Multiresolution surfaces are especially useful for fast rendering, real-time display and interactive manipulation of large and dense terrain surface models. This paper reviews major multiresolution terrain surface reconstruction techniques and analyses the corresponding data structures. We have proposed and implemented, based on Delaunay retriangulation, a greedy refinement algorithm with a str...

Title of dissertation: GENERALIZED MULTIRESOLUTION ANALYSIS: CONSTRUCTION AND MEASURE THEORETIC CHARACTERIZATION Juan R. Romero, Doctor of Philosophy, 2005 Dissertation directed by: Professor John J. Benedetto Department of Mathematics In this dissertation, we first study the theory of frame multiresolution analysis (FMRA) and extend some of the most significant results to d dimensional Euclide...

Efficiency of high-order essentially non-oscillatory (ENO) approximations of conservation laws can be drastically improved if ideas of multiresolution analysis are taken into account. These methods of data compression not only reduce the necessary amount of discrete data but can also serve as tools in detecting local low-dimensional features in the numerical solution. We describe the mathematic...

This paper presents a GPU-based multiresolution shooting and bouncing ray (MSBR) method with the kd-tree acceleration structure for the fast radar cross section (RCS) prediction of electrically large and complex targets. The multiresolution grid algorithm can greatly reduce the total number of ray tubes, as it adaptively adjusts the density of ray tubes for regions with different complexities o...

1 The popularity of Bayesian methods in image processing applications has generated a lot of interest in the eld of image modeling. A good image model needs to be non-homogeneous to be able to adapt to the local characteristics of the diierent regions in an image. Toward this end, we propose a non-homogeneous Markov random eld (MRF) model that has space-varying scale parameters. This formulatio...

Topological and metric aspects of the multiresolution representation of geographic maps are considered. The combinatorial structure of maps is mathematically modelled through abstract cell complexes, and maps at diierent detail are related through continuous functions over such complexes. Metric aspects of multiresolution are controlled through the concept of homotopy. Two alternative multireso...

Multiresolution representations of data are known to be powerful tools in analysis and processing, they particularly interesting for compression. In order obtain a proper definition the edges, good option is use nonlinear reconstructions. These reconstruction heart prediction processes which appear subdivision multiresolution schemes. We define study some reconstructions based on means, more co...