相关论文: Measuring Fractal Dimension using Discrete Global …

The Gromov--Wasserstein (GW) distance and its fused extension (FGW) are powerful tools for comparing heterogeneous data. Their computation is, however, challenging since both distances are based on non-convex, quadratic optimal transport…

Wireless mesh networks (WMNs) depend on the spatial distribution of nodes, which directly influences connectivity, routing efficiency, and overall network performance. Conventional models typically assume uniform or random node placement,…

Gaussian Splatting has been considered as a novel way for view synthesis of dynamic scenes, which shows great potential in AIoT applications such as digital twins. However, recent dynamic Gaussian Splatting methods significantly degrade…

Fractal structure of a system suggests the optimal way in which parts arranged or put together to form a whole. The ideas from fractals have a potential application to the researches on urban sustainable development. To characterize fractal…

This work presents a novel descriptor for texture images based on fractal geometry and its application to image analysis. The descriptors are provided by estimating the triangular prism fractal dimension under different scales with a weight…

Hyperspectral 3D imaging aims to acquire both depth and spectral information of a scene. However, existing methods are either prohibitively expensive and bulky or compromise on spectral and depth accuracy. In this work, we present Dispersed…

In modern computer vision, images are typically represented as a fixed uniform grid with some stride and processed via a deep convolutional neural network. We argue that deforming the grid to better align with the high-frequency image…

Multidimensional scaling (MDS) is a popular technique for mapping a finite metric space into a low-dimensional Euclidean space in a way that best preserves pairwise distances. We study a notion of MDS on infinite metric measure spaces,…

{\bf Purpose}: To develop a geometry-governed diffusion framework that explains differential tissue response under FLASH ultra-high dose rate (UHDR) irradiation by explicitly accounting for structural heterogeneity and anomalous transport…

Our goal in this paper is to develop an effective estimator of fractal dimension. We survey existing ideas in dimension estimation, with a focus on the currently popular method of Grassberger and Procaccia for the estimation of correlation…

3D reconstruction from unconstrained image collections presents substantial challenges due to varying appearances and transient occlusions. In this paper, we introduce Micro-macro Wavelet-based Gaussian Splatting (MW-GS), a novel approach…

Recent results from a number of redshift surveys suggest that the Universe is well described by an inhomogeneous, fractal distribution on the largest scales probed. This distribution has been found to have fractal dimension, D,…

The method of minimal geometric deformation (MGD) is used to derive static, strongly gravitating, spherically symmetric, compact stellar distributions. The trace and Weyl anomalies are then employed to probe the MGD in the holographic…

In this paper, we introduce Trim 3D Gaussian Splatting (TrimGS) to reconstruct accurate 3D geometry from images. Previous arts for geometry reconstruction from 3D Gaussians mainly focus on exploring strong geometry regularization. Instead,…

Perfect fractals are mathematical objects that, because they are generated by recursive processes, have self-similarity and infinite complexity. In particular, they also have a fractional dimension. Although several proposals for the study…

The Galerkin difference (GD) basis is a set of continuous, piecewise polynomials defined using a finite difference like grid of degrees of freedom. The one dimensional GD basis functions are naturally extended to multiple dimensions using…

Complex networks have recently attracted much attention in diverse areas of science and technology. Many networks such as the WWW and biological networks are known to display spatial heterogeneity which can be characterized by their fractal…

Contemporary automatic first break (FB) picking methods typically analyze 1D signals, 2D source gathers, or 3D source-receiver gathers. Utilizing higher-dimensional data, such as 2D or 3D, incorporates global features, improving the…

The functional features of spatial networks depend upon a non-trivial relationship between the topological and physical structure. Here, we explore that relationship for spatial networks with radial symmetry and disordered fractal…

In this paper, we tackle the problem of constructing a differentially private synopsis for two-dimensional datasets such as geospatial datasets. The current state-of-the-art methods work by performing recursive binary partitioning of the…