# A Projection-Based Augmented Reality System for Medical Applications

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## Abstract

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## Featured Application

**Projection-based Augmented Reality System for Medical Applications.**

## Abstract

## 1. Introduction

## 2. Methodology

#### 2.1. Image Alignment

- Let the floating point group corresponding to the patient’s facial features, extracted from the camera image, be F, where F = {f
_{i}(x,y,z),1 ≤ i ≤ N_{f}}, and let the floating data point group corresponding to the facial features, extracted from the CT images, be R, where R = {r_{j}(x,y,z),1 ≤ j ≤ N_{r}}. - Pick a random point from F, assume it is f, and seek its closest corresponding point in R by calculating the minimum distance between f and R, d, as:$$d(f,R)=\frac{1}{M}\underset{j\in \left(1,\dots N\right)}{\mathrm{min}}\parallel {f}_{i}-{r}_{j}\parallel $$
- Calculate the median distance, Median, of all the distances. Assume the distances are re-arranged in order, then:$$\mathrm{Median}(d)={d}_{j},\mathrm{where}j=\left(\right)open="\{">\begin{array}{c}\frac{{N}_{f}}{2},{N}_{f}isodd\\ \frac{{N}_{f}+1}{2},{N}_{f}iseven\end{array}$$
- Assign weight to each pair, based on the distance between each pair of points.$${{W}_{i}}_{}=\left(\right)open="\{">\begin{array}{l}1,if{d}_{i}median\\ \frac{median}{{d}_{i}},otherwise\end{array}$$
- Calculate the root mean squared error (RMS):$$\mathrm{RMS}=\sqrt{\frac{1}{{N}_{f}}{{\displaystyle \sum}}_{i=1}^{{N}_{f}}{W}_{i}\xb7{d}_{i}}$$
- Calculate and record the transformation matrix, T, of current pairs. If the termination condition, based on RMS, is reached, output T as the final transformation matrix. However, if the termination condition is not reached, but the RMS value is smaller than the previous iteration, then replace the optimal transformation matrix with the current T.
- If the termination condition is not reached, a perturbation mechanism is used; that is, applying a perturbation matrix on the current pairings. The probability of perturbation is based on the Gaussian distribution. The purpose of perturbation is allowing the search outside the current solution space, which may be small, and can allow for a locally optimum solution.
- Restart the ICP again.

#### 2.2. Capture the Position of the Observer

^{TM}camera was used to capture the position of the observer. The position of the observer was determined by using facial features. The Max-Margin Object Detector (MMOD) algorithm [25,26] was used to detect the observer’s face in the camera images, then five-point facial key points detection was performed to locate the edges of both eyes, and the nose tip [27], as shown in Figure 5.

^{TM}camera can rotate a total of 120 degrees, i.e., 60 degrees to each side of the patient, which is sufficient for the proposed application and so was set as the parameter used in the experiment.

#### 2.3. Three Dimensional Model Surface Correction

- Project a square matrix of scanlines onto the head of the patient or phantom.
- Use a video camera to capture the distortions of the scanlines on the surface. An example of the scanlines projected onto a head phantom is shown in Figure 6.
- Thin the captured scanlines in order to obtain a more accurate representation of the matrix, obtaining a matrix of regions.
- Determine which regions are still fully closed by using the flood filling algorithm from the center of each region. This is useful for obtaining the coordinates of the intersections of the scanlines.
- Mark out each region and obtain the coordinates of the intersections.
- In order to reduce calculations, the user is asked to mark out regions of interest (ROI).
- Geometric corrections are performed for each region in the ROI. An example of a blood vessel before and after adjustment is shown in Figure 7.
- Project the result.

## 3. Experimental Results

^{®}RTX2080Ti display card. 2. Two RealSenseTM D435 cameras. 3. One Optoma ML750 video projector. 4. Two head phantoms. The head phantoms and the markers used in the experiments are shown in Figure 9.

