Digital Image Fundamentals

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Digital Image Fundamentals

• Faculty of Science
• Silpakorn University

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Overviews

• Elements of Visual Perception
• Term of image
• Sampling and Quantization

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Term of image

• Pixel
• Resolution
• Neighbor of pixels
• Space and Frequency
• Vector

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PIXEL

• Pixel is a smallest component of digital image
• Pixel is a color point of digital image
• An image should be comprised of many Pixels.

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PIXEL
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RESOLUTION

• How quality of image
• With the same size of picture
• If high resolution, high memory is required to
  store data
• If low resolution, less memory is required to
  store data
• Its unit is call point per inch

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RESOLUTION
72
36
18
9
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Digital Image Representation
y
f(x,y)
x
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Neighbors of a pixel

• Neighbors of pixel are the pixels that are
  adjacent pixels of an identified pixel.
• Each pixel is a unit distance from the particular
  pixel.
• Some of the neighbors of pixel lie outside the
  digital image if its position is on the border of
  the image.

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Pixel at coordinate (column x, row y) can be
represented by f(x,y)
0 1 2 3 4 5 6 7 8 9 10 11 12
13 14 15
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
Pixel at the 7th column and 4th row is yellow
color
Zoom 1600
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4-neighbors of pixel

• 4-neighbors of pixel is denoted by N4(p)
• It is set of horizontal and vertical neighbors

f(x,y) is a yellow circle f(x,y-1) is top
one f(x-1,y) is left one f(x1,y) is right
one f(x,y1) is bottom one
(x1)
(x)
(x-1)
(y-1)
(y)
(y1)
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Diagonal neighbors of pixel

• Diagonal neighbors of pixel is denoted by ND(p)
• It is set of diagonal neighbors

f(x,y) is a yellow circle f(x-1,y-1) is top-left
one f(x1,y-1) is top-right one f(x-1,y1) is
bottom-left one f(x1,y1) is bottom-right one
(x1)
(x)
(x-1)
(y-1)
(y)
(y1)
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8-neighbors of pixel

• 8-neighbors of pixel is denoted by N8(p)
• 4-neighbors and Diagonal neighbors of pixel

f(x,y) is a yellow circle (x-1,y-1),
(x,y-1),(x1,y-1), (x-1,y), (x,y),
(x1,y), (x-1,y1),(x,y1), (x1,y1)
(x1)
(x)
(x-1)
(y-1)
(y)
(y1)
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Connectivity

• Establishing boundaries of objects and components
  of regions in an image.
• Group the same region by assumption that the
  pixels being the same color or equal intensity
  will are the same region

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Connectivity

• Let C is the set of colors used to define
• There are three type of connectivity
• 4-Connectivity 2 pixels (p and q) with value in
  C are 4-connectivity if q is in the set N4(p)
• 8-Connectivity 2 pixels (p and q) with value in
  C are 8-connectivity if q is in the set N8(p)
• M-Connectivity 2 pixels (p and q) with value in
  C are 8-connectivity if
• Q is in N4(p), or
• Q is in ND(p) and the set N4(p) n N4(q) is empty

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Binary Image Represent
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Example 4-Connectivity

• Set of color consists of color 1 C 1

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Example 8-Connectivity

• Set of color consists of color 1 C 1

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Example M-Connectivity

• Set of color consists of color 1 C 1

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Distance Measure

• For pixels p, q, and z, with coordinates (x,y),
  (s,t) and (u,v) respectively, D is a distance
  function or metric if
• D(p,q) 0 and
• D(p,q) 0 iff p q and
• D(p,q) D(q,p) and
• D(p,z) D(p,q) D(q,z)

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The D4 Distance

• Also called city-block distance
• Calculate between p and q is defined as
• D4(p,q) px- qx py- qy

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The D8 Distance

• Also called city-block distance
• Calculate between p and q is defined as
• D8(p,q) max( px- qx , py- qy )

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Labeling of connected Components

• Scan an image pixel by pixel from left to right
  and top to bottom
• There are 2 types of connectivity interested
• 4-connectivity
• 8-connectivity
• Equivalent labeling

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Step 4-connected components

• P is pixel scanned process
• If pixel p is color value 0 move on the next
  scaning
• If pixel p is color value 1 examine pixel top and
  left
• If top and left were 0, assign a new label to p
• If only one of themre 1, assign its label to p
• If both of themre 1 and have
• the same number, assign their label to p
• Different number, assign label of top to p and
  make note that two label is equivalent
• Sort all pairs of equivalent labels and assign
  each equivalent to be same type

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Example 4-connected components
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Equivalent Table
1 2
3 4


2
3
4
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Step 8-connected components

• Steps are same as 4-connected components
• But the pixel that are consider is 4 previous
  pixels ( top-left, top, top-right, and left )

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Example 8-connected components
1
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Multi-Color Labeling

• Well define the group of color clearly and
  independency.
• Then label each group independency.

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Example Multi-Color labeling
Group of color 1st Group consists of 1 2nd Group
consists of 2 3rd Group consists of 3
??? 0 ??? 1 ??? 2 ??? 3
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Color Labeling 1st Group
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Color Labeling 2st Group
2
4
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Color Labeling 3st Group
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Exercise

• If we want to label red and yellow is the same
  group.
• How many label we can get?