根據臨床統計惡性顱內腦瘤平均存活期約僅十五個月左右，兩年內的復發率更是幾乎百分之百，因此於早期進行評估、診斷和治療是非常重要的。同時於醫學影像技術中自動化的腦腫瘤辨識與分割任務的成功與否，對於醫生的診斷協助和患者疾病的診治策略扮演著重要角色。但由於醫生或醫事專家在核磁共振造影影像中手動標記腦瘤位置以及安排手術路徑與計畫需要耗費大量的時間，因此為了提高標記腦瘤位置和輪廓的準確率並同時降低醫生的時間與體力的負擔，本研究透過幾何深度學習模型訓練進行自動腦瘤影像辨識、分割與三維腫瘤體型重構。於研究中我們將使用 BraTS 2020資料集，其中資料集會先經過快速資料密度泛函轉換(fast Data Density Functional Transform)先進行腫瘤特徵強化，並結合能強化三微腦腫瘤特徵的Squeeze-and-excitation 模組於D-Unet (Dimension Fusion U- Net)的編碼器-解碼器架構(Encoder-Decoder Structure)中，以完成一系列的幾何深度學習模型並進行訓練。除了使用 D-Unet，我們也將使用其他各類深度學習模型，如nnU-Net、3D-U-net 等當代最熱門的腦腫瘤分割模型在模型計算複雜度以及Dice分割分數結果進行比較，再將Dice分數最高的模型進行改良以獲取最佳分割結果。我們的研究發現，經過快速資料密度泛函轉換之後的資料集，可以大幅縮短深度學習模型的訓練與推論時間(約在 50%以上)，並且還能提供模型的分割性能。

Clinical statistics reveal an average survival period of approximately fifteen months for malignant intracranial tumors, with an almost 100% recurrence rate within two years. Early assessment, diagnosis, and treatment are crucial in addressing this challenging prognosis. Therefore, the success of automated brain tumor recognition and segmentation tasks in medical imaging technology plays a vital role in assisting physicians with diagnosis and guiding patient treatment strategies. Manual annotation of tumor locations in magnetic resonance imaging (MRI) images and medical professionals planning surgical pathways is time-consuming. To improve the accuracy of tumor localization and contour marking while alleviating the burden on healthcare providers, this study employs geometric deep learning models for automatic brain
tumor image recognition, segmentation, and three-dimensional tumor volume reconstruction. In our research, we will use the BraTS 2020 dataset, which first undergoes fast data density functional transformation to enhance tumor features, and
combines it with Squeeze-and-excitation, which can enhance the features of three-microbrain tumors. The module is built into the Encoder-Decoder Structure of D-Unet(Dimension Fusion U-Net) to complete and train a series of geometric deep learning
models. In addition to using D-Unet, we will also use other types of deep learning models, such as nnU-Net, 3D-U-net and other contemporary most popular brain tumor segmentation models to compare the model computational complexity and Dice
segmentation score results, and then the model with the highest Dice score is improved to obtain the best segmentation results. Our research has found that the dataset after fast
data density functional transformation can significantly shorten the training and inference time of the deep learning model (about 50% or more), and can also improve the segmentation performance of the model.

參考文獻
[1] 台北榮民總醫院 腦瘤(brain tumors)治療準則
https://wd.vghtpe.gov.tw/hemaonco/files/Guide_BrainCA.pdf
[2] 中華民國 110 年癌症登記報告 CANCER REGISTRY ANNUAL REPORT,
2021 TAIWAN, 中華民國 112 年 12 月出版
[3] W. Wang, C. Chen, M. Ding, H. Yu, S. Zha, and J. Li, “TransBTS: Multimodal
brain tumor segmentation using transforme,” in Proc. Int. Conf. Med. Image Comput.
Comput.-Assist. Interv., 2021, pp. 109–119.
[4] F. Isensee, P. F. Jäger, P. M. Full, P. Vollmuth, and K. H. Maier-Hein, “nnU-Net
for brain tumor segmentation,” inProc. Int. MICCAI Brainlesion Workshop, 2021, pp.
118–132.
[5] Z. Zhang, Q. Liu, and Y. Wang, “Road extraction by deep residual u-net,” IEEE
Geosci. Remote Sens. Lett., vol. 15, no. 5, pp. 749–753, May 2018.
[6] Z. Zhou,M.M. Rahman Siddiquee, N. Tajbakhsh, and J. Liang, “UNet++: A
nested U-Net architecture for medical image segmentation,” in Proc. Deep Learn.
Med. Image Anal. Multimodal Learn. Clin. Decis. Support, 2018, pp. 3–11.
[7] R. McKinley, M. Rebsamen, R. Meier, and R. Wiest, “Triplanar ensemble of 3D-
to-2D CNNs with label-uncertainty for brain tumor segmentation,” in Proc. Int.