#### 3.1. Experiments for Speed

#### 3.2. Experiments for Accuracy

#### 3.3. Experiments for Systems Comparison Purposes

## 4. Discussion

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 7.**Image of blood vessel before (

**left**) and after (

**right**) geometric adjustment before projection.

**Figure 11.**Example of projections of blood vessels with observer at (

**a**) 0 degree, (

**b**) +30 degrees, (

**c**) +60 degrees, (

**d**) −30 degrees, and (

**e**) −60 degrees.

Algorithm | Precision | Std. Deviation | Recall | Std. Deviation |
---|---|---|---|---|

Haar | 80.23% | 5.12% | 44.56% | 30.04% |

HOG + SVM | 83.78% | 4.45% | 48.61% | 28.41% |

DNN | 89.33% | 2.17% | 70.94% | 13.86% |

MMOD | 98.14% | 1.08% | 80.26% | 9.79% |

Deg. | P1 | P2 | P3 | P4 | P5 | P.Avg. | Q1 | Q2 | Q3 | Q4 | Q Avg. |
---|---|---|---|---|---|---|---|---|---|---|---|

0 | 1.51 | 1.58 | 1.51 | 1.54 | 1.5 | 1.528 | 1.61 | 1.43 | 1.48 | 1.58 | 1.525 |

+10 | 1.53 | 1.54 | 1.53 | 1.5 | 1.58 | 1.536 | n.a. | n.a. | n.a. | n.a. | |

+20 | 1.54 | 1.55 | 1.54 | 1.51 | 1.53 | 1.534 | 1.57 | 1.54 | 1.67 | 1.61 | 1.598 |

+30 | 1.7 | 1.54 | 1.52 | 1.55 | 2.21 | 1.704 | n.a. | n.a. | n.a. | n.a. | |

+40 | 2.21 | 1.52 | 1.5 | * | 1.52 | 1.688 | 1.68 | 1.71 | 1.66 | 1.7 | 1.688 |

+50 | 2.5 | 1.55 | 1.7 | * | 1.54 | 1.823 | n.a. | n.a. | n.a. | n.a. | |

+60 | 2.4 | 1.52 | 1.78 | * | 1.54 | 1.81 | 1.69 | 1.62 | 1.73 | 1.77 | 1.703 |

−10 | 1.57 | 1.97 | 1.53 | 1.51 | 1.51 | 1.618 | n.a. | n.a. | n.a. | n.a. | |

−20 | 1.58 | 1.96 | 1.52 | 1.52 | 1.74 | 1.664 | 1.55 | 1.64 | 1.7 | 1.66 | 1.638 |

−30 | 1.56 | 2.4 | 1.56 | 1.51 | 1.68 | 1.742 | n.a. | n.a. | n.a. | n.a. | |

−40 | 1.53 | 2.33 | 1.58 | 1.59 | * | 1.758 | 1.51 | 1.49 | 1.47 | 1.53 | 1.5 |

−50 | 1.58 | 2.21 | 1.89 | 1.54 | * | 1.805 | n.a. | n.a. | n.a. | n.a. | |

−60 | 2.2 | * | 2.38 | 1.76 | * | 2.113 | 1.73 | 1.68 | 1.74 | 1.76 | 1.728 |

Total Avg. | 1.717 | 1.625 |

Deg. | P1 | P2 | P3 | P4 | P5 | P.Avg. | Q1 | Q2 | Q3 | Q4 | Q Avg. |
---|---|---|---|---|---|---|---|---|---|---|---|

0 | 1.62 | 1.75 | 1.71 | 1.64 | 1.66 | 1.676 | 1.78 | 1.83 | 1.76 | 1.85 | 1.805 |

+10 | 1.66 | 1.78 | 1.81 | 1.68 | 1.7 | 1.726 | n.a. | n.a. | n.a. | n.a. | . |

+20 | 1.7 | 1.77 | 1.68 | 1.76 | 1.71 | 1.724 | 1.86 | 1.84 | 1.79 | 1.81 | 1.825 |

+30 | 1.84 | 1.89 | 1.76 | 1.89 | 1.73 | 1.822 | n.a. | n.a. | n.a. | n.a. | |

+40 | 2.31 | 1.75 | 1.71 | * | 1.64 | 1.8525 | 1.91 | 1.88 | 1.93 | 1.94 | 1.915 |

+50 | 2.52 | 1.81 | 1.74 | * | 1.67 | 1.935 | n.a. | n.a. | n.a. | n.a. | |

+60 | 2.64 | 1.74 | 1.89 | * | 1.91 | 2.045 | 1.68 | 1.77 | 1.86 | 1.71 | 1.755 |

−10 | 1.59 | 1.67 | 1.64 | 1.77 | 1.64 | 1.662 | n.a. | n.a. | n.a. | n.a. | |

−20 | 1.91 | 1.67 | 1.76 | 1.72 | 1.69 | 1.75 | 1.37 | 1.69 | 1.58 | 1.92 | 1.64 |

