Related papers: RDA-INR: Riemannian Diffeomorphic Autoencoding via…

In this paper, we propose a new method to perform data augmentation in a reliable way in the High Dimensional Low Sample Size (HDLSS) setting using a geometry-based variational autoencoder. Our approach combines a proper latent space…

Data augmentation is a key element in training high-dimensional models. In this approach, one synthesizes new observations by applying pre-specified transformations to the original training data; e.g.~new images are formed by rotating old…

Recent advances in scene understanding benefit a lot from depth maps because of the 3D geometry information, especially in complex conditions (e.g., low light and overexposed). Existing approaches encode depth maps along with RGB images and…

In this paper we propose a generalization of deep neural networks called deep function machines (DFMs). DFMs act on vector spaces of arbitrary (possibly infinite) dimension and we show that a family of DFMs are invariant to the dimension of…

Classical archetypal analysis is appealing for its interpretability, but its linear geometry can limit performance on data with strongly non-linear structure; at the same time, existing neural extensions improve flexibility while often…

This paper introduces a new interpretation of the Variational Autoencoder framework by taking a fully geometric point of view. We argue that vanilla VAE models unveil naturally a Riemannian structure in their latent space and that taking…

We introduce the Linearized Diffusion Map (LDM), a novel linear dimensionality reduction method constructed via a linear approximation of the diffusion-map kernel. LDM integrates the geometric intuition of diffusion-based nonlinear methods…

Large-scale pre-training tasks like image classification, captioning, or self-supervised techniques do not incentivize learning the semantic boundaries of objects. However, recent generative foundation models built using text-based latent…

Accurate longitudinal analysis of brain MRI is often hindered by evolving lesions, which bias automated neuroimaging pipelines. While deep generative models have shown promise in inpainting these lesions, most existing methods operate…

Image generative models, particularly diffusion-based models, have surged in popularity due to their remarkable ability to synthesize highly realistic images. However, since these models are data-driven, they inherit biases from the…

Deep Learning in Image Registration (DLIR) methods have been tremendously successful in image registration due to their speed and ability to incorporate weak label supervision at training time. However, existing DLIR methods forego many of…

Decentralized optimization on Riemannian manifolds is foundational for many modern machine learning and signal processing applications in which data are non-Euclidean and generated and processed in a distributed manner. Although intrinsic…

Understanding the relationship between cognition and intrinsic brain activity through purely data-driven approaches remains a significant challenge in neuroscience. Resting-state functional magnetic resonance imaging (rs-fMRI) offers a…

Traditional deformable registration techniques achieve impressive results and offer a rigorous theoretical treatment, but are computationally intensive since they solve an optimization problem for each image pair. Recently, learning-based…

Data sets tend to live in low-dimensional non-linear subspaces. Ideal data analysis tools for such data sets should therefore account for such non-linear geometry. The symmetric Riemannian geometry setting can be suitable for a variety of…

Deformable templates, or atlases, are images that represent a prototypical anatomy for a population, and are often enhanced with probabilistic anatomical label maps. They are commonly used in medical image analysis for population studies…

Riemannian geometry provides the fundamental framework for optimization on nonlinear spaces such as matrix manifolds, which arise in machine learning, signal processing, and robotics. While the underlying theory is classical, existing…

The space of embedded submanifolds plays an important role in applications such as computational anatomy and shape analysis. We can define two different classes on Riemannian metrics on this space: so-called outer metrics are metrics that…

Image registration and in particular deformable registration methods are pillars of medical imaging. Inspired by the recent advances in deep learning, we propose in this paper, a novel convolutional neural network architecture that couples…

Depth estimation plays a pivotal role in advancing human-robot interactions, especially in indoor environments where accurate 3D scene reconstruction is essential for tasks like navigation and object handling. Monocular depth estimation,…