MICCAI Brainlesion Workshop, 2020, pp. 379–387.
[8] A. Vaswani et al., “Attention is all you need,” in Proc. 31st Neural Inf. Process.
Syst., 2017, pp. 5998–6008.
[9] C. Liu et al., “Auto-deeplab: Hierarchical neural architecture search for semantic
image segmentation,” in Proc. IEEE/CVF Conf. Comput. Vis. Pattern Recognit.,
2019, pp. 82–92.
[10] C. Szegedy et al., “Going deeper with convolutions,” in Proc. IEEE/CVF Conf.
Comput. Vis. Pattern Recognit., 2015, pp. 1–9.
[11] X. Wang, R. Girshick, A. Gupta, and K. He, “Non-local neural networks,” in
Proc. IEEE/CVF Conf. Comput. Vis. Pattern Recognit., 2018, pp. 7794–7803.
[12] J. Dai et al., “Deformable convolutional networks,” in Proc. IEEE Int. Conf.
Comput. Vis., 2017, pp. 764–773.
[13] L.-C. Chen, G. Papandreou, I. Kokkinos, K. Murphy, and A. L. Yuille, “Deeplab:
Semantic image segmentation with deep convolutional nets, atrous convolution, and
fully connected CRFs,” IEEE Trans. Pattern Anal. Mach. Intell., vol. 40, no. 4, pp.
834–848, Apr. 2018.
[14] L. Chi, B. Jiang, and Y. Mu, “Fast Fourier convolution,” in Proc. 34th Int. Conf.
Neural Inf. Process. Syst., 2020, pp. 4479–4488.
[15] L. Chi, G. Tian, Y. Mu, L. Xie, and Q. Tian, “Fast non-local neural networks
with spectral residual learning,” in Proc. 27th Assoc. Comput. Machinery Multimedia,
2019, pp. 2142–2151.
[16] D. Bahdanau, K. Cho, and Y. Bengio, “Neural machine translation by jointly
learning to align and translate,” in Proc. 3rd Int. Conf. Learn. Representations, 2015.
[17] A. Dosovitskiy et al., “An image is worth 16x16 words: Transformers for image
recognition at scale,” in Proc. Int. Conf. Learn. Representations, 2020.
[18] J. Long, E. Shelhamer, and T. Darrell, “Fully convolutional networks for
semantic segmentation,” in Proc. IEEE/CVF Conf. Comput. Vis. Pattern Recognit.,
2015, pp. 3431–3440.
[19] J. Chen et al., “Transunet: Transformers make strong encoders for medical image
segmentation,” 2021, arXiv:2102.04306.
[20] M. Dobko, D.-I. Kolinko, O. Viniavskyi, and Y. Yelisieiev, “Combining CNNs
With transformer for multimodal 3D MRI brain tumor segmentation with self-
supervised pretraining,” 2021, arXiv:2110.07919.
[21] N. Watters et al., “Visual interaction networks: Learning a physics simulator
from video,” in Proc. 31st Int. Neural Inf. Process. Syst., 2017, pp. 4542–4550.
[22] M. K. Abd-Ellah, A. I. Awad, A. A. M. Khalaf, and H. F. A. Hamed, “Two-
phase multi-model automatic brain tumour diagnosis system from magnetic resonance
images using convolutional neural networks,” J. Image Video Proc., vol. 97, pp. 1–10,
Sep. 2018.
[23] M. K. Abd-Ellah, A. I. Awad, A. A. M. Khalaf, and H. F. A. Hamed, “A review
on brain tumor diagnosis from MRI images: Practical implications, key achievements,
and lessons learned,” Magn. Reson. Imag., vol. 61, pp. 300–318, Sep. 2019.
[24] M. M. Bronstein, J. Bruna, Y. LeCun, A. Szlam, and P. Vandergheynst,
“Geometric deep learning: Going beyond euclidean data,” IEEE Signal Process.
Mag., vol. 34, no. 4, pp. 18–42, Jul. 2017.
[25] K. Gopinath, C. Desrosiers, and H. Lombaert, “Graph domain adaptation for
alignment-invariant brain surface segmentation,” in Proc. Uncertainty Safe Utilization
Mach. Learn. Med. Imag., Graphs Biomed. Image Anal., 2020, pp. 152–163.
[26] J. Liu et al., “Identification of early mild cognitive impairment using multimodal
data and graph convolutional networks,” BMC Bioinf., vol. 21, no. 6, pp. 1–12, 2020.
[27] S.-J. Huang, C.-C. Chen, Y. Kao, and H. H.-S. Lu, “Feature-aware unsupervised
lesion segmentation for brain tumor images using fast data density functional
transform,” Sci. Rep., vol. 13, no. 1, Aug. 2023, Art. no. 13582.
