# Path-Planning System for Radioisotope Identification Devices Using 4π Gamma Imaging Based on Random Forest Analysis

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## Abstract

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^{137}Cs point source. The results showed that

^{137}Cs point sources were identified using the few measurement positions suggested by the path-planning system.

## 1. Introduction

## 2. Investigation of Path-Planning System Using an Integrated Simulation Model

^{137}Cs (2 MBq) placed at 100 cm from the center of the detector for 20 min. For any measurement point in the simulation, the gamma image was calculated by rotating the basic response to the direction of a target source and transforming the intensity of the basic response to follow the inverse square law. Therefore, the background variation and uncertainty caused by the counting statistics in calculated gamma images were not considered in the following discussion.

^{137}Cs point sources and the possible measurement positions around the sources on the search area in the integrated simulation model. The point sources and the possible measurement positions were assumed to be on the same plane. The search area was 8 ≤ X ≤ 8 m and −8 ≤ Y ≤ 0 m. Measurement points A and B were selected from S0 to S44 positions on a 2 m grid in the search area, excluding the two source positions S20 and S24. The intensity ratio of the two sources ranged from 0.1 to 4.9.

^{3}/voxel) was performed under all possible conditions of source intensity ratio and for two measurement positions A and B. The output data were analyzed using RF, a machine learning model. First, to find the features in this RF analysis, the features in the decision tree analysis that were examined in our previous study [13] were selected as the candidates. Figure 2 shows the definitions of the eight candidate features listed below:

_{est}is the point closer to point C between the weighted centers of the estimated areas of sources #1 and #2, and G

_{pos}is the weighted center of the three points A, B, and G

_{est}.

_{est}is estimated within ±1 m of the true source location and the estimated source intensity is estimated within ±75% of the true source intensity, the objective function in the RF analysis was set as “detected” (i.e., “1”) or “not detected” (i.e., “0”).

_{j}, defined by Equation (1), represents the degree to which one variable is related to other variables, and multicollinearity is suspected if VIF is greater than 10.

_{j}on all other remaining variables, ${f}_{ji}$ is the ordinary least square regression of X

_{j}on the ith data, ${X}_{ji}$ is the X

_{j}value of the ith data, $\overline{{X}_{j}}$ is the mean of X

_{j}, and n is the number of data obtained by the simulation. Among the eight variables, $\left|\overrightarrow{{\mathrm{CG}}_{\mathrm{est}}}\right|$, $\left|\overrightarrow{{\mathrm{BG}}_{\mathrm{est}}}\right|$, and $\left|\overrightarrow{{\mathrm{G}}_{\mathrm{pos}}{\mathrm{G}}_{\mathrm{est}}}\right|$ had very large calculated VIFs; hence, these three variables were removed. The results of recalculation of the VIFs for five variables are listed in Table 1. The VIF of each feature became smaller (weaker correlation). Since G

_{est}is derived from the estimated source identification result, its uncertainty is likely to be larger than the uncertainties of A and B, which can be measured. Therefore, we selected $\left|\overrightarrow{\mathrm{AB}}\right|$ and $\left|\overrightarrow{\mathrm{CB}}\xb7\overrightarrow{{\mathrm{CG}}_{\mathrm{est}}}\right|$ as the features, and calculated the VIFs using each of $\left|\overrightarrow{{\mathrm{AG}}_{\mathrm{est}}}\right|$, $\frac{\left|\overrightarrow{{\mathrm{AG}}_{\mathrm{est}}}\right|}{\left|\overrightarrow{{\mathrm{BG}}_{\mathrm{est}}}\right|}$, and ∠AG

_{est}B as an additional variable. The VIF was the lowest when $\frac{\left|\overrightarrow{{\mathrm{AG}}_{\mathrm{est}}}\right|}{\left|\overrightarrow{{\mathrm{BG}}_{\mathrm{est}}}\right|}$ was included as a feature (see Table 2).

