digital image processing

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Sampling and Quantization
Dr. Ram Prakash Sharma
NIT Hamirpur
Reference: R. Gonzalez and R. Woods. Digital Image Processing, Prentice
Hall, 2008.
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Electromagnetic Spectrum
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What is a Digital Image?
• A digital image is a representation of a two-dimensional image as a
finite set of digital values, called picture elements or pixels
f(x,y) = reflectance(x,y) * illumination(x,y)
Reflectance in [0,1], illumination in [0,inf]
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What is a Digital Image?
Remember digitization implies that a digital image is an approximation
of a real scene
1 pixel
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What is an image?
• We can think of an image as a function, f:
• f( x, y ) gives the intensity at position ( x, y )
• Realistically, we expect the image only to be defined over a rectangle,
with a finite range:
• A color image is just three functions pasted together. We can
write this as a “vector-valued” function:
( , )
( , ) ( , )
( , )
r x y
f x y g x y
b x y
 
 

 
 
 
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What is a digital image?
• We usually operate on digital (discrete) images:
• Sample the 2D space on a regular grid
• Quantize each sample (round to nearest integer)
• If our samples are D apart, we can write this as:
f[i ,j] = Quantize{ f(i D, j D) }
• The image can now be represented as a matrix of integer values
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Sampling and Quantization
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Image Sampling And Quantisation
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Sampling and Quantization
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Representing Digital Images
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Spatial Resolution
The spatial resolution of an image is determined by how sampling was
carried out
Spatial resolution simply refers to the smallest discernable detail in an
image
• Vision specialists will
often talk about pixel
size
• Graphic designers will
talk about dots per
inch (DPI)
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Spatial Resolution (cont…)
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Spatial Resolution (cont…)
1024 * 1024 512 * 512 256 * 256
128 * 128 64 * 64 32 * 32
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Intensity Level Resolution
Intensity level resolution refers to the number of intensity levels used to
represent the image
• The more intensity levels used, the finer the level of detail discernable in an
image
• Intensity level resolution is usually given in terms of the number of bits used
to store each intensity level
Number of Bits
Number of Intensity
Levels
Examples
1 2 0, 1
2 4 00, 01, 10, 11
4 16 0000, 0101, 1111
8 256 00110011, 01010101
16 65,536 1010101010101010
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Intensity Level Resolution (cont…)
128 grey levels (7 bpp) 64 grey levels (6 bpp) 32 grey levels (5 bpp)
16 grey levels (4 bpp) 8 grey levels (3 bpp) 4 grey levels (2 bpp) 2 grey levels (1 bpp)
256 grey levels (8 bits per pixel)
Images
taken
from
Gonzalez
&
Woods,
Digital
Image
Processing
(2002)
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Relation between number of pixels and bits
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Intensity Level Resolution (cont…)
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Intensity Level Resolution (cont…)
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Intensity Level Resolution (cont…)
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Intensity Level Resolution (cont…)
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Image processing
• An image processing operation typically defines a new
image g in terms of an existing image f.
• We can transform either the range of f.
• Or the domain of f:
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