[28] C.-C. Chen, H.-H. Juan, M.-Y. Tsai, and H. H.-S. Lu, “Unsupervised learning
and pattern recognition of biological data structures with density functional theory
and machine learning,” Sci. Rep., vol. 8, no. 1, Jan. 2018, Art. no. 557.
[29] C.-C. Chen, M.-Y. Tsai, M.-Z. Kao, and H. H.-S. Lu, “Medical image
segmentation with adjustable computational complexity using data density
functionals,” Appl. Sci.-Basel, vol. 9, no. 8, Apr. 2019, Art. no. 1718.
[30] Z.-J. Su, T.-C. Chang, Y.-L. Tai, S.-J. Chang, and C.-C. Chen, “Attention U-net
with dimension-hybridized fast data density functional theory for automatic brain
tumor image segmentation,” in Proc. Int. MICCAI Brainlesion Workshop, 2021, pp.
81–92.
[31] Y.-L. Tai, S.-J. Huang, C.-C. Chen, and H. H.-S. Lu, “Computational complexity
reduction of neural networks of brain tumor image segmentation by introducing
fermi–Dirac correction functions,” Entropy, vol. 23, no. 2, Feb. 2021, Art. no. 223.
[32] J. Long, E. Shelhamer, T. Darrell, Fully convolutional networks for semantic
segmentation,in: Proceedings of the IEEE conference on computer vision and pattern
recognition, 2015, pp.3431–3440.
[33] O. Ronneberger, P. Fischer, T. Brox, U-net: Convolutional networks for
biomedical imagesegmentation, in: International Conference on Medical image
computing and computer-assisted intervention, Springer, 2015, pp. 234–241.
[34] F. Isensee, P. F. Jäger, P. M. Full, P. Vollmuth, and K. H. Maier-Hein, “nnU-Net
for brain tumor segmentation,” inProc. Int. MICCAI Brainlesion Workshop, 2021, pp.
118–132.
[35] Ö. Çiçek, A. Abdulkadir, S. S. Lienkamp, T. Brox, and O. Ronneberger, “3D U-
Net: Learning dense volumetric segmentation from sparse annotation,” in Proc. Int.
Conf. Med. Image Comput. Comput.-Assist. Interv., 2016, pp. 424–432.
[36] B. H. Menze et al., “The multimodal brain tumor image segmentation benchmark
(BRATS),” IEEE Trans. Med. Imag., vol. 34, no. 10, pp. 1993–2024, Oct. 2015.
[37] S. Bakas et al., “Advancing the cancer genome atlas glioma MRI collections with
expert segmentation labels and radiomic features,” Sci. Data, vol. 4, Sep. 2017, Art.
no. 170117.
[38] S. Bakas et al., “Identifying the best machine learning algorithms for brain tumor
segmentation, progression assessment, and overall survival prediction in the BRATS
challenge,” 2018, arXiv:1811.02629.
[39] S. Bakas et al., “Segmentation labels and radiomic features for the preoperative
scans of the TCGA-GBM collection,” The Cancer Imaging Archive, 2017. [Online].
Available:
https://wiki.cancerimagingarchive.net/pages/viewpage.action?pageId=24282666
[40] S. Bakas et al., “Segmentation labels and radiomic features for the pre-operative
scans of the TCGA-LGG collection,” The Cancer Imaging Archive, 2017. [Online].
Available:
https://wiki.cancerimagingarchive.net/pages/viewpage.action?pageId=24282668
[41] U. Baid et al., “The RSNA-ASNR-MICCAI BraTS 2021 benchmark on brain
tumor segmentation and radiogenomic classification,” 2021, arXiv:2107.02314.
[42] J. Phys. Chem. 1996, 100, 31, 12974–12980 Publication Date:August 1, 1996
https://doi.org/10.1021/jp960669l Copyright © 1996 American Chemical Society
RIGHTS &PERMISSIONS
[43] Y. Zhou, W. Huang, P. Dong, Y. Xia, and S. Wang, “D-UNet: A dimension-
fusion U shape network for chronic stroke lesion segmentation,” IEEE/ACM Trans.
Comput. Biol. Bioinf., vol. 18, no. 3, pp. 940–950, May/Jun. 2021.
[44] P. Molchanov, S. Tyree, T. Karras, T. Aila, and J. Kautz, “Pruning convolutional
neural networks for resource efficient inference,” in Proc. Int. Conf. Learn.
Representations, 2017, pp. 1–17.
[45] F. Isensee, P. F. Jäger, P. M. Full, P. Vollmuth, and K. H. Maier-Hein, “nnU-Net
for brain tumor segmentation,” inProc. Int. MICCAI Brainlesion Workshop, 2021, pp.
118–132.