1,557 research outputs found

    Analysis and Implementation of Median Type Filters

    Get PDF
    Median filters are a special class of ranked order filters used for smoothing signals. These filters have achieved- success in speech processing, image processing, and other impulsive noise environments where linear filters have proven inadequate. Although the implementation of a median filter requires only a simple digital operation, its properties are not easily analyzed. Even so, a number of properties have been exhibited in the literature. In this thesis, a new tool, known as threshold decomposition is introduced for the analysis and implementation of median type filters. This decomposition of multi-level signals into sets of binary signals has led to significant theoretical and practical breakthroughs in the area of median filters. A preliminary discussion on using the threshold decomposition as an algorithm for a fast and parallel VLSI Circuit implementation of ranked filters is also presented* In addition, the theory is developed both for determining the number of signals which are invariant to arbitrary window width median filters when any number of quantization levels are allowed and for counting or estimating the number of passes required to produce a root- i.e. invariant signal, for binary signals. Finally, the analog median filter is defined and proposed for analysis of the standard discrete median filter in cases with a large sample size or when the associated statistics would be simpler in the continuu

    Nonlinear smoothing filters and their realization

    Full text link

    Recursive Monte Carlo filters: Algorithms and theoretical analysis

    Full text link
    Recursive Monte Carlo filters, also called particle filters, are a powerful tool to perform computations in general state space models. We discuss and compare the accept--reject version with the more common sampling importance resampling version of the algorithm. In particular, we show how auxiliary variable methods and stratification can be used in the accept--reject version, and we compare different resampling techniques. In a second part, we show laws of large numbers and a central limit theorem for these Monte Carlo filters by simple induction arguments that need only weak conditions. We also show that, under stronger conditions, the required sample size is independent of the length of the observed series.Comment: Published at http://dx.doi.org/10.1214/009053605000000426 in the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

    A class of adaptive directional image smoothing filters

    Get PDF
    Cataloged from PDF version of article.The gray level distribution around a pixel of an image usually tends to be more coherent in some directions compared to other directions. The idea of adaptive directional filtering is to estimate the direction of higher coherence around each pixel location and then to employ a window which approximates aline segment in that direction. Hence, the details of the image may be preserved while maintaining a satisfactory level of noise suppression performance. In this paper we describe a class of adaptive directional image smoothing filters based on generalized Gaussian distributions. We propose a measure of spread for the pixel values based on the maximum likelihood estimate of a scale parameter involved in the generalized Gaussian distribution. Several experimental results indicate a significant improvement compared to some standard filters. Copyright (C) 1996 Pattern Recognition Society

    Characteristics of a detail preserving nonlinear filter.

