KEM

This repository provides python codes for the KEM kernel-based expectation-maximization (KEM) algorithm accompanying the paper A Semiparametric Gaussian Mixture Model for Chest CT-based 3D Blood Vessel Reconstruction by Qianhan Zeng, Jing Zhou, Ying Ji, and Hansheng Wang (Biostatistics, 2024).

Citation

@misc{zeng2024semiparametric,
      title={A Semiparametric Gaussian Mixture Model for Chest CT-based 3D Blood Vessel Reconstruction}, 
      author={Qianhan Zeng and Jing Zhou and Ying Ji and Hansheng Wang},
      year={2024},
      eprint={2403.19929},
      archivePrefix={arXiv},
      primaryClass={stat.AP}
}

Pre-requisites (Python Packages)

• pydicom
• SimpleITK
• tensorflow
• multiprocessing
• glob
• gc
• sklearn

File Tree

Below are the contents contained in this repo.

Paper_KEM
├── KEM_experiment
│   ├── 3D Reconstruction
│   ├── KEM_EXPE.py
│   ├── __pycache__
│   ├── experiment_SPE-2023-11-08.csv
│   ├── experiment_auxiliary.py
│   ├── 【LIDC】case_illustration(KEM_GT).ipynb
│   ├── 【LIDC】case_illustration.ipynb
│   └── 【LUNA0】SPE_experiment.ipynb
├── KEM_simulation
│   ├── KEM_SIMU.py
│   ├── Plot_Metrics_Compare.R
│   ├── __pycache__
│   ├── data_generate.py
│   ├── 【All0】simulation_study.ipynb
│   ├── 【Figure1】simulation_case_show.ipynb
│   ├── 【compare】simulation_case_show.ipynb
│   └── 【results】
├── Models
│   ├── GMM.py
│   ├── Kmeans.py
│   └── __pycache__
├── README.md
├── __pycache__
│   └── utils.cpython-39.pyc
└── utils.py

10 directories, 17 files

Codes Overview

The repository consists of two parts: part 1 is the code for simulation studies, and part 2 is that for real data experiment.

PART 1. Simulation

(1). Codes

• The following code files can be used to reproduce simulation results presented in the main paper.

File name	Description
data_generate.py	Python codes to generate parameters and synthetic responses in simulation.
KEM_SIMU.py	Python codes to implement the KEM algorithm in simulation.
【Figure1】simulation_case_show.ipynb	Jupyter notebook to plot Figure 1.
【All0】simulation_study.ipynb	Jupyter notebook to conduct the bandwidth selection and comparison between the KEM method, the $k$-means method and the GMM method. Results in Figure 2 are produced here.
Plot_Metrics_Compare.R	R codes to boxplot Figure 2.
【compare】simulation_case_show.ipynb	Jupyter notebook to visualize an example comparison between the KEM method, the $k$-means method and the GMM method. Only serve as an intuitive example.

(2). Results

• 【results】: the folder of the results in Figure 2

PART 2. Experiment

(1). Codes

• The following code files can be used to reproduce experiment results presented in the main paper.

File name	Description
experiment_auxiliary.py	Python codes for the auxiliary functions in the experiment.
KEM_EXPE.py	Python to implement the KEM algorithm tailored for the experiment, which is a little different from that of the simulation.
【LIDC】case_illustration.ipynb	Jupyter notebook to produce Figure 3.
【LIDC】case_illustration(KEM_GT).ipynb	Jupyter notebook to produce Figure D2 in the Supplementary Materials.
【LUNA0】SPE_experiment.ipynb	Jupyter notebook to produce the results in Figure 4.

1. Note that the dicom files should be load into RadiAnt (for example) for 3D visualization.
2. The colormaps used in this article are plt.cm.bone_r and plt.cm.bone.
3. I tried to directly use the KEM_SIMU.py in the real data experiment. However, sometimes the results were not satisfying. I found that it is better to use $\hat\mu^{(t)}$ in updating $\hat\sigma^{(t+1)}$ in the M step, rather than to use $\hat\mu^{(t+1)}$. This should be the only difference.

(2). Results

• experiment_SPE-2023-11-08.csv: the csv file of the results in Figure 4
• 3D Reconstruction: the folder of the 3D reconstructed dicom files