On the Utility of Equivariance and Symmetry Breaking in Deep Learning Architectures on Point Clouds

This paper explores the key factors that influence the performance of models working with point clouds, across different tasks of varying geometric complexity. In this work, we explore the trade-offs between flexibility and weight-sharing introduced by equivariant layers, assessing when equivariance boosts or detracts from performance. It is often argued that providing more information as input improves a model's performance. However, if this additional information breaks certain properties, such as $\SE(3)$ equivariance, does it remain beneficial? We identify the key aspects of equivariant and non-equivariant architectures that drive success in different tasks by benchmarking them on segmentation, regression, and generation tasks across multiple datasets with increasing complexity. We observe a positive impact of equivariance, which becomes more pronounced with increasing task complexity, even when strict equivariance is not required.

Uncertainty-aware retinal layer segmentation in OCT through probabilistic signed distance functions

In this paper, we present a new approach for uncertainty-aware retinal layer segmentation in Optical Coherence Tomography (OCT) scans using probabilistic signed distance functions (SDF). Traditional pixel-wise and regression-based methods primarily encounter difficulties in precise segmentation and lack of geometrical grounding respectively. To address these shortcomings, our methodology refines the segmentation by predicting a signed distance function (SDF) that effectively parameterizes the retinal layer shape via level set. We further enhance the framework by integrating probabilistic modeling, applying Gaussian distributions to encapsulate the uncertainty in the shape parameterization. This ensures a robust representation of the retinal layer morphology even in the presence of ambiguous input, imaging noise, and unreliable segmentations. Both quantitative and qualitative evaluations demonstrate superior performance when compared to other methods. Additionally, we conducted experiments on artificially distorted datasets with various noise types-shadowing, blinking, speckle, and motion-common in OCT scans to showcase the effectiveness of our uncertainty estimation. Our findings demonstrate the possibility to obtain reliable segmentation of retinal layers, as well as an initial step towards the characterization of layer integrity, a key biomarker for disease progression. Our code is available at \url{https://github.com/niazoys/RLS_PSDF}.

Conditioning 3D Diffusion Models with 2D Images: Towards Standardized OCT Volumes through En Face-Informed Super-Resolution

High anisotropy in volumetric medical images can lead to the inconsistent quantification of anatomical and pathological structures. Particularly in optical coherence tomography (OCT), slice spacing can substantially vary across and within datasets, studies, and clinical practices. We propose to standardize OCT volumes to less anisotropic volumes by conditioning 3D diffusion models with en face scanning laser ophthalmoscopy (SLO) imaging data, a 2D modality already commonly available in clinical practice. We trained and evaluated on data from the multicenter and multimodal MACUSTAR study. While upsampling the number of slices by a factor of 8, our method outperforms tricubic interpolation and diffusion models without en face conditioning in terms of perceptual similarity metrics. Qualitative results demonstrate improved coherence and structural similarity. Our approach allows for better informed generative decisions, potentially reducing hallucinations. We hope this work will provide the next step towards standardized high-quality volumetric imaging, enabling more consistent quantifications.