 0.10 mm | 0.12 mm |

Object Name | *.obj File | *.gltf File | *.gltf/Draco File |
---|---|---|---|

G200 | 425 MB | 154 MB | 21.4 MB |

Machine of B. | 157 MB | 59 MB | 8.0 MB |

Siemens Gyro | 495 MB | 120 MB | 7.6 MB |

Siemens LKu4 | 232 MB | 91 MB | 11.7 MB |

Ternstedt Gyro | 152 MB | 66 MB | 22.2 MB |

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**MDPI and ACS Style**

Fritsch, D.; Wagner, J.F.; Ceranski, B.; Simon, S.; Niklaus, M.; Zhan, K.; Mammadov, G.
Making Historical Gyroscopes Alive—2D and 3D Preservations by Sensor Fusion and Open Data Access. *Sensors* **2021**, *21*, 957.
https://doi.org/10.3390/s21030957

**AMA Style**

Fritsch D, Wagner JF, Ceranski B, Simon S, Niklaus M, Zhan K, Mammadov G.
Making Historical Gyroscopes Alive—2D and 3D Preservations by Sensor Fusion and Open Data Access. *Sensors*. 2021; 21(3):957.
https://doi.org/10.3390/s21030957

**Chicago/Turabian Style**

Fritsch, Dieter, Jörg F. Wagner, Beate Ceranski, Sven Simon, Maria Niklaus, Kun Zhan, and Gasim Mammadov.
2021. "Making Historical Gyroscopes Alive—2D and 3D Preservations by Sensor Fusion and Open Data Access" *Sensors* 21, no. 3: 957.
https://doi.org/10.3390/s21030957