Related papers: A Generalized Asymmetric Dual-front Model for Acti…

Two-region image segmentation is the process of dividing an image into two regions of interest, i.e., the foreground and the background. To this aim, Chan et al. [Chan, Esedo\=glu, Nikolova, SIAM Journal on Applied Mathematics 66(5),…

Voronoi tessellations have been used to model the geometric arrangement of cells in morphogenetic or cancerous tissues, however so far only with flat hypersurfaces as cell-cell contact borders. In order to reproduce the experimentally…

Curve evolution schemes for image segmentation based on a region based contour model allowing for junctions, vector-valued images and topology changes are introduced. Together with an a posteriori denoising in the segmented homogeneous…

We revisit a new type of a Voronoi diagram, in which distance is measured from a point to a pair of points. We consider a few more such distance functions, based on geometric primitives, and analyze the structure and complexity of the…

In this paper, we review the computational aspects of a multiscale dissipative particle dynamics model for complex fluid simulations based on the feature-rich geometry of the Voronoi tessellation. The geometrical features of the model are…

In distributed mobile sensing applications, networks of agents that are heterogeneous respecting both actuation as well as body and sensory footprint are often modelled by recourse to power diagrams --- generalized Voronoi diagrams with…

We use Lie sphere geometry to describe two large categories of generalized Voronoi diagrams that can be encoded in terms of the Lie quadric, the Lie inner product, and polyhedra. The first class consists of diagrams defined in terms of…

The forward and reverse Funk weak metrics are fundamental distance functions on convex bodies that serve as the building blocks for the Hilbert and Thompson metrics. In this paper we study Voronoi diagrams under the forward and reverse Funk…

Purpose: The purpose of this work is to investigate the hypothesis that uniform sampling measurements that are endowed with antipodal symmetry play an important role when the raw data and image data are related through the Fourier…

Image segmentation is the initial step for every image analysis task. A large variety of segmentation algorithm has been proposed in the literature during several decades with some mixed success. Among them, the fuzzy energy based active…

This paper presents a comprehensive derivation and implementation of the Chan-Vese active contour model for image segmentation. The model, derived from the Mumford-Shah variational framework, evolves contours based on regional intensity…

In this article, we investigate vacuum leakage detection problems in composite manufacturing. Our approach uses Voronoi diagrams, a well-known structure in discrete geometry. The Voronoi diagram of the vacuum connection positions partitions…

The problem of image segmentation is known to become particularly challenging in the case of partial occlusion of the object(s) of interest, background clutter, and the presence of strong noise. To overcome this problem, the present paper…

We present an image segmentation method that iteratively evolves a polygon. At each iteration, the vertices of the polygon are displaced based on the local value of a 2D shift map that is inferred from the input image via an encoder-decoder…

Many methods for modelling spatial processes assume global smoothness properties; such assumptions are often violated in practice. We introduce a method for modelling spatial processes that display heterogeneity or contain discontinuities.…

Continuous image morphing is a classical task in image processing. The metamorphosis model proposed by Trouv\'e, Younes and coworkers casts this problem in the frame of Riemannian geometry and geodesic paths between images. The associated…

The choice of data representation is a key factor in the success of deep learning in geometric tasks. For instance, DUSt3R recently introduced the concept of viewpoint-invariant point maps, generalizing depth prediction and showing that all…

The Hilbert metric is a distance function defined for points lying within a convex body. It generalizes the Cayley-Klein model of hyperbolic geometry to any convex set, and it has numerous applications in the analysis and processing of…

In this paper, we propose a novel locally statistical variational active contour model based on I-divergence-TV denoising model, which hybrides geodesic active contour (GAC) model with active contours without edges (ACWE) model, and can be…

A novel locally statistical active contour model (ACM) for image segmentation in the presence of intensity inhomogeneity is presented in this paper. The inhomogeneous objects are modeled as Gaussian distributions of different means and…