Related papers: Probabilistic Diffeomorphic Registration: Represen…

Diffusion models have emerged as a key pillar of foundation models in visual domains. One of their critical applications is to universally solve different downstream inverse tasks via a single diffusion prior without re-training for each…

Superresolution theory and techniques seek to recover signals from samples in the presence of blur and noise. Discrete image registration can be an approach to fuse information from different sets of samples of the same signal. Quantization…

Deformable medical image registration is a fundamental task in medical image analysis. While deep learning-based methods have demonstrated superior accuracy and computational efficiency compared to traditional techniques, they often…

The Bayesian inversion method demonstrates significant potential for solving inverse problems, enabling both point estimation and uncertainty quantification (UQ). However, Bayesian maximum a posteriori (MAP) estimation may become unstable…

The rapid progress of diffusion models highlights the growing need for detecting generated images. Previous research demonstrates that incorporating diffusion-based measurements, such as reconstruction error, can enhance the…

Pseudospectral approximation provides a means to approximate the dynamics of delay differential equations (DDE) by ordinary differential equations (ODE). This article develops a computer-aided algorithm to determine the distance between the…

Uncertainty quantification for full-waveform inversion provides a probabilistic characterization of the ill-conditioning of the problem, comprising the sensitivity of the solution with respect to the starting model and data noise. This…

This paper discusses the mathematical framework for designing methods of large deformation matching (LDM) for image registration in computational anatomy. After reviewing the geometrical framework of LDM image registration methods, a…

Diffeomorphic image registration (DIR) is a fundamental task in 3D medical image analysis that seeks topology-preserving deformations between image pairs. To ensure diffeomorphism, a common approach is to model the deformation field as the…

There are two major types of uncertainty one can model. Aleatoric uncertainty captures noise inherent in the observations. On the other hand, epistemic uncertainty accounts for uncertainty in the model -- uncertainty which can be explained…

Embedding methods have achieved success in face recognition by comparing facial features in a latent semantic space. However, in a fully unconstrained face setting, the facial features learned by the embedding model could be ambiguous or…

As one of the most popular generative models, Variational Autoencoder (VAE) approximates the posterior of latent variables based on amortized variational inference. However, when the decoder network is sufficiently expressive, VAE may lead…

Nonstationary Gaussian processes (GPs) are essential for modeling complex, locally heterogeneous spatial data. A common modeling approach is the spatial deformation method that warps the domain to recover isotropy. However, this static…

Parameter identification problems are formulated in a probabilistic language, where the randomness reflects the uncertainty about the knowledge of the true values. This setting allows conceptually easily to incorporate new information, e.g.…

This paper addresses the challenging problem of category-level pose estimation. Current state-of-the-art methods for this task face challenges when dealing with symmetric objects and when attempting to generalize to new environments solely…

Image registration techniques usually assume that the images to be registered are of a certain type (e.g. single- vs. multi-modal, 2D vs. 3D, rigid vs. deformable) and there lacks a general method that can work for data under all…

Identifying and quantifying $\gamma$-emitting radionuclides, considering spectral deformation from $\gamma$-interactions in radioactive source surroundings, present a significant challenge in $\gamma$-ray spectrometry. In that context, a…

Recovering camera poses from a set of images is a foundational task in 3D computer vision, which powers key applications such as 3D scene/object reconstructions. Classic methods often depend on feature correspondence, such as keypoints,…

Epistemic Uncertainty is a measure of the lack of knowledge of a learner which diminishes with more evidence. While existing work focuses on using the variance of the Bayesian posterior due to parameter uncertainty as a measure of epistemic…

Uncertainty quantification for image data is dominated by complex deep learning methods, yet the field lacks an interpretable, mathematically grounded baseline. We propose Bayesian scattering to fill this gap, serving as a first-step…