This is a survey on tropical polytopes from the combinatorial point of view and with a focus on algorithms. Tropical convexity is interesting because it relates a number of combinatorial concepts including ordinary convexity, monomial ideals, subdivisions of products of simplices, matroid theory, finite metric spaces, and the tropical Grassmannians. The relationship between these topics is expl...

This paper describes a technique used to approximate the surface of an object’s visual hull. The hull’s basic structure is initially represented by a partitioned 3D space using voxels. The marching cubes algorithm then assigns polygonal patches to surface voxels depending on a certain criteria. It is less computationally intensive to manipulate a few triangular patches than a number of six-face...

The “convex hull problem” is a catch-all phrase for computing various descriptions of a polytope that is either specified as the convex hull of a finite point set in R or as the intersection of a finite number of halfspaces. We first define the various problems and discuss their mutual relationships (Section 26.1). We discuss the very special case of the irredundancy problem in Section 26.2. We...

The paper studies local convexity properties of digital curves. We locally define convex and concave parts from the slope of maximal digital straight segments and arithmetically characterize the smallest digital pattern required for checking convexity. Moreover, we introduce the concepts of digital edge and digital hull, a digital hull being a sequence of increasing or decreasing digital edges....

In this paper, an effective method with time complexity of O(K3/2N2 log K ǫ0 ) is introduced to find an approximation of the convex hull for N points in dimension n, where K is close to the number of vertices of the approximation. Since the time complexity is independent of dimension, this method is highly suitable for the data in high dimensions. Utilizing a greedy approach, the proposed metho...

We present a system for rendering novel viewpoints from a set of calibrated and silhouette-segmented images using the visual hull together with multi-view stereo. The visual hull predicted from the object silhouettes is used to restrict the search range of the multi-view stereo. This reduces redundant computation and the possibility of incorrect matches. Unlike previous visual hull approaches, ...

The dot comparison task, in which participants select the more numerous of two dot arrays, has become the predominant method of assessing Approximate Number System (ANS) acuity. Creation of the dot arrays requires the manipulation of visual characteristics, such as dot size and convex hull. For the task to provide a valid measure of ANS acuity, participants must ignore these characteristics and...

Given a graph G = (V,E), the closed interval of a pair of vertices u, v ∈ V , denoted by I[u, v], is the set of vertices that belongs to some shortest (u, v)-path. For a given S ⊆ V , let I[S] = ⋃ u,v∈S I[u, v]. We say that S ⊆ V is a convex set if I[S] = S. The convex hull Ih[S] of a subset S ⊆ V is the smallest convex set that contains S. We say that S is a hull set if Ih[S] = V . The cardina...

The hulls of codes from the row span over Fp, for any prime p, of incidence matrices of connected k-regular graphs are examined, and the dimension of the hull is given in terms of the dimension of the row span of A+kI over Fp, where A is an adjacency matrix for the graph. If p = 2, for most classes of connected regular graphs with some further form of symmetry, it was shown in [8] that the hull...

This paper presents a magnetization modeling method combined with material sensitivity information to identify the unknown magnetization distribution of a hull and improve the accuracy of the predicted fields. First, based on the magnetization modeling, the hull surface was divided into three-dimensional sheet elements, where the individual remanent magnetization was assumed to be constant. For...