## 3. Verification of the Path-Planning System

#### 3.1. Verification Based on the Integrated Simulation Model

^{137}Cs point source (activity: 1.8 MBq) was set within the search area (Figure 5). This search area was designed identically to that in the experiment described in Section 3.2. The source location was at (2.5, 5.5, 0.0), and the initial measurement position was (0, 0, 0) in m. The acquisition time for 4π gamma imaging at each position was 10 min. The distance per step to the next measurement position was 1.5 m. The detector could be moved up to 0.1 m close to the obstacles (i.e., walls) in the search area. The path-planning system was used for selecting the measurement positions. Two patterns of detector movement—Path I selected by the path-planning system, and Path II selected by tracing the edges of the walls in the search area—were investigated, as shown in Figure 5.

#### 3.2. ^{137}Cs Source Identification by a Prototype Device by 4π Gamma Imaging with the Path-Planning System

^{3}, and the total number of pixels were 8 × 12 × 15 = 1440. These 1440 pixels were arranged in a three-dimensional structure. The energy deposited on each pixel because of the incident gamma rays was recorded as listmode data. The basic performance of the detector as the 4π gamma imager was reported in our previous papers [10,11].

^{137}Cs point source was placed at (1.7, 4.3, 0.2) m, as shown in Figure 8.

^{137}Cs single source identification.

## 4. Conclusions

^{137}Cs source identification. The simulation and experimental results showed that the

^{137}Cs point source was identified with fewer movement steps and high accuracy by using the path-planning system.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**Locations of two-point sources and possible measurement positions around the sources on the search area in the integrated simulation model. The positions of the two sources are indicated in red.

**Figure 2.**Definition of the candidates of features in the case that the weighted center of the estimated area of source #1 is closer to point C and chosen as the point G

_{est}.

**Figure 6.**Estimated source intensities and locations in a three-dimensional (3D) voxel space obtained by (

**a**) Path I and (

**b**) Path II.

**Figure 7.**Top view of the room map obtained by simultaneous localization and mapping (SLAM) with the locations of the source and measurement points.

**Figure 9.**High-angle view of the search area (

**left**), estimated source intensity and location in the 3D voxel area (

**middle**), and estimation results in the xy plane at z = 0.2 (

**right**) for each measurement position.

**Table 1.**Variance inflation factors (VIFs) for five candidate features for radiation source identification.

$\left|\overrightarrow{\mathbf{A}\mathbf{B}}\right|$ | $\left|\overrightarrow{\mathbf{A}{\mathbf{G}}_{\mathbf{e}\mathbf{s}\mathbf{t}}}\right|$ | $\frac{\left|\overrightarrow{\mathbf{A}{\mathbf{G}}_{\mathbf{e}\mathbf{s}\mathbf{t}}}\right|}{\left|\overrightarrow{\mathbf{B}{\mathbf{G}}_{\mathbf{e}\mathbf{s}\mathbf{t}}}\right|}$ | ∠AG_{est}B | $\left|\overrightarrow{\mathbf{C}\mathbf{B}}\xb7\overrightarrow{\mathbf{C}{\mathbf{G}}_{\mathbf{e}\mathbf{s}\mathbf{t}}}\right|$ |
---|---|---|---|---|

16 | 14 | 15 | 7.9 | 3.9 |

$\left|\overrightarrow{\mathbf{A}\mathbf{B}}\right|$ | $\frac{\left|\overrightarrow{\mathbf{A}{\mathbf{G}}_{\mathbf{e}\mathbf{s}\mathbf{t}}}\right|}{\left|\overrightarrow{\mathbf{B}{\mathbf{G}}_{\mathbf{e}\mathbf{s}\mathbf{t}}}\right|}$ | $\left|\overrightarrow{\mathbf{C}\mathbf{B}}\xb7\overrightarrow{\mathbf{C}{\mathbf{G}}_{\mathbf{e}\mathbf{s}\mathbf{t}}}\right|$ |
---|---|---|

5.3 | 2.8 | 2.7 |

$\left|\overrightarrow{\mathbf{A}\mathbf{B}}\right|$ | $\frac{\left|\overrightarrow{\mathbf{A}{\mathbf{G}}_{\mathbf{e}\mathbf{s}\mathbf{t}}}\right|}{\left|\overrightarrow{\mathbf{B}{\mathbf{G}}_{\mathbf{e}\mathbf{s}\mathbf{t}}}\right|}$ | $\left|\overrightarrow{\mathbf{C}\mathbf{B}}\xb7\overrightarrow{\mathbf{C}{\mathbf{G}}_{\mathbf{e}\mathbf{s}\mathbf{t}}}\right|$ | |
---|---|---|---|

Model based on all 50 trees | 0.36 | 0.26 | 0.39 |

Decision tree extracted from the model | 0.35 | 0.27 | 0.38 |

**Table 4.**Summary of the estimated source intensities and locations obtained by Path I in the integrated simulation model.

Movement Sequence | #1 | #2 | #3 | #4 |
---|---|---|---|---|

Area where a source is located (voxels) | 1208 | 796 | 154 | 22 |

Estimated source location (m) | (3.8, 5.8, 0.0) | (4.1, 6.3, 0.0) | (3.2, 6.3, 0.1) | (2.8, 5.5, 0.0) |

Error from true source position (m) | (1.3, 0.3, 0.0) | (1.6, 0.8, 0.0) | (0.7, 0.8, 0.1) | (0.3, 0, 0) |

Estimated source activity (MBq) | 3.2 ± 3.2 | 3.8 ± 3.0 | 3.5 ± 2.0 | 2.6 ± 0.9 |

**Table 5.**Summary of the estimated source intensities and locations obtained by Path II in the integrated simulation model.

Movement Sequence | #1 | #2 | #3 | #4 | #5 |
---|---|---|---|---|---|

Area where a source is located (voxels) | 1208 | 1058 | 746 | 330 | 23 |

Estimated source location (m) | (3.8, 5.8, 0.0) | (3.8, 6.0, 0.0) | (3.1, 6.1, 0.0) | (3.1, 6.5, 0.0) | (2.6, 5.9, 0.0) |

Error from true source position (m) | (1.3, 0.3, 0.0) | (1.3, 0.5, 0.0) | (0.6, 0.6, 0.0) | (0.6, 1.0, 0.0) | (0.1, 0.4, 0.0) |

Estimated source activity (MBq) | 3.2 ± 3.2 | 3.1 ± 2.6 | 2.8 ± 1.9 | 3.2 ± 1.6 | 2.8 ± 0.8 |

Movement Sequence | #1 | #2 | #3 | #4 |
---|---|---|---|---|

Area where a source is located (voxels) | 29,551 | 13,348 | 592 | 58 |

Estimated source location (m) | (2.3, 5.8, 0.6) | (2.2, 5.7, 0.3) | (1.5, 4.1, 0.4) | (2.0, 4.1, 0.4) |

Error from true source position (m) | (0.5, 1.5, 0.4) | (0.5, 1.4, 0.1) | (−0.2, −0.2, 0.2) | (0.3, −0.2, 0.2) |

Estimated source activity (MBq) | 3.1 ± 3.1 | 3.4 ± 3.1 | 1.6 ± 1.0 | 2.1 ± 0.8 |

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**MDPI and ACS Style**

Tomita, H.; Hara, S.; Mukai, A.; Yamagishi, K.; Ebi, H.; Shimazoe, K.; Tamura, Y.; Woo, H.; Takahashi, H.; Asama, H.;
et al. Path-Planning System for Radioisotope Identification Devices Using 4π Gamma Imaging Based on Random Forest Analysis. *Sensors* **2022**, *22*, 4325.
https://doi.org/10.3390/s22124325

**AMA Style**

Tomita H, Hara S, Mukai A, Yamagishi K, Ebi H, Shimazoe K, Tamura Y, Woo H, Takahashi H, Asama H,
et al. Path-Planning System for Radioisotope Identification Devices Using 4π Gamma Imaging Based on Random Forest Analysis. *Sensors*. 2022; 22(12):4325.
https://doi.org/10.3390/s22124325

**Chicago/Turabian Style**

Tomita, Hideki, Shintaro Hara, Atsushi Mukai, Keita Yamagishi, Hidetake Ebi, Kenji Shimazoe, Yusuke Tamura, Hanwool Woo, Hiroyuki Takahashi, Hajime Asama,
and et al. 2022. "Path-Planning System for Radioisotope Identification Devices Using 4π Gamma Imaging Based on Random Forest Analysis" *Sensors* 22, no. 12: 4325.
https://doi.org/10.3390/s22124325