Notes 20110201 CIS 6320 Image Processing

From SnOwy - Ed's Wiki Notebook

Contents 1 Classical Logic 2 Fuzzy Logic 2.1 Minimum Properties 2.2 Additional Properties Depending on Textbook 2.3 More on Fuzzy Logic 2.4 Commutative -- T Norm (∧ = conjunction, ∩ = intersection) 2.5 Associative -- T-Conorm (∨ = disjunction, ∪ = union) 2.6 Notation Note 3 Image Operations 4 Operations 5 Fourier Transform 6 Effective Presentations

Classical Logic

• ¬ | {0,1} → {0,1}
• ¬ (0) = 1
• ¬ (1) = 0

Fuzzy Logic

Minimum Properties

• ¬ | [0,1] → [0,1]
• ¬ | [0,1] → [0,1] -- boundary conditions
• ∀ (p,q) ∈ [0,1]², p ≤ q → &not(p) ≥ &not(q) -- monotonic non-increasing

Additional Properties Depending on Textbook

• ∀ p ∈ [0,1], ¬(¬(p)) = p -- involutive
• ∀x₀ ∈ [0,1], ∀ ε ∈ ]0,+∞[, ∃η ∈ ]0,∞[, ∀x ∈ [0,1], |x-x₀| < η → |¬(x)-¬(x₀)| < ε -- continuous

More on Fuzzy Logic

• ... see remaining note in previous.

Commutative -- T Norm (∧ = conjunction, ∩ = intersection)

• ∀(p,q) ∈ [0,1]², t(p,q) = t(q,r) -- commutative
• ∀(p,q,r) ∈ [0,1]³, t(t(p,q),r) = t(p,t(q,r)) -- associative
• t | [0,1]² → [0,1]
• t | (p,q) |→ min(p,q) -- standard
• t | (p,q) |→ pq -- algebraic

Associative -- T-Conorm (∨ = disjunction, ∪ = union)

• t | (p,q) |→ max(p,q) -- standard
• t | (p,q) |→ p + q - pq -- algebraic

Notation Note

• [0,255] == [0;255] -- the comma is a radix point in Europe -- the semicolon is universal :D

Image Operations

• arithmetic transformation ...
• subtracting a pixel from a corresponding pixel in two frames of video allows detection of intruder
  • intruders produce a difference in grey-level
• image registration ...
• given two images, map tied points to one another
• interpolation transformation needed T_s
• f₁|Z² → R
• f₂|Z² → R
• colour or multispectral transformation ...
• input image → T₁ output image (T₁ works on Red band)
• input image → T₂ output image (T₂ works on Green band)
• input image → T₃ output image (T₃ works on Blue band)
• in some cases, it's not possible to consider each band in isolation
• example -- transforming RGB to CMYK (but we need to define a colourspace)

Operations

1. single pixel -- undergrand
2. neighbourhood operations
3. geometric spatial transformations
4. image transforms -- what we're interested in
5. logical transforms
6. arithmetic transforms
7. registration transforms
8. multispectral transforms

Fourier Transform

• next ...

Effective Presentations

• title slide
  • title, name, affiliation, [class], [semester]
• slides ...
• emphasis, complement speaking
• prompts, outlines
  • outlines should be numbered (sequence)
• four questions that are answered in the presentation ...
  1. what (subject)
  2. who (audience)
  3. where (auditorium)
  4. how (delivery)
• introduction ...
  • give a precise idea about what the talk is about
  • outline may come later, after the introduction
  • slide numbers
  • mental breaks are good -- even a few seconds between topics
• text size
• serif fonts are difficult to read in slide shows
• in general ...
  • no more than three slides per minute
  • no more than six lines per slide
  • no more than six words per line
• bullets and numbers
  • sequences MUST be numbered (a tuple)
  • bullets for sets