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Voronoi tessellation, also known as Voronoi diagram, is an important computational geometry technique that has applications in various scientific disciplines. It involves dividing a given space into regions based on the proximity to a set…
Although large-scale visual foundation models (VFMs) achieve remarkable performance in semantic understanding, they still underperform in instance-aware dense prediction tasks. They exhibit different biases in representation: for instance,…
This paper introduces a novel approach that combines unsupervised active contour models with deep learning for robust and adaptive image segmentation. Indeed, traditional active contours, provide a flexible framework for contour evolution…
The Voronoi diagram is a geometric object which is widely used in many areas. Recently it has been shown that under mild conditions Voronoi diagrams have a certain continuity property: small perturbations of the sites yield small…
We propose an active learning approach to image segmentation that exploits geometric priors to speed up and streamline the annotation process. It can be applied for both background-foreground and multi-class segmentation tasks in 2D images…
This paper describes an interdisciplinary approach to geometry modeling of geospatial boundaries. The objective is to extract surfaces from irregular spatial patterns using differential geometry and obtain coherent directional predictions…
In stark contrast to the case of images, finding a concise, learnable discrete representation of 3D surfaces remains a challenge. In particular, while polygon meshes are arguably the most common surface representation used in geometry…
In this paper, we propose a novel variational active contour model based on Aubert-Aujol (AA) denoising model, which hybrides geodesic active contour (GAC) model with active contours without edges (ACWE) model and can be used to segment…
For the analysis of systems consisting of small, regular objects, the methods of mathematical morphology applied to images of these systems are well-suited. One of these methods is the use of Voronoi polygons. It was found that the Voronoi…
Active contour models based on partial differential equations have proved successful in image segmentation, yet the study of their geometric formulation on arbitrary geometric graphs is still at an early stage. In this paper, we introduce…
The world is covered with millions of buildings, and precisely knowing each instance's position and extents is vital to a multitude of applications. Recently, automated building footprint segmentation models have shown superior detection…
Estimating the depth of omnidirectional images is more challenging than that of normal field-of-view (NFoV) images because the varying distortion can significantly twist an object's shape. The existing methods suffer from troublesome…
Spatial statistical analysis of multivariate volumetric data can be challenging due to scale, complexity, and occlusion. Advances in topological segmentation, feature extraction, and statistical summarization have helped overcome the…
Qualifying the discrepancy between 3D geometric models, which could be represented with either point clouds or triangle meshes, is a pivotal issue with board applications. Existing methods mainly focus on directly establishing the…
The construction of anisotropic triangulations is desirable for various applications, such as the numerical solving of partial differential equations and the representation of surfaces in graphics. To solve this notoriously difficult…
Voronoi diagrams naturally produce convex, watertight, and topologically consistent cells, making them an appealing representation for 3D shape reconstruction. However, standard differentiable Voronoi approaches typically optimize generator…
The Voronoi diagram is a certain geometric data structure which has numerous applications in various scientific and technological fields. The theory of algorithms for computing 2D Euclidean Voronoi diagrams of point sites is rich and…
Given two point sets in the plane, we study the minimization of the bottleneck distance between a point set B and an equally-sized subset of a point set A under translations. We relate this problem to a Voronoi-type diagram and derive…
This study proposes an innovative approach to analyze spatial patterns of behavior by integrating information in weighted Voronoi diagrams. The objective of the research is to analyze the temporal distribution of an experimental subject in…
Voronoi diagrams are essential geometrical structures with numerous applications, particularly astrophysics-driven finite volume methods. While serial algorithms for constructing these entities are well-established, parallel construction…