This document will be filled during the course with very brief summaries (with literature references and lists of hand-outs) of the lectures.

The chapters, hand-outs, and additional texts mentioned below are the course requirements for the exam.

L01:

Literature

• FSFL: 1.1-1.3, 1.5

Hand-outs

• L. Zadeh, Fuzzy Sets, 1965

Contents

• Introduction to the course.
• Beginning of Chapter 1, basics of fuzzy sets.

Slides

• L1.pdf - Introduction

L02:

Literature

• FSFL: 1.3-1.4

Contents

• Rest of Chapter 1, basics of fuzzy sets.

L03:

Literature

• FSFL: 2.1-2.3

Contents

• Chapter 2, extension principle.

L04:

Literature

• FSFL: 10 and 9.1-9.4

Contents

• Going through some tasks from Ch. 1 & 2.
• Constructing fuzzy sets I
• Characterizing fuzzy sets I
  Uncertainty measures

Slides

• L4.pdf - Membership functions and uncertainty

Hand-outs

• S. Pal and A. Rosenfeld, Image enhancement and thresholding by optimization of fuzzy compactness, 1988

L05:

Literature

• FSFL: 13.2

Contents

• Assignment 1 - Fuzzy thresholding
• Fuzzy thresholding
• Fuzzy c-means clustering

Slides

• L5.pdf - Fuzzy thresholding and clustering

Hand-outs

• Huang and Wang, Image thresholding by minimizing the measures of fuzziness, 1995

L06:

Literature

• N. Sladoje, "Reviews of Scientific Papers on Fuzzy Shape Analysis", CBA Internal report No. 32, 2005
• ( N. Sladoje, "On analysis of discrete spatial fuzzy sets in 2 and 3 dimensions", Ph.D. thesis, 2005 )

Contents

• Different approaches for extending features of crisp sets to fuzzy sets.
• Area, perimeter, moments.
• Interrelations between features.
• Feature estimations, definitions, error bounds, balance between spatial and membership resolution.
• Pixel coverage representation.

Slides

• L6.pdf - Features of fuzzy sets

L07:

Literature

• I. Bloch. On fuzzy distances and their use in image processing under imprecision. Pattern Recognition, 32:1873-1895, 1999.

Contents

• Distances between fuzzy sets
• Point to point distances in fuzzy sets

Slides

• L7.pdf - Distances on and between fuzzy sets

L08:

Literature

• FSFL: 3

Contents

• Types of set operations, complements, intersections and unions
• Combinations of operators
• Aggregation operators
• Brief intro on fuzzy morphologies
• Assignment 2 - Fuzzy morphologies

Slides

• L8.pdf - Operations on fuzzy sets

L09:

Literature

• FSFL: 4 and 15.7

Contents

• Interval numbers and interval arithmetics
• Fuzzy numbers and fuzzy arithmetics
• Partial ordering of fuzzy numbers, MAX and MIN
• Briefly on fuzzy equations
• An example on fuzzy linear programming

Slides

• L9.pdf - Fuzzy numbers and fuzzy arithmetics

L10:

Literature

• FSFL: 5.3, 8, and 11

Contents

• Fuzzy logic
• Fuzzy implications
• Binary fuzzy relations
• Approximate reasoning

Slides

• L10.pdf - Fuzzy logic and approximate reasoning

L11:

Literature

• FSFL: 12

Contents

• Fuzzy control
  • What is a control system?
  • Conventional control systems
  • Fuzzy control systems
  •   ...in five easy steps
  • A small example
• Fuzzy expert systems

Slides

• L11.pdf - Fuzzy control

L12:

Contents

• Fuzzy connectedness segmentation
  • Motivation
  • Fuzzy sets (recap)
  • Fuzzy connectedness theory
    • Fuzzy digital space
    • Affinity and paths
    • Fuzzy connected object
    • Algorithm
  • FC variants and details
    • Defining fuzzy spel affinity
    • Efficient computation
    • Vectorial and relative fuzzy connectedness
  • Applications
• Pixel coverage segmentations
  • Pixel coverage representations
  • Segmentation based on
    • continuous model
    • fuzzy thresholding and mathematical morphology
    • relative distance
    • local unmixing

Slides

• L12.pdf - Fuzzy connectedness
• L12b.pdf - Coverage segmentations

L13:

Literature

• FSFL: 12.6

Contents

• Defuzzification to a point
• Defuzzification to a set
• Defuzzification respecting the fuzzification
• Defuzzification by feature distance minimization

Slides

• L13.pdf - Defuzzification
• L13b.pdf - Defuzzification by feature distance minimization

L14:

Contents

• Summary of the course

Slides

• L14.pdf - Summary of the course
  
• Old exam with very brief solutions.