Related papers: Progressive Convex Hull Simplification

We study a natural extension to the well-known convex hull problem by introducing multiplicity: if we are given a set of convex polygons, and we are allowed to partition the set into multiple components and take the convex hull of each…

Convexity prior is one of the main cue for human vision and shape completion with important applications in image processing, computer vision. This paper focuses on characterization methods for convex objects and applications in image…

Computing the convex hull of a planar $n$-point set $P$ is one of the most fundamental problems in computational geometry. It has an $\Omega(n \log n)$ lower bound in the algebraic computation tree model, and many convex hull algorithms…

Given a set of disjoint simple polygons $\sigma_1, \ldots, \sigma_n$, of total complexity $N$, consider a convexification process that repeatedly replaces a polygon by its convex hull, and any two (by now convex) polygons that intersect by…

Computationally efficient and automated generation of convex hulls is desirable for high throughput materials discovery of thermodynamically stable multi-species crystal structures. A convex hull genetic algorithm is proposed that uses…

Creation of collision objects for 3D models is a time-consuming task, requiring modelers to manually place primitives such as bounding boxes, capsules, spheres, and other convex primitives to approximate complex meshes. While there has been…

A novel 2-D method for computing the convex hull of a sufficiently dense set of n integer points is introduced. The approach employs a ranking function that avoids sorting the points directly thus reducing the overall time complexity. The…

In this work, we present a new efficient method for convex shape representation, which is regardless of the dimension of the concerned objects, using level-set approaches. Convexity prior is very useful for object completion in computer…

The convex hull is a fundamental geometrical structure for many applications where groups of points must be enclosed or represented by a convex polygon. Although efficient sequential convex hull algorithms exist, and are constantly being…

Seeking the convex hull of an object is a very fundamental problem arising from various tasks. In this work, we propose two variational convex hull models using level set representation for 2-dimensional data. The first one is an exact…

Imprecise measurements of a point set P = (p1, ..., pn) can be modelled by a family of regions F = (R1, ..., Rn), where each imprecise region Ri contains a unique point pi. A retrieval models an accurate measurement by replacing an…

We present a new fully dynamic algorithm for maintaining convex hulls under insertions and deletions while supporting geometric queries. Our approach combines the logarithmic method with a deletion-only convex hull data structure, achieving…

We describe convex hulls of the simplest compact space curves, reducible quartics consisting of two circles. When the circles do not meet in complex projective space, their algebraic boundary contains an irrational ruled surface of degree…

In this paper we present several results on the expected complexity of a convex hull of $n$ points chosen uniformly and independently from a convex shape. (i) We show that the expected number of vertices of the convex hull of $n$ points,…

Volume approximation is an important problem found in many applications of computer graphics, vision, and image processing. The problem is about computing an accurate and compact approximate representation of 3D volumes using some simple…

In the preprocessing framework one is given a set of regions that one is allowed to preprocess to create some auxiliary structure such that when a realization of these regions is given, consisting of one point per region, this auxiliary…

We present a simple and efficient acceleration technique for an arbitrary method for computing the Euclidean projection of a point onto a convex polytope, defined as the convex hull of a finite number of points, in the case when the number…

In this article, a new solution for the convex hull problem has been presented. The convex hull is a widely known problem in computational geometry. As nature is a rich source of ideas in the field of algorithms, the solution has been…

This article describes a method to compute successive convex approximations of the convex hull of a set of points in R^n that are the solutions to a system of polynomial equations over the reals. The method relies on sums of squares of…

We develop a sketching algorithm to find the point on the convex hull of a dataset, closest to a query point outside it. Studying the convex hull of datasets can provide useful information about their geometric structure and their…