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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