Multi-Resolution Analysis of Multiplicity d: Applications to Dyadic Interpolation

A Multi-dimensional Resolution of Singularities with Applications to Analysis

We formulate a resolution of singularities algorithm for analyzing the zero sets of real-analytic functions in dimensions ≥ 3. Rather than using the celebrated result of Hironaka, the algorithm is modeled on a more explicit and elementary approach used in the contemporary algebraic geometry literature. As an application, we define a new notion of the height of real-analytic functions, compute t...

Multi-resolution Field D

We present a multi-resolution path planner and replanner capable of efficiently generating paths across very large environments. Our approach extends recent work on interpolation-based planning to produce direct paths through non-uniform resolution grids. The resulting algorithm produces plans with costs almost exactly the same as those generated by the most effective uniform resolution grid-ba...

Applications of shift - invariant space theory to some problems of multi - resolution analysis of L 2 ( R d )

Given a frame multi-resolution analysis of L2(Rd) with a set of multiple scaling functions that is a quasi-stable generating set for V0, we give some neccessary and su cient conditions under which the standard generating set for V1 is also a quasi-stable generating set. We also give some equivalent conditions for W0 to admit a quasi-stable generating set by means of the re nement equation mask,...

Applications of quadratic D-forms to generalized quadratic forms

In this paper, we study generalized quadratic forms over a division algebra with involution of the first kind in characteristic two. For this, we associate to every generalized quadratic from a quadratic form on its underlying vector space. It is shown that this form determines the isotropy behavior and the isometry class of generalized quadratic forms.

Multi Resolution Fuzzy Segmentation of Satellite Images