A new algorithm for the determination of the relative convex hull in the plane of a simple polygon A with respect to another simple polygon B which contains A, is proposed. The relative convex hull is also known as geodesic convex hull, and the problem of its determination in the plane is equivalent to find the shortest curve among all Jordan curves lying in the difference set of B and A and en...

One useful generalization of the convex hull of a set S of n points is the-strongly convex-hull. It is deened to be a convex polygon P with vertices taken from S such that no point in S lies farther than outside P and such that even if the vertices of P are perturbed by as much as , P remains convex. It was an open question 1 as to whether an-strongly convex O()-hull existed for all positive. W...

The problem of finding the digital convex fuzzy hull of a digital fuzzy set, whose support is made of some digital points (centroids) in Z, is considered here. A region is DL−convex if, for any two pixels belonging to it, there exists a digital straight line between them, all of whose pixels belong to the region. An algorithm how to compute the DL−convex hull of a digital region is described. A...

Figure 1: Size of hull vs. size of set 1 has a very small number of points on its convex hull in relation to the size of the whole set. In set P2, all points in the set are on the convex hull. Is there an algorithm which is output sensitive in relation to the number of points on the convex hull? It turns out there is such an algorithm KirkpatrickSeidel Marriage Before Conquest. Its complexity, ...

Normal support vector machine (SVM) is not suitable for classification of large data sets because of high training complexity. Convex hull can simplify the SVM training. However, the classification accuracy becomes lower when there exist inseparable points. This paper introduces a novel method for SVM classification, called convex–concave hull SVM (CCH-SVM). After grid processing, the convex hu...

Given a set S of n points in the plane, an -strongly convex -hull of S is de0ned as a convex polygon P with the vertices taken from S such that no point of S lies farther than outside P and such that even if the vertices of P are perturbed by as much as , P remains convex. This paper presents the 0rst parallel robust method for this generalized convex hull problem (note that the convex hull of ...

Convex hulls are fundamental geometric tools used in a number of algorithms. This paper presents a fast, simple to implement and robust Smart Convex Hull (S-CH) algorithm for computing the convex hull of a set of points in . This algorithm is based on “spherical” space subdivision. The main idea of the S-CH algorithm is to eliminate as many input points as possible before the convex hull constr...

In this paper, we study properties of general closed convex sets that determine the closed-ness and polyhedrality of the convex hull of integer points contained in it. We first present necessary and sufficient conditions for the convex hull of integer points contained in a general convex set to be closed. This leads to useful results for special class of convex sets such as pointed cones, stric...

A convex hull is a polygon which encloses all given set of points.Euler number or Euler characteristic of an image has proven to be an important feature in many image analyses and visual inspection applications. This paper presents an algorithm for fast computing the convex hull of a planar scattered point set, which pre-strike an initial convex hull boundary, remove internal points in the boun...

Inthispaper, (L,M)-fuzzy domain finiteness and (L,M)-fuzzy restricted hull spaces are introduced, and several characterizations of the category (L,M)-CS of (L,M)-fuzzy convex spaces are obtained. Then, (L,M)-fuzzy stratified (resp. weakly induced, induced) convex spaces are introduced. It is proved that both categories, the category (L,M)-SCS of (L,M)-fuzzy stratified convex spaces and the cate...