Characteristics of a detail preserving nonlinear filter.

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

2 CONVERGENCE THEOREMS ON DETERMINISTIC PROPERTIES OF MEDIAN FILTERS

In this correspondence, two convergence theorems on deterministic properties of median filters are obtained. The results can be used to analyze the root and recurrent signals of median filters, and to estimate the convergence rates. The concept of convergence point introduced here may be a useful new tool for analyzing the median filters