−30 | 1.86 | 1.99 | 1.73 | 1.68 | 1.81 | 1.814 | n.a. | n.a. | n.a. | n.a. | |

−40 | 1.84 | 2.6 | 1.78 | 1.76 | * | 1.995 | 1.84 | 1.93 | 1.78 | 1.82 | 1.843 |

−50 | 1.76 | 2.6 | 1.86 | 1.61 | * | 1.958 | n.a. | n.a. | n.a. | n.a. | |

−60 | 2.1 | * | 2.8 | 1.86 | * | 2.253 | 1.76 | 1.71 | 1.77 | 1.83 | 1.768 |

Total Avg. | 1.862 | 1.793 |

Deg. | P1 | P2 | P3 | P4 | P5 | P.Avg. | Q1 | Q2 | Q3 | Q4 | Q Avg. |
---|---|---|---|---|---|---|---|---|---|---|---|

0 | 2.16 | 2.39 | 2.86 | 2.44 | 2.54 | 2.478 | 2.56 | 2.43 | 2.12 | 2.41 | 2.38 |

+10 | 2.34 | 2.76 | 2.45 | 2.67 | 2.78 | 2.6 | n.a. | n.a. | n.a. | n.a. | . |

+20 | 3.7 | 3.1 | 2.87 | 2.64 | 2.31 | 2.924 | 2.11 | 2.27 | 2.19 | 2.45 | 2.255 |

+30 | 2.51 | 1.97 | 1.88 | 2.34 | 1.92 | 2.124 | n.a. | n.a. | n.a. | n.a. | |

+40 | 3.41 | 2.67 | 2.46 | * | 2.74 | 2.82 | 2.55 | 2.43 | 2.69 | 2.17 | 2.46 |

+50 | 2.57 | 2.44 | 2.41 | * | 2.67 | 2.523 | n.a. | n.a. | n.a. | n.a. | |

+60 | 3.11 | 2.87 | 2.92 | * | 2.96 | 2.965 | 2.16 | 2.58 | 2.41 | 2.09 | 2.31 |

−10 | 2.21 | 2.34 | 2.4 | 2.41 | 2.39 | 2.35 | n.a. | n.a. | n.a. | n.a. | |

−20 | 2.37 | 2.6 | 2.78 | 2.61 | 2.21 | 2.514 | 2.76 | 2.88 | 2.43 | 2.22 | 2.573 |

−30 | 2.7 | 2.44 | 2.56 | 2.17 | 2.67 | 2.508 | n.a. | n.a. | n.a. | n.a. | |

−40 | 3.57 | 3.24 | 3.51 | 3.09 | * | 3.353 | 2.08 | 1.98 | 2.34 | 2.06 | 2.115 |

−50 | 3.87 | 3.8 | 3.66 | 3.91 | * | 3.81 | n.a. | n.a. | n.a. | n.a. | |

−60 | 3.14 | * | 3.02 | 2.86 | * | 3.007 | 2.61 | 2.14 | 1.92 | 2.68 | 2.338 |

Total Avg. | 2.767 | 2.347 |

System | P1 | P2 | P3 | P4 | P5 | P.Avg. | Q1 | Q2 | Q3 | Q4 | Q Avg. |
---|---|---|---|---|---|---|---|---|---|---|---|

NDI | 1.34 | 1.81 | 1.62 | 1.55 | 1.83 | 1.63 | 1.53 | 1.62 | 1.67 | 1.69 | 1.630 |

Proposed | 1.54 | 1.51 | 1.58 | 1.51 | 1.5 | 1.528 | 1.48 | 1.37 | 1.41 | 1.53 | 1.448 |

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## Share and Cite

**MDPI and ACS Style**

Chien, J.-C.; Lee, J.-D.; Chang, C.-W.; Wu, C.-T.
A Projection-Based Augmented Reality System for Medical Applications. *Appl. Sci.* **2022**, *12*, 12027.
https://doi.org/10.3390/app122312027

**AMA Style**

Chien J-C, Lee J-D, Chang C-W, Wu C-T.
A Projection-Based Augmented Reality System for Medical Applications. *Applied Sciences*. 2022; 12(23):12027.
https://doi.org/10.3390/app122312027

**Chicago/Turabian Style**

Chien, Jong-Chih, Jiann-Der Lee, Chai-Wei Chang, and Chieh-Tsai Wu.
2022. "A Projection-Based Augmented Reality System for Medical Applications" *Applied Sciences* 12, no. 23: 12027.
https://doi.org/10.3390/app122312027