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.

An impulsive noise reduction agent for rigid body motion data using B-spline wavelets

Abstract: A B-spline wavelet-based agent is proposed in this paper to remove impulsive noise embedded in noisy rigid body motion data. The motion of a rigid body consists of translation and orientation; the former is described by a space curve in three-dimensional Euclidean space, whereas the latter is represented by a curve in the unit quaternion space. Rigid body motion data acquired from electronic measurement devices usually contain noise of various patterns and magnitudes, and may contain structured noise such as impulsive spikes. In order to remove such impulsive noise from noisy motion data, the noisy motion data are decomposed using multiresolution analysis, and the noise components are identified as coefficients of high magnitude. By smoothing these high-magnitude coefficients, a smoother representation of noisy motion data is achieved.

Perceptual Scale-Space and Its Applications

Abstract: When an image is viewed at varying resolutions, it is known to create discrete perceptual jumps or transitions amid the continuous intensity changes. In this paper, we study a perceptual scale-space theory which differs from the traditional image scale-space theory in two aspects. (i) In representation, the perceptual scale-space adopts a full generative model. From a Gaussian pyramid it computes a sketch pyramid where each layer is a primal sketch representation (Guo et al. in Comput. Vis. Image Underst. 106(1):5---19, 2007)--an attribute graph whose elements are image primitives for the image structures. Each primal sketch graph generates the image in the Gaussian pyramid, and the changes between the primal sketch graphs in adjacent layers are represented by a set of basic and composite graph operators to account for the perceptual transitions. (ii) In computation, the sketch pyramid and graph operators are inferred, as hidden variables, from the images through Bayesian inference by stochastic algorithm, in contrast to the deterministic transforms or feature extraction, such as computing zero-crossings, extremal points, and inflection points in the image scale-space. Studying the perceptual transitions under the Bayesian framework makes it convenient to use the statistical modeling and learning tools for (a) modeling the Gestalt properties of the sketch graph, such as continuity and parallelism etc; (b) learning the most frequent graph operators, i.e. perceptual transitions, in image scaling; and (c) learning the prior probabilities of the graph operators conditioning on their local neighboring sketch graph structures. In experiments, we learn the parameters and decision thresholds through human experiments, and we show that the sketch pyramid is a more parsimonious representation than a multi-resolution Gaussian/Wavelet pyramid. We also demonstrate an application on adaptive image display--showing a large image in a small screen (say PDA) through a selective tour of its image pyramid. In this application, the sketch pyramid provides a means for calculating information gain in zooming-in different areas of an image by counting a number of operators expanding the primal sketches, such that the maximum information is displayed in a given number of frames.

Multiscale Systematic Risk

Abstract: In this paper we propose a new approach to estimating systematic risk (the beta of an asset). The proposed method is based on a wavelet multiscaling approach that decomposes a given time series on a scale-by-scale basis. The empirical results from different economies show that the relationship between the return of a portfolio and its beta becomes stronger as the wavelet scale increases. Therefore, the predictions of the CAPM model should be investigated considering the multiscale nature of risk and return.

Hierarchical Stereo with Thin Structures and Transparency

Abstract: Dense stereo algorithms rely on matching over a range of disparities. To speed up the search and reduce match ambiguity, processing can be embedded in the hierarchical, or coarse-to-fine (CTF), framework using image pyramids. However, this technique is limited when resolving thin structures, as they are poorly represented at coarser scales. In this paper we exploit alternative pyramid and search space techniques. We propose matching with the Magnitude-extended Laplacian Pyramid (MeLP) - a generalization of the Laplacian pyramid that explicitly encodes the energy magnitude component of the band-passed images. In essence, MeLP effectively encodes fine scale details in low resolution images, which allows for accurate recovery of thin structures during CTF processing. Furthermore, transparencies can be resolved for common cases when spatial frequency structure is locally different for each layer. Algorithmic instantiations for local block matching and global Graph Cuts formulations are presented. Extensive experimental evaluation demonstrates the benefits of the proposed techniques.