Convex hull is widely used in computer graphic, image processing, CAD/CAM and pattern recognition. In this work, we derive some new convex hull properties and then propose a fast algorithm based on these new properties to extract convex hull of the object in binary image. It is achieved by computing the extreme points, dividing the binary image into several regions, scanning the regions existin...

The dynamic maintenance of the convex hull of a set of points in the plane is one of the most important problems in computational geometry. We present a data structure supporting point insertions in amortized O(log n · log log logn) time, point deletions in amortized O(log n · log logn) time, and various queries about the convex hull in optimal O(log n) worst-case time. The data structure requi...

When using the convex hull approach in the boundary modeling process, ModelBased Calibration (MBC) software suites – such as Model-Based Calibration Toolbox from MathWorks – can be computationally intensive depending on the amount of data modeled. The reason for this is that the half-space representation of the convex hull is used. We discuss here another representation of the convex hull, the ...

Given a measurable set A ⊂ R of positive measure, it is not difficult to show that |A+A| = |2A| if and only if A is equal to its convex hull minus a set of measure zero. We investigate the stability of this statement: If (|A + A| − |2A|)/|A| is small, is A close to its convex hull? Our main result is an explicit control, in arbitrary dimension, on the measure of the difference between A and its...

We investigate the problem of finding the twodimensional convex hull of a set of points on a coarsegrained parallel computer. Recently Goodrich has devised a parallel sorting algorithm for n items on P processors which achieves an optimal number of communication phases for all ranges of P n. Ferreira et al. have recently introduced a deterministic convex hull algorithm with a constant number of...

Writing an uncomplicated, robust, and scalable three-dimensional convex hull algorithm is challenging and problematic. This includes, coplanar and collinear issues, numerical accuracy, performance, and complexity trade-offs. While there are a number of methods available for finding the convex hull based on geometric calculations, such as, the distance between points, but do not address the tech...

This lecture describes a data structure for representing convex polytopes and a divide and conquer algorithm for computing convex hull in 3 dimensions. Let S be a set of n points in . Convex hull of S (CH(S)) is the smallest convex polytope that contains all n points. Since the boundary of this polytope is planar, it can be efficiently represented by the data structure described in the next sec...

The vertices of the convex hull of a uniform sample from the interior of a convex polygon are known to be concentrated close to the vertices of the polygon. Furthermore, the remaining area of the polygon outside of the convex hull is concentrated close to the vertices of the polygon. In order to see what happens in a corner of the polygon given by two adjacent edges, we consider—in view of affi...