Chapter 2: Digital Image Fundamentals

Fall 2003, 劉震昌

Outline Elements of Visual Perception Image sensing and acquisition Image sampling and quantization Relationships between pixels

Understanding visual perception

Most image processing operations are based on math. and probability

Why understanding visual perception? Human intuition plays an important role in

the choice of processing technique

Structure of the Human eye

角膜虹膜

網膜

水晶體

Diameter:20mm

2 class of receptors: cones and rods

Distribution of cones and rods

1 cone -> 1 nerve

Many rods -> 1 nerve

Discrete nature of human vision

Area of cones

15mm

Cone density: 150,000 per mm

Image formation in the Eye

Image Sensing and Acquisition

Images?Illumination source

scene

reflection

Image sensors Incoming energy is transformed

into a voltage by the combination of input electrical power and sensor material

(continuous)

Single sensor with motion

Sensor strips Flat-bed scanner aircraft

Sensor arrays CCD arrays in digital camera

Image sampling and quantization

Image sampling and quantization

continuousdata

digitaldata

Sampling: digitize the coordinate values

Quantization: digitize the amplitude values

Why? Limited representation power in digital computers

discretize

Image sampling and quantization (cont.) Sometimes, the sampling and

quantization are done mechanically Limitation on the sensing equipment

sensor array

Sampling rule 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

Sampling rule (cont.)

Representing digital images

Representing digital images (cont.) Matrix form

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

… …

f(M-1,0) f(M-1,1) … f(M-1,N-1)MxN

bits to store the image = M x N x kgray level = 2k

Representing digital images (cont.)

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 dull, washed out gray look

Spatial and gray-level resolution L-level digital image of size MxN = digital image having

a spatial resolution MxN pixels a gray-level resolution of L levels

Spatial resolution in real-world space line width=W cm

space width=W cm

Resolution = 1/2W (line/cm)

Spatial and gray-level resolution (cont.) Resolution of printer or screen

dpi(dot per inch) pixel/unit of distance

When an digital image of size MxN is to be printed or viewed using devices with resolution k dpi, how large will be the output image?

Multi-rate image processing Down-sampling

Up-sampling neighboring pixel duplication interpolation

2

2

Down-sampling operations

See the information loss due to down-sampling

Gray-level reduction

Gray-level reduction

falsecontouring

Empirical study of resolutions 2k-level digital image of size NxN How K and N affect the image quality

Increased details

Empirical study of resolutions(cont.) iso-preference curses

*shift up and right

*A detailed image may need less gray levels

Zoom and Shrink Operations applied to digital

images Zoom: up-sampling

Pixel duplication Bi-linear interpolation

Shrink: down-sampling

Zoom and shrink: idea

Idea: adjust the gridsize over the originalimage

Zooming: example

pixelduplication

bilinearinterpolation

Relationships Between Pixels

Neighbors of a pixel 4-neighbors of p: N4(p)

Diagonal neighbors: ND(p)

8-neighbors = 4-neighbors+diagonal neighbors : N8(p)

p

p

Adjacency, connectivity, regions, and boundaries Connectivity of pixels

They are neighbors Their gray levels satisfy a specified

criterion of similarity Concept about regions and boundaries

Adjacency 4-adjacency: p and q with intensity

from V and q is in N4(p) 8-adjacency: p and q with intensity

from V and q is in N8(p)

Connectivity and adjacency (cont.)

m-adjacency(mixed adjacency): p and q having intensity from V and

q is in N4(p), or q is in ND(p) and N4(p) N4(q) has no

pixels whose values are from V

Path A path from p: (x,y) to q: (s,t) is a

sequence of pixels:

Length = n It’s a k-path if it is 4-, 8-, and m-

adjacency

(x,y), (x1,y1), (x2,y2),…, , (xn-1,yn-1),(s,t)

consecutive pixels are adjacency

Growth of definitions

adjacency

path

connectedcomponent

connectedset (region)

S

S

Sboundary

Summary We need solid mathematical

definitions to let the algorithm run on a computer

Distance measure p: (x,y), q: (s,t) Euclidean distance

De(p,q)=[(x-s)2+(y-t)2]1/2

D4 distance D4(p,q)=|x-s|+|y-t|

D8 distance D8(p,q)=max(|x-s|,|y-t|)

r

22 1 2

2 1 0 1 22 1 2

22 2 2 2 22 1 1 1 22 1 0 1 22 1 1 1 22 2 2 2 2

Pixel-wise operation For example, how does image I divide

d by image M? Division is carried out between correspon

ding pixels in the two images Matlab: Q = I./M

Linear and non-linear operations H be an operator whose input and out

put are images H is linear if

H(af+bg) = aH(f)+bH(g) Otherwise non-linear

We have well-understood theoretical and practical results about linear operators

Announcement !!! There are solutions to the marked pro

blems in the textbook http://www.imageprocessingbook.com/teaching/proble

m_solutions.htm HW#1