Multi-view Classifier and Fast Brain Tumor Segmentation Using Geometric Fast Data Density Functional Transform

The article proposed a new architecture for fast brain tumor image segmentation based on their intrinsic geometric properties using the geometric fast data density functional transform (g-fDDFT). The g-fDDFT, as a feature pre-extractor, utilized the structure of AutoEncoder to provide global convolutions on images for extracting global features. It also exploited the geometric properties of energy landscapes offered by functional operations to reduce the computational costs caused by convolutional operations efficiently. Under the g-fDDFT framework, the computational complexity would reduce from $\mathcal{O}(n^3)$ to $\mathcal{O}(n\,\text{log}\, n)$. To verify its performance on tasks of brain tumor image segmentation and the recognition of oriented views of MRI data, we employed open-access resources from BraTS 2020 and clinical image datasets. We also used the U-Net, 3D-Unet, D-UNet, and nnU-Net as our backbone models for tumor segmentation. Experimental results validated that the training and inference time using the proposed g-fDDFT significantly reduced by 57% and 52%, respectively, compared to that using the naïve D-UNet. Meanwhile, the accuracy estimations of brain tumor image segmentation had comparable results between the backbone models and utilizing the g-fDDFT. The geometric multi-view classifier also benefited the recognition and segmentation of tumor and necrotic/peritumoral edema images of the clinical dataset. The capability of selecting tumor candidates and fast labeling also exhibits the exclusive performance of g-fDDFT. Its flexibility and corresponding physical constraints also reveal the possibility of model extension.