Related papers: Recursively-Regular Subdivisions and Applications

Convergence and normal continuity analysis of a bivariate non-stationary (level-dependent) subdivision scheme for 2-manifold meshes with arbitrary topology is still an open issue. Exploiting ideas from the theory of asymptotically…

A class of spherical functions is studied which can be viewed as the matrix generalization of Bessel functions. We derive a recursive structure for these functions. We show that they are only special cases of more general radial functions…

We construct recursion categories from categories of coalgebras. Let $F$ be a nontrivial endofunctor on the category of sets that weakly preserves pullbacks and such that the category $\textbf{Set}_F$ of $F$-coalgebras is complete. The…

We consider consecutive random subdivision of polygons described as follows. Given an initial convex polygon with $d\ge 3$ edges, we choose a point at random on each edge, such that the proportions in which these points divide edges are…

We construct differential algebras in which spaces of (one-dimensional) periodic ultradistributions are embedded. By proving a Schwartz impossibility type result, we show that our embeddings are optimal in the sense of being consistent with…

This paper provides a self-contained exploration of subdivisions of simplicial complexes, with emphasis on barycentric subdivision. We present formal definitions of subdivisions, show how the realization of a complex is preserved under…

In this paper, we further develop the theory of circles of partition by introducing the notion of complex circles of partition. This work generalizes the classical framework, extending from subsets of the natural numbers as base sets to…

Recursive distinctioning (RD) is a name coined by Joel Isaacson in his original patent document describing how fundamental patterns of process arise from the systematic application of operations of distinction and description upon…

View synthesis methods using implicit continuous shape representations learned from a set of images, such as the Neural Radiance Field (NeRF) method, have gained increasing attention due to their high quality imagery and scalability to high…

Underpinning the success of deep learning is effective regularizations that allow a variety of priors in data to be modeled. For example, robustness to adversarial perturbations, and correlations between multiple modalities. However, most…

Many approaches to 3D image segmentation are based on hierarchical clustering of supervoxels into image regions. Here we describe a distributed algorithm capable of handling a tremendous number of supervoxels. The algorithm works…

We introduce toric complexes as polyhedral complexes consisting of rational cones together with a set of integral generators for each cone, and we define their associated face rings. Abstract simplicial complexes and rational fans can be…

Given a trivalent graph in the 3-dimensional Euclidean space, we call it a discrete surface because it has a tangent space at each vertex determined by its neighbor vertices. To abstract a continuum object hidden in the discrete surface, we…

The interior polynomial was originally defined for hypergraphs and later shown to coincide with the Ehrhart polynomial of the root polytope of an associated bipartite graph. In previous work, we derived an alternating cycle recursion…

A novel algorithm is proposed for segmenting an image into multiple levels using its mean and variance. Starting from the extreme pixel values at both ends of the histogram plot, the algorithm is applied recursively on sub-ranges computed…

This work is motivated by two problems: 1) The approach of manifolds and spaces by triangulations. 2) The complexity growth in sequences of polyhedra. Considering both problems as related, new criteria and methods for approximating smooth…

Consider a geodesic triangle on a surface of constant curvature and subdivide it recursively into 4 triangles by joining the midpoints of its edges. We show the existence of a uniform $\delta>0$ such that, at any step of the subdivision,…

We develop a theory of simple pentagonal subdivision of quadrilateral tilings, on orientable as well as non-orientable surfaces. Then we apply the theory to answer questions related to pentagonal tilings of surfaces, especially those…

Generic polyhedra are interesting mathematical objects to study in their own right. In this paper, we initialize a systematic study of two-dimensional generic polyhedra with an eye towards applications to low-dimensional topology,…

We propose an efficient linear-time graph-based divisive cluster analysis approach called Reductive Clustering. The approach tries to reveal the hierarchical structural information through reducing the graph into a more concise one…