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We consider estimating the parameters of a Gaussian mixture density with a given number of components best representing a given set of weighted samples. We adopt a density interpretation of the samples by viewing them as a discrete Dirac…
Novel View Synthesis (NVS) from unconstrained photo collections is challenging in computer graphics. Recently, 3D Gaussian Splatting (3DGS) has shown promise for photorealistic and real-time NVS of static scenes. Building on 3DGS, we…
Ordinary differential equations (ODE) have been widely used for modeling dynamical complex systems. For high-dimensional ODE models where the number of differential equations is large, it remains challenging to estimate the ODE parameters…
3D Gaussian Splatting (3DGS) has become increasingly popular in 3D scene reconstruction for its high visual accuracy. However, uncertainty estimation of 3DGS scenes remains underexplored and is crucial to downstream tasks such as asset…
Effective image tokenization is crucial for both multi-modal understanding and generation tasks due to the necessity of the alignment with discrete text data. To this end, existing approaches utilize vector quantization (VQ) to project…
Image interpolation algorithms pervade many modern image processing and analysis applications. However, when their weighting schemes inefficiently generate very unrealistic estimates, they may negatively affect the performance of the end…
Gaussian processes are a powerful framework for quantifying uncertainty and for sequential decision-making but are limited by the requirement of solving linear systems. In general, this has a cubic cost in dataset size and is sensitive to…
Practical diffusion sampling is a numerical approximation problem: under a fixed inference budget, one must simulate a reverse-time ODE or SDE using only a limited number of denoising steps, so discretization error is often the dominant…
We investigate whether there is a relationship between the discrete Bakry-\'{E}mery curvature of a graph and the smooth curvature of an ambient surface into which the graph is embedded geodesically. As we used weighted graphs as test…
Machine learning methods for computational imaging require uncertainty estimation to be reliable in real settings. While Bayesian models offer a computationally tractable way of recovering uncertainty, they need large data volumes to be…
Accurate quantum tomography is a vital tool in both fundamental and applied quantum science. It is a task that involves processing a noisy measurement record in order to construct a reliable estimate of an unknown quantum state, and is…
Over the past three decades, defocus has consistently provided groundbreaking depth information in scene images. However, accurately estimating depth from 2D images continues to be a persistent and fundamental challenge in the field of 3D…
This article revisits the problem of Bayesian shape-restricted inference in the light of a recently developed approximate Gaussian process that admits an equivalent formulation of the shape constraints in terms of the basis coefficients. We…
Gaussian processes are a powerful framework for uncertainty-aware function approximation and sequential decision-making. Unfortunately, their classical formulation does not scale gracefully to large amounts of data and modern hardware for…
Large-scale precision matrix estimation is of fundamental importance yet challenging in many contemporary applications for recovering Gaussian graphical models. In this paper, we suggest a new approach of innovated scalable efficient…
Minimization of boundary curvature is a classic regularization technique for image segmentation in the presence of noisy image data. Techniques for minimizing curvature have historically been derived from descent methods which could be…
We develop a new estimator of the inverse covariance matrix for high-dimensional multivariate normal data using the horseshoe prior. The proposed graphical horseshoe estimator has attractive properties compared to other popular estimators,…
The 3D Gaussian splatting methods are getting popular. However, they work directly on the signal, leading to a dense representation of the signal. Even with some techniques such as pruning or distillation, the results are still dense. In…
Depth information is useful in many image processing applications. However, since taking a picture is a process of projection of a 3D scene onto a 2D imaging sensor, the depth information is embedded in the image. Extracting the depth…
We propose GauS-SLAM, a dense RGB-D SLAM system that leverages 2D Gaussian surfels to achieve robust tracking and high-fidelity mapping. Our investigations reveal that Gaussian-based scene representations exhibit geometry distortion under…