Related papers: Grassmannian diffusion maps based dimension reduct…

In the automatic reassembly of fragments acquired using laser scanners to reconstruct objects, a crucial step is the matching of fractured surfaces. In this paper, we propose a novel local descriptor that uses the Gaussian Mixture Model…

Various Graph Neural Networks (GNNs) have been successful in analyzing data in non-Euclidean spaces, however, they have limitations such as oversmoothing, i.e., information becomes excessively averaged as the number of hidden layers…

In this paper, we extend the class of kernel methods, the so-called diffusion maps (DM), and its local kernel variants, to approximate second-order differential operators defined on smooth manifolds with boundaries that naturally arise in…

Direct diffusion modeling of high-resolution spatiotemporal fields is computationally challenging. Parameter-efficient primitives address this by representing high-dimensional data with a compact set of parameters. In this paper, we…

Analyzing relationships between objects is a pivotal problem within data science. In this context, Dimensionality reduction (DR) techniques are employed to generate smaller and more manageable data representations. This paper proposes a new…

The Riemannian geometry of covariance matrices has been essential to several successful applications, in computer vision, biomedical signal and image processing, and radar data processing. For these applications, an important ongoing…

Diffusion models have achieved great progress in face generation. However, these models amplify the bias in the generation process, leading to an imbalance in distribution of sensitive attributes such as age, gender and race. This paper…

In this paper, we propose a novel space-time geometric representation of human landmark configurations and derive tools for comparison and classification. We model the temporal evolution of landmarks as parametrized trajectories on the…

One of the key advantages of 3D rendering is its ability to simulate intricate scenes accurately. One of the most widely used methods for this purpose is Gaussian Splatting, a novel approach that is known for its rapid training and…

Despite the success of diffusion models (DMs), we still lack a thorough understanding of their latent space. To understand the latent space $\mathbf{x}_t \in \mathcal{X}$, we analyze them from a geometrical perspective. Our approach…

Finding meaningful representations and distances of hierarchical data is important in many fields. This paper presents a new method for hierarchical data embedding and distance. Our method relies on combining diffusion geometry, a central…

We present Bayesian Diffusion Models (BDM), a prediction algorithm that performs effective Bayesian inference by tightly coupling the top-down (prior) information with the bottom-up (data-driven) procedure via joint diffusion processes. We…

Diffusion models are distinguished by their exceptional generative performance, particularly in producing high-quality samples through iterative denoising. While current theory suggests that the number of denoising steps required for…

Establishing reliable correspondences is crucial for all registration tasks, including 2D image registration, 3D point cloud registration, and 2D-3D image-to-point cloud registration. However, these tasks are often complicated by challenges…

In this paper, we propose a novel large deformation diffeomorphic registration algorithm to align high angular resolution diffusion images (HARDI) characterized by orientation distribution functions (ODFs). Our proposed algorithm seeks an…

The length of the geodesic between two data points along a Riemannian manifold, induced by a deep generative model, yields a principled measure of similarity. Current approaches are limited to low-dimensional latent spaces, due to the…

Dimensionality reduction algorithms map high-dimensional data into visualizable 2D or 3D spaces, but traditionally rely on a discrete point-cloud paradigm. This discrete abstraction is susceptible to visual occlusion and artificial…

Deep generative models are universal tools for learning data distributions on high dimensional data spaces via a mapping to lower dimensional latent spaces. We provide a study of latent space geometries and extend and build upon previous…

Can robots imagine or generate maps like humans do, especially when only limited information can be perceived like blind people? To address this challenging task, we propose a novel group diffusion model (GDM) based architecture for robots…

Graphs are ubiquitous, and learning on graphs has become a cornerstone in artificial intelligence and data mining communities. Unlike pixel grids in images or sequential structures in language, graphs exhibit a typical non-Euclidean…