Digital Image Fundamentals For View

Digital Image Processing,

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Chapter 2: Digital Image Fundamentals

• Eye Physiology

E. Fatemizadeh, Sharif University of Technology, 2006

Digital Image Processing,

http://ee.sharif.edu/~dip

Chapter 2: Digital Image Fundamentals

• Cones: Highly Sensitive to Color #(6-7)×106 • Rods: Highly Sensitive to Low Levels of Illumination #(75-150) ×106 E. Fatemizadeh, Sharif University of Technology, 2006

Digital Image Processing,

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Chapter 2: Digital Image Fundamentals

• Image Formation in the Eye

E. Fatemizadeh, Sharif University of Technology, 2006

Digital Image Processing,

http://ee.sharif.edu/~dip

Chapter 2: Digital Image Fundamentals

• Brightness Adaptation and Discrimination: – Eyes can adapts a large dynamic ranges of intensity (1010) But NOT Simultaneously.

Brightness Adaptation

E. Fatemizadeh, Sharif University of Technology, 2006

Digital Image Processing,

http://ee.sharif.edu/~dip

Chapter 2: Digital Image Fundamentals

• Brightness Discrimination

E. Fatemizadeh, Sharif University of Technology, 2006

Digital Image Processing,

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Chapter 2: Digital Image Fundamentals

• Weber Ratio Rods Cons

ΔIC =Increment of illumination discriminable 50% times

E. Fatemizadeh, Sharif University of Technology, 2006

Digital Image Processing,

http://ee.sharif.edu/~dip

Chapter 2: Digital Image Fundamentals

• Match Bands

E. Fatemizadeh, Sharif University of Technology, 2006

Digital Image Processing,

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Chapter 2: Digital Image Fundamentals

• Simultaneous Contrast

Appear Darker

E. Fatemizadeh, Sharif University of Technology, 2006

Digital Image Processing,

http://ee.sharif.edu/~dip

Chapter 2: Digital Image Fundamentals

• Eye illusions

E. Fatemizadeh, Sharif University of Technology, 2006

Digital Image Processing,

http://ee.sharif.edu/~dip

Chapter 2: Digital Image Fundamentals

• Image Acquisition: Ignored!

E. Fatemizadeh, Sharif University of Technology, 2006

Digital Image Processing,

http://ee.sharif.edu/~dip

Chapter 2: Digital Image Fundamentals

• Image Quantization

Scan Line

E. Fatemizadeh, Sharif University of Technology, 2006

Digital Image Processing,

http://ee.sharif.edu/~dip

Chapter 2: Digital Image Fundamentals

• Result of Quantization

E. Fatemizadeh, Sharif University of Technology, 2006

Digital Image Processing,

http://ee.sharif.edu/~dip

Chapter 2: Digital Image Fundamentals

• A Simple Image Formation: f ( x , y ) = i ( x, y ) r ( x, y ) • 0 < i ( x, y ) < ∞ : Illumination • 0 < r ( x, y ) < 1: Reflection

• Gray Level :Intensity of monochrome images.

E. Fatemizadeh, Sharif University of Technology, 2006

Digital Image Processing,

http://ee.sharif.edu/~dip

Chapter 2: Digital Image Fundamentals

• Digital Images Representations

E. Fatemizadeh, Sharif University of Technology, 2006

Digital Image Processing,

http://ee.sharif.edu/~dip

Chapter 2: Digital Image Fundamentals

• Image in Matrix Form: f(0,0) f(0,1) f(1,0) f(0,1) f(M-1,0) f(M-1,1)

… f(0,N-1) … f(1,N-1) … … … f(M-1,N-1)

bits to store the image = M x N x k gray level = L = 2k E. Fatemizadeh, Sharif University of Technology, 2006

MxN

Digital Image Processing,

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Chapter 2: Digital Image Fundamentals

• If M=N

E. Fatemizadeh, Sharif University of Technology, 2006

Digital Image Processing,

http://ee.sharif.edu/~dip

Chapter 2: Digital Image Fundamentals

• Image Sampling and Quantization: – Spatial and Gray Level Resolution – How to determine the sampling rate? – Nyquist sampling theorem • If input is a band-limited signal with maximum frequency ΩN • The input can be uniquely determined if sampling rate ΩS > 2ΩN – Nyquist frequency : ΩN – Nyquist rate : ΩS

E. Fatemizadeh, Sharif University of Technology, 2006

Digital Image Processing,

http://ee.sharif.edu/~dip

Chapter 2: Digital Image Fundamentals

• L- level digital image of size MxN – Means: A digital image having: • A spatial resolution MxN pixels • A gray-level resolution of L levels (0-L-1)

• Spatial resolution in real-world space line width=W cm space width=W cm Resolution = 1/2W (line/cm) E. Fatemizadeh, Sharif University of Technology, 2006

Digital Image Processing,

http://ee.sharif.edu/~dip

Chapter 2: Digital Image Fundamentals

• L = 2k gray levels, gray scales [0,…,L-1] • The dynamic range of an image – [min(image) max(image)] – If the dynamic range of an image spans a significant portion of the gray scale → high contrast – Otherwise, low dynamic range results in a washed out gray look

