The decomposition of images into their meaningful components is one of the major tasks in computer vision. Tadmor, Nezzar and Vese [1] have proposed a general approach for multiscale hierarchical decomposition of images. On the basis of this work, we propose a multiscale hierarchical decomposition of functions on graphs. The decomposition is based on a discrete variational framework that makes ...

In this paper we present an extended Truncated Hierarchical Catmull-Clark Subdivision (eTHCCS) method, which improves the efficiency of local refinement in Truncated Hierarchical Catmull-Clark Subdivision (THCCS). We first generalize Stam’s Catmull-Clark basis functions for elements with more than one extraordinary node. In this manner we build a set of basis functions over arbitrary quadrilate...

PHT-splines (polynomials splines over hierarchical T-meshes) are a generalization of B-splines over hierarchical T-mesheswhich possess a very efficient local refinement property. This property makes PHT-splines preferable in geometric processing, adaptive finite elements and isogeometric analysis. In this paper, we first make analysis of the previously constructed basis functions of PHT-splines...

This paper proposes a theoretical framework in which generalized hierarchical approaches for the adaptive finite element mesh refinement can be easily designed. Such a generalized approach aims at coupling the classical h version hierarchical adaptive finite element method and the adaptive remeshing strategy. On one hand, the hierarchical aspect should provide such an approach with its iterativ...

It is studied how the introduction of ordered hierarchies in 4-regular grid network structures decreases distances remarkably, while at the same time allowing for simple topological routing schemes. Both meshes and tori are considered; In both cases non-hierarchical structures have powerlaw dependencies between the number of nodes and the distances in the structures. The perfect square mesh is ...

In this paper we introduce a new mesh refinement method for subdivision surfaces. It generates a semiregular 4-direction hierarchical structure from control meshes representing 2D manifolds of arbitrary topology. The main advantage of this structure is that it allows the extraction of conforming variable-resolution meshes based on spatially varying adaptation functions. We also present a smooth...

In this paper we discuss the implementation of parallel multigrid methods on unstructured locally refined meshes for 2D linear elasticity calculations. The problem of rebalancing the workload of the processors during execution of the program is discussed in detail and a load balancing algorithm suited for hierarchical meshes is proposed. For large problems the efficiency per multigrid iteration...

Hierarchical spatial decompositions play a fundamental role in many disparate areas of scientific and mathematical computing since they enable adaptive sampling of large problem domains. Although the use of quadtrees, octrees, and their higher dimensional analogues is ubiquitous, these structures generate meshes with cracks, which can lead to discontinuities in functions defined on their domain...