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Abstract
Linear pixel shuffling (LPS) is a method of ordering pixels (the elements of a rectangular matrix or analogies in higher dimensions) based on an arithmetic progression with wrap-around (modular arithmetic). For appropriate choices of the progression's Fibonacci numbers and the golden mean, we parameters based on generalizations of achieve uniformly distributed collections of pixels formed by intervals of the pixel progression or ``shuffle.''
We illustrate LPS with a novel approach to progressive rendering of synthetic images, and we note several opportunities for applications to other areas of image processing.
LPS, in an infinite analog, provides an unlimited, uniform sampling of points in the unit cube (of any dimension), which is useful for Monte Carlo integration and the placement of feature centers for neural networks.
This talk will present the basic ideas of LPS and show how it can be applied to computer graphics (progressive rendering), image processing (halftoning), and neural networks (radial basis function centering and feed forward net weight setting).
Professor Peter G. Anderson has been the chairman of RIT's graduate computer science program since 1980. Prior to joining RIT, he worked for RCA's computer division and was a faculty member at Princeton, New Jersey Institute of Technology, and Seton Hall.
He has had consulting relationships with several companies.
His B.S. and Ph.D. are in Mathematics from MIT, in 1962 and 1964; his dissertation was in Algebraic Topology, culminating a life long interest in Klein bottles.
His current research interests are in the areas of neural network and their applications to image processing, genetic (and related) algorithms image processing and computer graphics, number theory (Fibonacci numbers), computing aspects of mathematics, and mathematical aspects of computing.
In his spare time, he studies Chinese, swims, and trains his dogs.
Abstract
A genetic algorithm (GA) is an indirect method for rapidly searching for good solutions for hard problems. The problems that GAs are particularly suited for are those that have no straight-forward algorithmic solution-generators but do have methods for evaluating how good a proposed solution is. Such problems are typified by scheduling and lens design.
GAs are patterned on nature's evolution ("survival of the fittest") or selective breeding. A GA maintains a large population of trial solutions to the problem, selects some with higher fitness, and recombines their components to form new solutions. Over time, the population contains more and more solutions with higher and higher fitness.
This is a short, elementary course to introduce GAs to participants with a computer programming background. GA programs, tools, and applications will be provided.
The aim of the Tutorial is to give a two hours overview of the most relevant aspects in the area of fuzzy rule extraction supported by neural networks. Attendees to the Tutorial are expected to have a basic knowledge of feedforward neural networks and approximate reasoning in the frame of fuzzy logic. (If requested, the tutorial may be extended (to a total of 4 hours) to include these introductory aspects).
Introduction
The tutorial will discuss first the "when" and "why" of data-driven modeling and introduce some of the classical approaches, like the Wang-Mendel algorithm [WaM 92] or statistical regression. Following this, the motivation for the neuro-fuzzy approach will be given [TMB 99].
Core: (The "how" of data-driven modeling)
The discussion of neuro-fuzzy rule extraction begins with an analysis of the ANFIS-System [Jan 92], [Jan 93], [JaS 95], [Jan 97] and of ANFIS-like systems (e.g. [GBB 92], [KTT 92], [YiO 92], [MoH 96]) including the case of using triangular fuzzy sets to represent the linguistic terms of the premises [God 97] Positive aspects and constraints for the rule extraction with ANFIS will be discussed. Possibilities of alleviating constraints by clustering or by an evolutionary design [MeM 96], [MFS 99] of the front end of ANFIS will be considered. Special emphasis will be drawn upon the intepretability of the obtained rules [ADT 97],[Rot 99]. ANFIS architectures with direct crisp outputs (Takagi-Sugeno, Tsukamoto) and fuzzy outputs (including possibly a defuzzification module) will be shown [Bra 93].
The second important approach to neuro-fuzzy rule extraction is based on the NARA-System [TaH 91], [TSK 92] and NARA-like systems [HaM 96]. A comparative analysis will be done between NARA and ANFIS as well as between NARA and neuro-fuzzy systems based on RFB-networks [JaS 93] [BeB 97]. Refinements of NARA leading to splitting or chaining of rules will be presented [MoH 96]. A discussion on the interpretability of the extracted rules will close this chapter [Cra 96].
