Topic
Multiresolution analysis
About: Multiresolution analysis is a research topic. Over the lifetime, 4032 publications have been published within this topic receiving 140743 citations. The topic is also known as: Multiresolution analysis, MRA.
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TL;DR: A novel multiresolution color image segmentation (MCIS) algorithm which uses Markov random fields (MRF's) is proposed, a relaxation process that converges to the MAP (maximum a posteriori) estimate of the segmentation.
Abstract: Image segmentation is the process by which an original image is partitioned into some homogeneous regions. In this paper, a novel multiresolution color image segmentation (MCIS) algorithm which uses Markov random fields (MRF's) is proposed. The proposed approach is a relaxation process that converges to the MAP (maximum a posteriori) estimate of the segmentation. The quadtree structure is used to implement the multiresolution framework, and the simulated annealing technique is employed to control the splitting and merging of nodes so as to minimize an energy function and therefore, maximize the MAP estimate. The multiresolution scheme enables the use of different dissimilarity measures at different resolution levels. Consequently, the proposed algorithm is noise resistant. Since the global clustering information of the image is required in the proposed approach, the scale space filter (SSF) is employed as the first step. The multiresolution approach is used to refine the segmentation. Experimental results of both the synthesized and real images are very encouraging. In order to evaluate experimental results of both synthesized images and real images quantitatively, a new evaluation criterion is proposed and developed. >
530 citations
TL;DR: An algorithm for fast elastic multidimensional intensity-based image registration with a parametric model of the deformation that is computationally more efficient than other alternatives and capable of accepting expert hints in the form of soft landmark constraints.
Abstract: We present an algorithm for fast elastic multidimensional intensity-based image registration with a parametric model of the deformation. It is fully automatic in its default mode of operation. In the case of hard real-world problems, it is capable of accepting expert hints in the form of soft landmark constraints. Much fewer landmarks are needed and the results are far superior compared to pure landmark registration. Particular attention has been paid to the factors influencing the speed of this algorithm. The B-spline deformation model is shown to be computationally more efficient than other alternatives. The algorithm has been successfully used for several two-dimensional (2-D) and three-dimensional (3-D) registration tasks in the medical domain, involving MRI, SPECT, CT, and ultrasound image modalities. We also present experiments in a controlled environment, permitting an exact evaluation of the registration accuracy. Test deformations are generated automatically using a random hierarchical fractional wavelet-based generator.
526 citations
01 Jan 2005
TL;DR: This paper presents an algorithm for Decomposing Multi-dimensional Non-manifold Objects into Nearly Manifold Components for Shape Reconstruction from Clouds of Points and discusses 3D Triangulations, Thinning, and Modelling.
Abstract: Compression.- Recent Advances in Compression of 3D Meshes.- Shape Compression using Spherical Geometry Images.- Data Structures.- A Survey on Data Structures for Level-of-Detail Models.- An Algorithm for Decomposing Multi-dimensional Non-manifold Objects into Nearly Manifold Components.- Encoding Level-of-Detail Tetrahedral Meshes.- Multi-Scale Geographic Maps.- Modelling.- Constrained Multiresolution Geometric Modelling.- Multi-scale and Adaptive CS-RBFs for Shape Reconstruction from Clouds of Points.- Parameterization.- Surface Parameterization: a Tutorial and Survey.- Variations on Angle Based Flattening.- Subdivision.- Recent Progress in Subdivision: a Survey.- Optimising 3D Triangulations: Improving the Initial Triangulation for the Butterfly Subdivision Scheme.- Simple Computation of the Eigencomponents of a Subdivision Matrix in the Fourier Domain.- Subdivision as a Sequence of Sampled Cp Surfaces.- Reverse Subdivision.- $$\sqrt 5 $$ -subdivision.- Geometrically Controlled 4-Point Interpolatory Schemes.- Thinning.- Adaptive Thinning for Terrain Modelling and Image Compression.- Simplification of Topologically Complex Assemblies.- Topology Preserving Thinning of Vector Fields on Triangular Meshes.- Wavelets.- Periodic and Spline Multiresolution Analysis and the Lifting Scheme.- Nonstationary Sibling Wavelet Frames on Bounded Intervals: the Duality Relation.- Haar Wavelets on Spherical Triangulations.
449 citations
TL;DR: The results demonstrate that the new subband-adaptive shrinkage function outperforms Bayesian thresholding approaches in terms of mean-squared error and the spatially adaptive version of the proposed method yields better results than the existing spatiallyadaptive ones of similar and higher complexity.
Abstract: We develop three novel wavelet domain denoising methods for subband-adaptive, spatially-adaptive and multivalued image denoising. The core of our approach is the estimation of the probability that a given coefficient contains a significant noise-free component, which we call "signal of interest". In this respect, we analyze cases where the probability of signal presence is 1) fixed per subband, 2) conditioned on a local spatial context, and 3) conditioned on information from multiple image bands. All the probabilities are estimated assuming a generalized Laplacian prior for noise-free subband data and additive white Gaussian noise. The results demonstrate that the new subband-adaptive shrinkage function outperforms Bayesian thresholding approaches in terms of mean-squared error. The spatially adaptive version of the proposed method yields better results than the existing spatially adaptive ones of similar and higher complexity. The performance on color and on multispectral images is superior with respect to recent multiband wavelet thresholding.
443 citations
TL;DR: An additional algorithm for multiwavelet processing of two-dimensional (2-D) signals, two rows at a time, is described, and a new family of multiwavelets (the constrained pairs) are developed that is well-suited to this approach.
Abstract: Multiwavelets are a new addition to the body of wavelet theory. Realizable as matrix-valued filterbanks leading to wavelet bases, multiwavelets offer simultaneous orthogonality, symmetry, and short support, which is not possible with scalar two-channel wavelet systems. After reviewing this theory, we examine the use of multiwavelets in a filterbank setting for discrete-time signal and image processing. Multiwavelets differ from scalar wavelet systems in requiring two or more input streams to the multiwavelet filterbank. We describe two methods (repeated row and approximation/deapproximation) for obtaining such a vector input stream from a one-dimensional (1-D) signal. Algorithms for symmetric extension of signals at boundaries are then developed, and naturally integrated with approximation-based preprocessing. We describe an additional algorithm for multiwavelet processing of two-dimensional (2-D) signals, two rows at a time, and develop a new family of multiwavelets (the constrained pairs) that is well-suited to this approach. This suite of novel techniques is then applied to two basic signal processing problems, denoising via wavelet-shrinkage, and data compression. After developing the approach via model problems in one dimension, we apply multiwavelet processing to images, frequently obtaining performance superior to the comparable scalar wavelet transform.
443 citations