    Get PDF
    by Lai Wai Kuen.Thesis (M.Phil.)--Chinese University of Hong Kong, 1993.Includes bibliographical references (leaves [119-125]).Abstract --- p.iAcknowledgement --- p.iiTable of Contents --- p.iiiChapter Chapter 1 --- IntroductionChapter 1.1 --- Background - The Need for Nonlinear Filtering --- p.1.1Chapter 1.2 --- Nonlinear Filtering --- p.1.2Chapter 1.3 --- Goal of the Work --- p.1.4Chapter 1.4 --- Organization of the Thesis --- p.1.5Chapter Chapter 2 --- An Overview of Robust Estimator Based Filters Morphological FiltersChapter 2.1 --- Introduction --- p.2.1Chapter 2.2 --- Signal Representation by Sets --- p.2.2Chapter 2.3 --- Robust Estimator Based Filters --- p.2.4Chapter 2.3.1 --- Filters based on the L-estimators --- p.2.4Chapter 2.3.1.1 --- The Median Filter and its Derivations --- p.2.5Chapter 2.3.1.2 --- Rank Order Filters and Derivations --- p.2.9Chapter 2.3.2 --- Filters based on the M-estimators (M-Filters) --- p.2.11Chapter 2.3.3 --- Filter based on the R-estimators --- p.2.13Chapter 2.4 --- Filters based on Mathematical Morphology --- p.2.14Chapter 2.4.1 --- Basic Morphological Operators --- p.2.14Chapter 2.4.2 --- Morphological Filters --- p.2.18Chapter 2.5 --- Chapter Summary --- p.2.20Chapter Chapter 3 --- Multi-Structuring Element Erosion FilterChapter 3.1 --- Introduction --- p.3.1Chapter 3.2 --- Problem Formulation --- p.3.1Chapter 3.3 --- Description of Multi-Structuring Element Erosion Filter --- p.3.3Chapter 3.3.1 --- Definition of Structuring Element for Multi-Structuring Element Erosion Filter --- p.3.4Chapter 3.3.2 --- Binary multi-Structuring Element Erosion Filter --- p.3.9Chapter 3.3.3 --- Selective Threshold Decomposition --- p.3.10Chapter 3.3.4 --- Multilevel Multi-Structuring Element Erosion Filter --- p.3.15Chapter 3.3.5 --- A Combination of Multilevel Multi-Structuring Element Erosion Filter and its Dual --- p.3.21Chapter 3.4 --- Chapter Summary --- p.3.21Chapter Chapter 4 --- Properties of Multi-Structuring Element Erosion FilterChapter 4.1 --- Introduction --- p.4.1Chapter 4.2 --- Deterministic Properties --- p.4.2Chapter 4.2.1 --- Shape of Invariant Signal --- p.4.3Chapter 4.2.1.1 --- Binary Multi-Structuring Element Erosion Filter --- p.4.5Chapter 4.2.1.2 --- Multilevel Multi-Structuring Element Erosion Filter --- p.4.16Chapter 4.2.2 --- Rate of Convergence of Multi-Structuring Element Erosion Filter --- p.4.25Chapter 4.2.2.1 --- Convergent Rate of Binary Multi-Structuring Element Erosion Filter --- p.4.25Chapter 4.2.2.2 --- Convergent Rate of Multilevel Multi-Structuring Element Erosion Filter --- p.4.28Chapter 4.3 --- Statistical Properties --- p.4.30Chapter 4.3.1 --- Output Distribution of Multi-Structuring Element Erosion Filter --- p.4.30Chapter 4.3.1.1 --- One-Dimensional Statistical Analysis of Multilevel Multi-Structuring Element Erosion Filter --- p.4.31Chapter 4.3.1.2 --- Two-Dimensional Statistical Analysis of Multilevel Multi-Structuring Element Erosion Filter --- p.4.32Chapter 4.3.2 --- Discussions on Statistical Properties --- p.4.36Chapter 4.4 --- Chapter Summary --- p.4.40Chapter Chapter 5 --- Performance EvaluationChapter 5.1 --- Introduction --- p.5.1Chapter 5.2 --- Performance Criteria --- p.5.2Chapter 5.2.1 --- Noise Suppression --- p.5.5Chapter 5.2.2 --- Subjective Criterion --- p.5.16Chapter 5.2.3 --- Computational Requirement --- p.5.20Chapter 5.3 --- Chapter Summary --- p.5.23Chapter Chapter 6 --- Recapitulation and Suggestions for Further WorkChapter 6.1 --- Recapitulation --- p.6.1Chapter 6.2 --- Suggestions for Further Work --- p.6.4Chapter 6.2.1 --- Probability Measure Function for the Two-Dimensional Filter --- p.6.4Chapter 6.2.2 --- Hardware Implementation --- p.6.5ReferencesAppendice

    Rank Conditioned Rank Selection Filters for Signal Restoration

    Get PDF
    A class of nonlinear filters called rank conditioned rank selection (RCRS) filters is developed and analyzed in this paper. The RCRS filters are developed within the general framework of rank selection(RS) filters, which are filters constrained to output an order statistic from the observation set. Many previously proposed rank order based filters can be formulated as RS filters. The only difference between such filters is in the information used in deciding which order statistic to output. The information used by RCRS filters is the ranks of selected input samples, hence the name rank conditioned rank selection filters. The number of input sample ranks used is referred to as the order of the RCRS filter. The order can range from zero to the number of samples in the observation window, giving the filters valuable flexibility. Low-order filters can give good performance and are relatively simple to optimize and implement. If improved performance is demanded, the order can be increased but at the expense of filter simplicity. In this paper, many statistical and deterministic properties of the RCRS filters are presented. A procedure for optimizing over the class of RCRS filters is also presented. Finally, extensive computer simulation results that illustrate the performance of RCRS filters in comparison with other techniques in image restoration applications are presented

    Langevin and Hamiltonian based Sequential MCMC for Efficient Bayesian Filtering in High-dimensional Spaces

    Full text link
    Nonlinear non-Gaussian state-space models arise in numerous applications in statistics and signal processing. In this context, one of the most successful and popular approximation techniques is the Sequential Monte Carlo (SMC) algorithm, also known as particle filtering. Nevertheless, this method tends to be inefficient when applied to high dimensional problems. In this paper, we focus on another class of sequential inference methods, namely the Sequential Markov Chain Monte Carlo (SMCMC) techniques, which represent a promising alternative to SMC methods. After providing a unifying framework for the class of SMCMC approaches, we propose novel efficient strategies based on the principle of Langevin diffusion and Hamiltonian dynamics in order to cope with the increasing number of high-dimensional applications. Simulation results show that the proposed algorithms achieve significantly better performance compared to existing algorithms
    corecore