Related papers: The Simplex Projection: Lossless Visualization of …

Perspective functions arise explicitly or implicitly in various forms in applied mathematics and in statistical data analysis. To date, no systematic strategy is available to solve the associated, typically nonsmooth, optimization problems.…

Compositional data are commonly known as multivariate observations carrying relative information. Even though the case of vector or even two-factorial compositional data (compositional tables) is already well described in the literature,…

We extend recent computer-assisted design and analysis techniques for first-order optimization over structured functions--known as performance estimation--to apply to structured sets. We prove "interpolation theorems" for smooth and…

Obtaining compositional mappings is important for the model to generalize well compositionally. To better understand when and how to encourage the model to learn such mappings, we study their uniqueness through different perspectives.…

Understanding dynamic 3D scenes is crucial for extended reality (XR) and autonomous driving. Incorporating semantic information into 3D reconstruction enables holistic scene representations, unlocking immersive and interactive applications.…

Recovering dense and long-range pixel motion in videos is a challenging problem. Part of the difficulty arises from the 3D-to-2D projection process, leading to occlusions and discontinuities in the 2D motion domain. While 2D motion can be…

This paper targets high-fidelity and real-time view synthesis of dynamic 3D scenes at 4K resolution. Recently, some methods on dynamic view synthesis have shown impressive rendering quality. However, their speed is still limited when…

By using Moreau's decomposition theorem for projecting onto cones, the problem of projecting onto a simplicial cone is reduced to finding the unique solution of a nonsmooth system of equations. It is shown that Picard's method applied to…

As an important method of handling potential uncertainties in numerical simulations, ensemble simulation has been widely applied in many disciplines. Visualization is a promising and powerful ensemble simulation analysis method. However,…

We consider estimating a compact set from finite data by approximating the support function of that set via sublinear regression. Support functions uniquely characterize a compact set up to closure of convexification, and are sublinear…

We propose SparseFusion, a sparse view 3D reconstruction approach that unifies recent advances in neural rendering and probabilistic image generation. Existing approaches typically build on neural rendering with re-projected features but…

A folded type model is developed for analyzing compositional data. The proposed model involves an extension of the $\alpha$-transformation for compositional data and provides a new and flexible class of distributions for modeling data…

In Geographical Information search, map visualization can challenge the user because results can consist of a large set of heterogeneous items, increasing visual complexity. We propose a novel visualization model to address this issue. Our…

Compositional data, representing proportions constrained to the simplex, arise in diverse fields such as geosciences, ecology, genomics, and microbiome research. Existing nonparametric density estimation methods often rely on…

Accurate depth estimation from monocular videos remains challenging due to ambiguities inherent in single-view geometry, as crucial depth cues like stereopsis are absent. However, humans often perceive relative depth intuitively by…

We propose a linear time and constant space algorithm for computing Euclidean projections onto sets on which a normalized sparseness measure attains a constant value. These non-convex target sets can be characterized as intersections of a…

There are two prevalent ways to constructing 3D scenes: procedural generation and 2D lifting. Among them, panorama-based 2D lifting has emerged as a promising technique, leveraging powerful 2D generative priors to produce immersive,…

For a plane symmetric object we can find two views - mirrored at the plane of symmetry - that will yield the exact same image of that object. In consequence, having one image of a plane symmetric object and a calibrated camera, we can…

Random projection (RP) is a classical technique for reducing storage and computational costs. We analyze RP-based approximations of convex programs, in which the original optimization problem is approximated by the solution of a…

Dense 3D reconstruction and tracking of dynamic scenes from monocular video remains an important open challenge in computer vision. Progress in this area has been constrained by the scarcity of high-quality datasets with dense, complete,…