13,532 research outputs found
New approaches to texture coding in segmentation and feature-based image coding schemes
Peer ReviewedPostprint (published version
Strong edge features for image coding
A two-component model is proposed for perceptual image coding. For the first component of the model, the watershed operator is used to detect strong edge features. Then, an efficient morphological interpolation algorithm reconstructs the smooth areas of the image from the extracted edge information, also known as sketch data. The residual component, containing fine textures, is separately coded by a subband coding scheme. The morphological operators involved in the coding of the primary component perform very efficiently compared to conventional techniques like the LGO operator, used for the edge extraction, or the diffusion filters, iteratively applied for the interpolation of smooth areas in previously reported sketch-based coding schemes.Peer ReviewedPostprint (published version
Multiscale Representations for Manifold-Valued Data
We describe multiscale representations for data observed on equispaced grids and taking values in manifolds such as the sphere , the special orthogonal group , the positive definite matrices , and the Grassmann manifolds . The representations are based on the deployment of Deslauriers--Dubuc and average-interpolating pyramids "in the tangent plane" of such manifolds, using the and maps of those manifolds. The representations provide "wavelet coefficients" which can be thresholded, quantized, and scaled in much the same way as traditional wavelet coefficients. Tasks such as compression, noise removal, contrast enhancement, and stochastic simulation are facilitated by this representation. The approach applies to general manifolds but is particularly suited to the manifolds we consider, i.e., Riemannian symmetric spaces, such as , , , where the and maps are effectively computable. Applications to manifold-valued data sources of a geometric nature (motion, orientation, diffusion) seem particularly immediate. A software toolbox, SymmLab, can reproduce the results discussed in this paper
A Multiscale Pyramid Transform for Graph Signals
Multiscale transforms designed to process analog and discrete-time signals
and images cannot be directly applied to analyze high-dimensional data residing
on the vertices of a weighted graph, as they do not capture the intrinsic
geometric structure of the underlying graph data domain. In this paper, we
adapt the Laplacian pyramid transform for signals on Euclidean domains so that
it can be used to analyze high-dimensional data residing on the vertices of a
weighted graph. Our approach is to study existing methods and develop new
methods for the four fundamental operations of graph downsampling, graph
reduction, and filtering and interpolation of signals on graphs. Equipped with
appropriate notions of these operations, we leverage the basic multiscale
constructs and intuitions from classical signal processing to generate a
transform that yields both a multiresolution of graphs and an associated
multiresolution of a graph signal on the underlying sequence of graphs.Comment: 16 pages, 13 figure
The solution of multi-scale partial differential equations using wavelets
Wavelets are a powerful new mathematical tool which offers the possibility to
treat in a natural way quantities characterized by several length scales. In
this article we will show how wavelets can be used to solve partial
differential equations which exhibit widely varying length scales and which are
therefore hardly accessible by other numerical methods. As a benchmark
calculation we solve Poisson's equation for a 3-dimensional Uranium dimer. The
length scales of the charge distribution vary by 4 orders of magnitude in this
case. Using lifted interpolating wavelets the number of iterations is
independent of the maximal resolution and the computational effort therefore
scales strictly linearly with respect to the size of the system
- …