E. Fatemizadeh, Sharif University of Technology, 2006

Digital Image Processing,

http://ee.sharif.edu/~dip

Chapter 2: Digital Image Fundamentals

• Multi-rate Image Processing: – Down-Sampling (Shrink): 2

– Up-Sampling (Zoom): • neighboring pixel duplication • Interpolation (Linear, Bilinear, Cubic, spline) 2 E. Fatemizadeh, Sharif University of Technology, 2006

Digital Image Processing,

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Chapter 2: Digital Image Fundamentals

• Image Down-Sampling

E. Fatemizadeh, Sharif University of Technology, 2006

Digital Image Processing,

http://ee.sharif.edu/~dip

Chapter 2: Digital Image Fundamentals

• Image DownSampling and then UpSampling

E. Fatemizadeh, Sharif University of Technology, 2006

Digital Image Processing,

http://ee.sharif.edu/~dip

Chapter 2: Digital Image Fundamentals

E. Fatemizadeh, Sharif University of Technology, 2006

Digital Image Processing,

http://ee.sharif.edu/~dip

Chapter 2: Digital Image Fundamentals

E. Fatemizadeh, Sharif University of Technology, 2006

Digital Image Processing,

http://ee.sharif.edu/~dip

Chapter 2: Digital Image Fundamentals

E. Fatemizadeh, Sharif University of Technology, 2006

Digital Image Processing,

http://ee.sharif.edu/~dip

Chapter 2: Digital Image Fundamentals

shift up and right A detailed image may need less gray levels E. Fatemizadeh, Sharif University of Technology, 2006

Digital Image Processing,

http://ee.sharif.edu/~dip

Chapter 2: Digital Image Fundamentals

E. Fatemizadeh, Sharif University of Technology, 2006

Digital Image Processing,

http://ee.sharif.edu/~dip

Chapter 2: Digital Image Fundamentals

E. Fatemizadeh, Sharif University of Technology, 2006

Digital Image Processing,

http://ee.sharif.edu/~dip

Chapter 2: Digital Image Fundamentals

• Paradigm of image processing: – Low-level processing • Inputs and outputs are images • Primitive operations: de-noise, enhancement, sharpening, …

– Mid-level processing • Inputs are images, outputs are attributes extracted from images • Segmentation, classification,…

– High-level processing • “Make sense” of an ensemble of recognized objects by machines E. Fatemizadeh, Sharif University of Technology, 2006

Digital Image Processing,

http://ee.sharif.edu/~dip

Chapter 2: Digital Image Fundamentals

• Basic Relationships Between Pixels: – 4-Neighbors

N 4 ( p ) : {( x + 1, y ) , ( x − 1, y ) , ( x, y + 1) , ( x, y − 1)}

– Diagonal Neighbors N D ( p ) : {( x + 1, y + 1) , ( x + 1, y − 1) , ( x − 1, y + 1) , ( x − 1, y − 1)}

– 8-Neighbors: N8 ( p ) : N 4 ( p ) ∪ N D ( p )

E. Fatemizadeh, Sharif University of Technology, 2006

Digital Image Processing,

http://ee.sharif.edu/~dip

Chapter 2: Digital Image Fundamentals

• Basic Relationships Between Pixels: ⎡0 1 0⎤ N 4 = ⎢⎢1 1 1 ⎥⎥ ⎢⎣0 1 0 ⎥⎦

E. Fatemizadeh, Sharif University of Technology, 2006

⎡1 0 1 ⎤ N D = ⎢⎢ 0 1 0 ⎥⎥ ⎢⎣1 0 1 ⎥⎦

⎡1 1 1⎤ N8 = ⎢⎢1 1 1⎥⎥ ⎢⎣1 1 1⎥⎦

Digital Image Processing,

http://ee.sharif.edu/~dip

Chapter 2: Digital Image Fundamentals

• Adjacency: – p and q are 4-adjacent: q ∈ N 4 ( p ) – p and q are 8-adjacent: q ∈ N8 ( p ) – p and q are m-adjacent:

{q ∈ N ( p )} or {{q ∈ N ( p )} and { N ( p ) ∩ N ( q )} = ∅} 4

4

D

8

E. Fatemizadeh, Sharif University of Technology, 2006

4

m

Digital Image Processing,

http://ee.sharif.edu/~dip

Chapter 2: Digital Image Fundamentals

•

Distance Measure: a. D ( p,q ) ≥ 0 D ( p,q ) = 0 iff

p=q

b. D ( p,q ) = D ( q,p ) b. D ( p,q ) ≤ D ( p,r ) + D ( r,q )

•

Examples: – Euclidean: D ( p, q ) = ( x − s ) + ( y − t ) – D4 (City Block or Manhattan): D ( p, q ) = x − s + y − t – D8 (Chessboard):D ( p, q ) = Max { x − s , y − t } 2

2

e

4

8

E. Fatemizadeh, Sharif University of Technology, 2006