Related papers: On Clustering Induced Voronoi Diagrams
Recently, significant progress has been made on image denoising with strong supervision from large-scale datasets. However, obtaining well-aligned noisy-clean training image pairs for each specific scenario is complicated and costly in…
The Voronoi Entropy (VE) and the continuous measure of symmetry (CSM) characterize the orderliness of a set of points on a 2D plane. The Voronoi entropy is the Shannon entropy of the Voronoi tessellation of the plane into polygons,…
Clustering algorithms are one of the main analytical methods to detect patterns in unlabeled data. Existing clustering methods typically treat samples in a dataset as points in a metric space and compute distances to group together similar…
Clustering is an important phenomenon in turbulent flows laden with inertial particles. Although this process has been studied extensively, there are still open questions about both the fundamental physics and the reconciliation of…
Masked Image Modeling (MIM) offers a promising approach to self-supervised representation learning, however existing MIM models still lag behind the state-of-the-art. In this paper, we systematically analyze target representations, loss…
Irregular arrangements of vesicles filled with excitable and precipitating chemical systems are imitated by Voronoi automata --- finite-state machines defined on a planar Voronoi diagram. Every Voronoi cell takes four states: resting,…
Various Vision Transformer (ViT) models have been widely used for image recognition tasks. However, existing visual explanation methods can not display the attention flow hidden inside the inner structure of ViT models, which explains how…
Vortex-induced vibration (VIV) is a typical nonlinear fluid-structure interaction phenomenon, which widely exists in practical engineering (the flexible riser, the bridge and the aircraft wing, etc). The conventional finite element model…
Cellular structures manifest their outstanding mechanical properties in many biological systems. One key challenge for designing and optimizing these geometrically complicated structures lies in devising an effective geometric…
The transition from ordered to disordered structures in Voronoi tessellation is obtained by perturbing the seeds that were originally identified with two types of lattice in 2D and one type in 3D. The area in 2D and the volume in 3D are…
Masked Image Modeling (MIM) is a new self-supervised vision pre-training paradigm using a Vision Transformer (ViT). Previous works can be pixel-based or token-based, using original pixels or discrete visual tokens from parametric tokenizer…
We introduce a novel method for acquiring boundary representations (B-Reps) of 3D CAD models which involves a two-step process: it first applies a spatial partitioning, referred to as the ``split``, followed by a ``fit`` operation to derive…
Clustering points in a vector space or nodes in a graph is a ubiquitous primitive in statistical data analysis, and it is commonly used for exploratory data analysis. In practice, it is often of interest to "refine" or "improve" a given…
Crowdedness caused by overlapping among similar objects is a ubiquitous challenge in the field of 2D visual object detection. In this paper, we first underline two main effects of the crowdedness issue: 1) IoU-confidence correlation…
This paper presents a new approach to obtaining nearly complete coverage paths (CP) with low overlapping on 3D general surfaces using mesh models. The CP is obtained by segmenting the mesh model into a given number of clusters using…
In this thesis we study sets of points in the plane and their Voronoi diagrams, in particular when the points coincide. We bring together two ways of studying point sets that have received a lot of attention in recent years: Voronoi…
Graph clustering is an unsupervised machine learning method that partitions the nodes in a graph into different groups. Despite achieving significant progress in exploiting both attributed and structured data information, graph clustering…
The size distributions of 2D and 3D Voronoi cells and of cells of $V_p(2,3)$,--2D cut of 3D Voronoi diagram--are explored, with the single-parameter (re-scaled) gamma distribution playing a central role in the analytical fitting.…
Voronoi mosaics inspired by the seed points placed on the Archimedes Spirals are reported. Voronoi entropy was calculated for these patterns. Equidistant and non-equidistant patterns are treated. Voronoi mosaics built from cells of equal…
Nowadays, big data of digital media (including images, videos and 3D graphical models) are frequently modeled as low-dimensional manifold meshes embedded in a high-dimensional feature space. In this paper, we summarized our recent work on…