02-Sampling & Quantization

7/30/2019 02-Sampling & Quantization

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Digital Image Processing

(Theory, Practice, and Applications)


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A simple image model

Image: a two-dimensional light-intensity function

;f(x,y) = i(x,y) r(x,y)Why? (the 1st, the 2nd)

where, illumination 0 < i(x,y)< ,

reflectance components 0 < r(x,y) < 1- illumination: the amount of source light incident on the

scene being viewed

- reflectance: the amount of light reflected by the objects

in the scene The interval [Lmin,Lmax]

: called the gray scale [0,L]


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Examples showing that perceived brightness is not

a simple function of intensity.


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Example of simultaneous contrast: all the small squares have exactly the same intensity, but they appear

progressively darker as the background becomes lighter.


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A/D:PCM (Pulse Code Modulation)

()

Max

Min

Max

Min

1/2

1/2

1/4

1/4 1/81/8

(0)

(0) (0)

(1) (1)

(1)

1 0 1

3bit


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Sampling & Quantization (1)

f(x,y): digitized both spatially and in amplitude

Digitization of the spatial coordinates (x, y)

: called image sampling Amplitude digitization

: calledgray-levelquantization

Resolution:the degree of discernible detailof an

image depends strongly on the number of

samples and gray-levels


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Scanning & Sampling

Sampling

Case of progressive scan

Progressive scan

Case of interlaced scan

Interlaced scan

Scanning


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Uniformvs.Non-uniform

(Uniform Quantizer): (ti ti+1)

(Non-uniform Quantizer):

t: , l:

0

ti+1ti

li+1


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The more parameters (the number ofsamples and graylevels) are increased, the closer the digitized arrayapproximates the original image.

The digitization process requires decisions about valuesforN,M, and the number of discrete gray levels allowedfor each pixel.

N= 2n, M= 2

kand G = 2

m

b =NMmwhere, G: the number of gray levels

b: the number of bits required to store a digitized

image


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Effects according to spatial resolution &

number of bits

Effects of reducing spatial resolution

; pixel replication

produced a checkerboard effect

Fig. 2.9

Effects produced by decreasing the number of bits

used to represent the number of gray levels in an

image. A 10241024 image displayed in 256, 128, 64, 32,

16, 8, 4, and 2 levels, respectively.

Fig. 2.10


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Effect of reducing spatial resolution: (a) 10241024, 256-level digital image of a rose

(b)~(f) results of reducing the spatial resolution fromN=1024 toN=512,

256, 128, 64, and 32, respectively.


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Effect of decreasing the number of bits: (a) 10241024, 256-level digital image of a rose

(b)~(f) results of reducing the number of bits from m=7 to m=1,

respectively.


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Isopreference curve correspond to images

of equal subjective quality

- the quality of the images tends to increase asNandm are increased.

- a decrease in m generally increases the apparent

contrast of an image.

for images with a larger amount of detail only afew gray levels are needed.


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Isopreference curves


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Non-uniform sampling and quantization

: depends on the characteristics of the image

- Fine sampling is required in the neighborhood ofsharp gray-level transitions, whereas coarse samplingmay be utilized in relatively smooth regions.

- When the number of gray levels must be kept small,the use ofunequally spaced levels in the quantizationprocess usually is desirable ( called taperedquantization in Ch. 6).


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Implementation

(ex) Click !
http://localhost/var/www/apps/conversion/tmp/scratch_10/Myproj.exehttp://localhost/var/www/apps/conversion/tmp/scratch_10/Myproj.exe


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Discussion (Q&A)

Documents

02-Sampling & Quantization