Related papers: Minimum-Error Triangulations for Sea Surface Recon…
Image processing on surfaces has drawn significant interest in recent years, particularly in the context of denoising. Salt-and-pepper noise is a special type of noise which randomly sets a portion of the image pixels to the minimum or…
This paper proposes improvements to the physically-based surface triangulation method, bubble meshing. The method simulates physical bubbles to automatically generate mesh vertices, resulting in high-quality Delaunay triangles. Despite its…
In this paper, we propose a novel technique to reconstruct 3D surface of an underwater object using stereo images. Reconstructing the 3D surface of an underwater object is really a challenging task due to degraded quality of underwater…
We introduce a continuous global optimization method to the field of surface reconstruction from discrete noisy cloud of points with weak information on orientation. The proposed method uses an energy functional combining flux-based…
The multiway-cut problem is, given a weighted graph and k >= 2 terminal nodes, to find a minimum-weight set of edges whose removal separates all the terminals. The problem is NP-hard, and even NP-hard to approximate within 1+delta for some…
We present a method for reconstructing triangle meshes from point clouds. Existing learning-based methods for mesh reconstruction mostly generate triangles individually, making it hard to create manifold meshes. We leverage the properties…
Precise 3D measurements of rigid surfaces are desired in many fields of application like quality control or surgery. Often, views from all around the object have to be acquired for a full 3D description of the object surface. We present a…
For any given metric space, obtaining an offline optimal solution to the classical $k$-server problem can be reduced to solving a minimum-cost partial bipartite matching between two point sets $A$ and $B$ within that metric space. For…
In this survey article, we are interested on minimal triangulations of closed pl manifolds. We present a brief survey on the works done in last 25 years on the following: (i) Finding the minimal number of vertices required to triangulate a…
Two-dimensional Delaunay triangulation is a fundamental aspect of computational geometry. This paper presents a novel algorithm that is specifically designed to ensure the correctness of 2D Delaunay triangulation, namely the Polygonal…
In this work, we study the perception problem for sampled surfaces (possibly with boundary) using tools from computational topology, specifically, how to identify their underlying topology starting from point-cloud samples in space, such as…
Learning the fine-scale details of a coastal ocean simulation from a coarse representation is a challenging task. For real-world applications, high-resolution simulations are necessary to advance understanding of many coastal processes,…
We present the winning implementation of the Seventh Computational Geometry Challenge (CG:SHOP 2025). The task in this challenge was to find non-obtuse triangulations for given planar regions, respecting a given set of constraints…
Let $P$ be a set of $n$ points in the plane. A crossing-free structure on $P$ is a plane graph with vertex set $P$. Examples of crossing-free structures include triangulations of $P$, spanning cycles of $P$, also known as polygonalizations…
In the Sparse Linear Regression (SLR) problem, given a $d \times n$ matrix $M$ and a $d$-dimensional query $q$, the goal is to compute a $k$-sparse $n$-dimensional vector $\tau$ such that the error $||M \tau-q||$ is minimized. This problem…
We study the problem of reconstructing an unknown point in $\mathbb{R}^d$ from approximate linear queries. This setting arises naturally in applications ranging from low-dimensional remote sensing and signal recovery to high-dimensional…
Precise three-dimensional (3D) reconstruction of wave free surfaces and associated velocity fields is essential for developing a comprehensive understanding of ocean physics. To address the high computational cost of dense visual…
We present improved distributed algorithms for triangle detection and its variants in the CONGEST model. We show that Triangle Detection, Counting, and Enumeration can be solved in $\tilde{O}(n^{1/2})$ rounds. In contrast, the previous…
A fundamental challenge in ocean dynamics is disentangling balanced motions and internal waves. Extracting internal tidal (IT) imprints from surface data is a central part of this challenge. Traditional harmonic analysis can fail under…
We consider the complexity of Delaunay triangulations of sets of points in R^3 under certain practical geometric constraints. The spread of a set of points is the ratio between the longest and shortest pairwise distances. We show that in…