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TetCNN: Convolutional Neural Networks on Tetrahedral Meshes
Feb 14, 2023
Convolutional neural networks (CNN) have been broadly studied on images, videos, graphs, and triangular meshes. However, it has seldom been studied on tetrahedral meshes. Given the merits of using volumetric meshes in applications like brain image analysis, we introduce a novel interpretable graph CNN framework for the tetrahedral mesh structure. Inspired by ChebyNet, our model exploits the volumetric Laplace-Beltrami Operator (LBO) to define filters over commonly used graph Laplacian which lacks the Riemannian metric information of 3D manifolds. For pooling adaptation, we introduce new objective functions for localized minimum cuts in the Graclus algorithm based on the LBO. We employ a piece-wise constant approximation scheme that uses the clustering assignment matrix to estimate the LBO on sampled meshes after each pooling. Finally, adapting the Gradient-weighted Class Activation Mapping algorithm for tetrahedral meshes, we use the obtained heatmaps to visualize discovered regions-of-interest as biomarkers. We demonstrate the effectiveness of our model on cortical tetrahedral meshes from patients with Alzheimer's disease, as there is scientific evidence showing the correlation of cortical thickness to neurodegenerative disease progression. Our results show the superiority of our LBO-based convolution layer and adapted pooling over the conventionally used unitary cortical thickness, graph Laplacian, and point cloud representation.
OTRE: Where Optimal Transport Guided Unpaired Image-to-Image Translation Meets Regularization by Enhancing
Feb 09, 2023
Non-mydriatic retinal color fundus photography (CFP) is widely available due to the advantage of not requiring pupillary dilation, however, is prone to poor quality due to operators, systemic imperfections, or patient-related causes. Optimal retinal image quality is mandated for accurate medical diagnoses and automated analyses. Herein, we leveraged the Optimal Transport (OT) theory to propose an unpaired image-to-image translation scheme for mapping low-quality retinal CFPs to high-quality counterparts. Furthermore, to improve the flexibility, robustness, and applicability of our image enhancement pipeline in the clinical practice, we generalized a state-of-the-art model-based image reconstruction method, regularization by denoising, by plugging in priors learned by our OT-guided image-to-image translation network. We named it as regularization by enhancing (RE). We validated the integrated framework, OTRE, on three publicly available retinal image datasets by assessing the quality after enhancement and their performance on various downstream tasks, including diabetic retinopathy grading, vessel segmentation, and diabetic lesion segmentation. The experimental results demonstrated the superiority of our proposed framework over some state-of-the-art unsupervised competitors and a state-of-the-art supervised method.
Optimal Transport Guided Unsupervised Learning for Enhancing low-quality Retinal Images
Feb 06, 2023
Real-world non-mydriatic retinal fundus photography is prone to artifacts, imperfections and low-quality when certain ocular or systemic co-morbidities exist. Artifacts may result in inaccuracy or ambiguity in clinical diagnoses. In this paper, we proposed a simple but effective end-to-end framework for enhancing poor-quality retinal fundus images. Leveraging the optimal transport theory, we proposed an unpaired image-to-image translation scheme for transporting low-quality images to their high-quality counterparts. We theoretically proved that a Generative Adversarial Networks (GAN) model with a generator and discriminator is sufficient for this task. Furthermore, to mitigate the inconsistency of information between the low-quality images and their enhancements, an information consistency mechanism was proposed to maximally maintain structural consistency (optical discs, blood vessels, lesions) between the source and enhanced domains. Extensive experiments were conducted on the EyeQ dataset to demonstrate the superiority of our proposed method perceptually and quantitatively.
Anisotropic Multi-Scale Graph Convolutional Network for Dense Shape Correspondence
Oct 17, 2022
This paper studies 3D dense shape correspondence, a key shape analysis application in computer vision and graphics. We introduce a novel hybrid geometric deep learning-based model that learns geometrically meaningful and discretization-independent features with a U-Net model as the primary node feature extraction module, followed by a successive spectral-based graph convolutional network. To create a diverse set of filters, we use anisotropic wavelet basis filters, being sensitive to both different directions and band-passes. This filter set overcomes the over-smoothing behavior of conventional graph neural networks. To further improve the model's performance, we add a function that perturbs the feature maps in the last layer ahead of fully connected layers, forcing the network to learn more discriminative features overall. The resulting correspondence maps show state-of-the-art performance on the benchmark datasets based on average geodesic errors and superior robustness to discretization in 3D meshes. Our approach provides new insights and practical solutions to the dense shape correspondence research.