ANFIS and all ANFIS-like systems extract fuzzy if-then rules such that the premises are connected by a t-norm [Men 42], [ScS 83], [Web 83]. The t-norm being used is the product, because it is continuous and all over differentiable. It will be shown with simple examples, that there are real world problems that cannot conveniently be modelled by using t-norms to connect the premises [Mor 00a], [MoT 01]. Compensating operators are required [Dom 82], [DuP 85], [KMP 96]. It will be shown that fuzzy if-then rules using the compensating operator symmetric sum [Sil 79] may be extracted by using feedforward neural networks with one hidden layer using the standard logistic activation function [Ben 98], [BCR 97]. It will further be shown that there is a whole class of S-shaped activation forms supporting a similar transformation [THM 99], [MoT 01]. Furthermore it will be shown [Mor 00b], [Mor 01] how to modify an ANFIS system to extract rules using the additive Gamma operator [ZiZ 80], [ZiZ 83] as well as weighted connectives [Dub 83], which are compensating operators.
The Tutorial will close with a discussion on achievements, limits and trends.
This tutorial will be addressed in English and Spanish.
Speaker: Professor CJ Harris, FREng
Department of Electronics and Computer Science
University of Southampton, Highfield, Southampton, Hants, SO17 1BJ, UK
Fax: +44 (0) 23 8059 2978
Keywords
Abstract
This Advanced Tutorial on Neurofuzzy Systems lasts about 2 hours plus about an hour for questions ,and is aimed at real time nonlinear dynamic modelling, control and estimation problems for academics, industrialists and commercial workers interested in this technology . It is a PowerPoint presentation with several video inserts covering applications and demonstrations. It is an extended version of the IEE 2000 Tustin Lecture.
The term "soft-computing" has been introduced by Zadeh in 1994. Soft-computing provides an appropriate paradigm to program malleable and smooth concepts. For example, it can be used to introduce flexibility in artificial systems improving their Intelligent Quotient. The good performance of this approach is claimed by the fact that digital images are examples of fuzzy entities, where geometry of shapes are not always describable by exact equations and their approximation can be very complex. Aim of this paper is to describe methods and applications of soft-computing to early vision problems. The following topics will be covered:
Biodata
Vito Di Gesù was born in Turin (Italy) in 1945. He is graduated in physics from Palermo University. He has been visiting professors in several universities and research Laboratories, among them UC-Berkeley (USA), Stanford University (USA), Cambridge (UK), Tel Aviv University (Israel), ISI (Calcutta, India), ICSI Berkeley, EPRI (Palo Alto, USA), IBM Research Institute (Palo Alto, USA). He received international acknowledges for his scientific work: I.A.P.R.-Italian Chapter prize, for scientific and organizing activities in image processing and computer vision (1993); Mahalanobis prize, for scientific activities in pattern recognition (1994); IAPR fellow nomination for researches in pattern recognition and machine vision (1994). His research cover image analysis and processing, machine vision and soft visual systems with applications to astronomy, biology and remote sensing imaging. He is editor of books on data analysis, image processing and artificial perception. At the present he is full professor at the Palermo University and head of the computer vision group at the Department of Applied Mathematics.
We are proud to present this tutorial as a related event to the NF 2002.
It will be held at the ISPJAE Institute and is free for all interested, not only participants of the conference.
It will be held in Spanish.
Please note that although no fees are required for this tutorial, attendance to the NF 2002 conference, which is held at the 'Capitolio' congress centre, requires a registration always.
The main aim of this Tutorial is introducing the foundations of Fuzzy Controllers Design in order to promote and disseminate the knowledge on these approaches and techniques among the young cuban professionals and students. From this point of view, and in agreemet with NF’2002 organizers, the tutorial will be addressed in spanish language and people from ISPJAE will introduce some special topics on hardware developments. The tutorial lasts about 2.5 hours plus half one hour approximately for questions on current worldwide practical realisations and possible developments in Cuba of the Fuzzy Controllers. Along the first 2.5 hours, the following topics will be covered: