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Rapid Interactive and Intuitive Segmentation of 3D Medical Images Using Radial Basis Function Interpolation^{ †}

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## Abstract

**:**

## 1. Introduction

## 2. Methods

#### 2.1. Smart Brush

#### 2.2. Control Point Extraction

#### 2.3. Control Point Merging

#### 2.3.1. Contour Intersection

#### 2.3.2. Classification and Merging

#### 2.4. 3D Interpolation

#### 2.5. Surface Reconstruction

## 3. Evaluation and Results

#### 3.1. Smart Brush Evaluation

#### 3.2. 3D Interpolation Evaluation

## 4. Discussion

## 5. Conclusions

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## Disclaimer

## Abbreviations

A-HRBF | Adaptive Hermite Radial Basis Function |

HRBF | Hermite Radial Basis Function |

RBF | Radial Basis Function |

MRI | Magnetic Resonance Imaging |

ROI | Region of Interest |

CP | Control Point |

## References

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**Figure 1.**Segmentation pipeline. The first image from the left shows the 3D volume as input. In the next step, single slices are segmented using the Smart Brush functionality. Third, the control points of the contours are extracted. Fourth, the 2D and 3D normal vectors are computed for the Hermite radial basis function interpolation. In the final image, the interpolated surface is visualized ([2] Reproduced with permission).

**Figure 2.**(

**a**) Initialization of the smart brush in red and the smart brush is propagated which is illustrated as yellow circle; (

**b**) Correct segmented area under the brush using adaptive thresholding and propagation checking.

**Figure 3.**(

**a**) A rough surface with initial equidistant points in red and convexity defect points in blue; (

**b**) A rough surface with increased number of points in green ([2] Reproduced with permission).

**Figure 4.**Two orthogonal planes are segmented in red, and the resulting intersection points are depicted in yellow.

**Figure 5.**Possible intersection points of annotated non-parallel image slices. (

**a**) The intersection occurs in multiple points; (

**b**) the intersection occurs in the form of one line.

**Figure 6.**Control points extracted from three different orientations, where N points have a 2D normal vector (green) and M points with 3D normal vector (blue).

**Figure 9.**The 3D interpolation evaluation results: (

**a**) the A-HRBF result with average Dice coefficient of 0.91, 0.95, and 0.96 for one, three, and five slices per orientation, respectively; (

**b**) the HRBF result with average Dice coefficient of 0.69, 0.63 and 0.69 for one, three, and five slices per orientation, respectively.

**Figure 10.**The ground truth (red) and the result of 3D interpolation (blue) are shown. The interpolation is obtained based on only one reference slice per orientation. Each row depicts a different orientation (axial, sagittal, and coronal). It is expected that the closer to the reference slice, the higher Dice coefficient is obtained ([2], Reproduced with permission).

**Figure 11.**Normal vector orientation for left ventricle segmentation with an ambiguous boundary: (

**a**,

**b**) control points (yellow) and associated normal vectors (blue) based on intensity gradients for the HRBF method; (

**c**,

**d**) control points (yellow) and associated normal vectors (blue) based on the drawn contour (red) for our proposed method ([2], Reproduced with permission).

**Figure 12.**(

**a**) the overlaid ground truth shown in red and the smart brush patch shown with a yellow rectangle; (

**b**) the extracted patch from the smart brush; (

**c**) the pre-segmented mask that is obtained by eroding the extracted patch; (

**d**) the segmentation result by using the smart brush, which is different to the ground truth patch due to the same intensity rage values.

© 2017 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Kurzendorfer, T.; Fischer, P.; Mirshahzadeh, N.; Pohl, T.; Brost, A.; Steidl, S.; Maier, A.
Rapid Interactive and Intuitive Segmentation of 3D Medical Images Using Radial Basis Function Interpolation. *J. Imaging* **2017**, *3*, 56.
https://doi.org/10.3390/jimaging3040056

**AMA Style**

Kurzendorfer T, Fischer P, Mirshahzadeh N, Pohl T, Brost A, Steidl S, Maier A.
Rapid Interactive and Intuitive Segmentation of 3D Medical Images Using Radial Basis Function Interpolation. *Journal of Imaging*. 2017; 3(4):56.
https://doi.org/10.3390/jimaging3040056

**Chicago/Turabian Style**

Kurzendorfer, Tanja, Peter Fischer, Negar Mirshahzadeh, Thomas Pohl, Alexander Brost, Stefan Steidl, and Andreas Maier.
2017. "Rapid Interactive and Intuitive Segmentation of 3D Medical Images Using Radial Basis Function Interpolation" *Journal of Imaging* 3, no. 4: 56.
https://doi.org/10.3390/jimaging3040056