Lecture 2 - Image Processing techniques - Useful for high level analysis

Image process techniques

1. KA – Digital Image Processing – Unit I – Jan, 2013, PSNACET
Digital ImageDigital Image
ProcessingProcessing
Dr. K. Adalarasu
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2. KA – Digital Image Processing – Unit I – Jan, 2013, PSNACET
Textbook and MaterialsTextbook and Materials
Rafael C. Gonzalez, Richard E.
Woods, “Digital Image Processing”,
2
nd
Edition, Pearson Education, 2003
Power Point Presentation
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3. KA – Digital Image Processing – Unit I – Jan, 2013, PSNACET
ReferenceReference
William K. Pratt, “Digital Image Processing” ,
John Willey ,2001
Millman Sonka, Vaclav Hlavac, Roger Boyle,
Broos/Colic, Thompson Learniy, Vision,
“Image Processing Analysis and Machine”,
1999.
Jain A.K., “Fundamentals of Digital Image
Processing”, PHI, 1995.
Chanda Dutta Magundar, “Digital Image
Processing and Applications”, PHI, 2000
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4. KA – Digital Image Processing – Unit I – Jan, 2013, PSNACET
Digital Image Digital Image
Fundamentals and Fundamentals and
TransformsTransforms
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5. KA – Digital Image Processing – Unit I – Jan, 2013, PSNACET
Representing Digital ImagesRepresenting Digital Images
Discrete levels are equally spaced
Integers in interval [0, L-1]
Bits required to store a digitized
image (b)
b=M*N*k
Where k bits
When M=N
b = N
2
k
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6. KA – Digital Image Processing – Unit I – Jan, 2013, PSNACET
Representing Digital ImagesRepresenting Digital Images
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7. KA – Digital Image Processing – Unit I – Jan, 2013, PSNACET
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8. KA – Digital Image Processing – Unit I – Jan, 2013, PSNACET
Spatial and Gray-Level ResolutionSpatial and Gray-Level Resolution
Sampling
Principal factor determining spatial resolution
of an image
Construct a chart
Vertical lines of width W
Space between lines also having width W
Line pair
One such line and its adjacent space
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9. KA – Digital Image Processing – Unit I – Jan, 2013, PSNACET
Spatial and Gray-Level ResolutionSpatial and Gray-Level Resolution
Width of a line pair is 2W
1/2W line pairs per unit distance
Smallest number of “discernible line pairs”
per unit distance
Gray-level resolution
Smallest discernible change in gray level
Measuring discernible changes in gray level
is a highly subjective process
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10. KA – Digital Image Processing – Unit I – Jan, 2013, PSNACET
Spatial and Gray-Level ResolutionSpatial and Gray-Level Resolution
Most common number is 8 bits
If enhancement of specific gray-level ranges
is necessary
16 bits being used
Digitize gray levels of an image with 10 or 12
bits of accuracy
Example
512*512 image was obtained by deleting every
other row and column from the 1024*1024
image
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11. KA – Digital Image Processing – Unit I – Jan, 2013, PSNACET
Spatial and Gray-Level ResolutionSpatial and Gray-Level Resolution
256*256 image was generated by
deleting every other row and column
in 512*512 image
Number of allowed gray levels was
kept at 256
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12. KA – Digital Image Processing – Unit I – Jan, 2013, PSNACET

13. KA – Digital Image Processing – Unit I – Jan, 2013, PSNACET
Spatial and Gray-Level ResolutionSpatial and Gray-Level Resolution
Example
Keep number of samples constant
Reduce number of gray levels from
256 to 2
In integer powers of 2
452*374 CAT projection image
Displayed with k=8(256 gray
levels)
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14. KA – Digital Image Processing – Unit I – Jan, 2013, PSNACET
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(a) 452*374,
256-level image.
(b)–(d) Image
displayed in 128,
64, and 32 gray
levels, while
keeping the
spatial resolution
constant

15. KA – Digital Image Processing – Unit I – Jan, 2013, PSNACET
Spatial and Gray-Level ResolutionSpatial and Gray-Level Resolution
Obtained by reducing number of bits
from k=7to k=1
While keeping spatial resolution
constant at 452*374 pixels
256, 128, and 64-level images are
visually identical for all practical
purposes
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16. KA – Digital Image Processing – Unit I – Jan, 2013, PSNACET
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(e)–(g)
Image
displayed in
16, 8,
4, and 2
gray
levels

17. KA – Digital Image Processing – Unit I – Jan, 2013, PSNACET
Spatial and Gray-Level ResolutionSpatial and Gray-Level Resolution
Images of size 256*256 pixels and 64
gray levels are about the smallest
images that can be expected to be
reasonably free of objectionable
sampling checkerboards and false
contouring
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18. KA – Digital Image Processing – Unit I – Jan, 2013, PSNACET
QuestionsQuestions
Define Image?
What is the need for digital Image
processing ?
What do you mean by sampling and
quantization ?
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19. KA – Digital Image Processing – Unit I – Jan, 2013, PSNACET
Aliasing and Moiré PatternsAliasing and Moiré Patterns
Function is under-sampled
Then a phenomenon called aliasing corrupts
sampled image
Corruption is in form of “additional frequency
components” being introduced into sampled
function
Sampling rate in images is number of
samples taken (in both spatial directions) per
unit distance
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20. KA – Digital Image Processing – Unit I – Jan, 2013, PSNACET
Aliasing and Moiré PatternsAliasing and Moiré Patterns
Principal approach for reducing aliasing
effects on an image
To reduce its high-frequency components
by blurring image prior to sampling
Aliasing is always present in a sampled
image
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21. KA – Digital Image Processing – Unit I – Jan, 2013, PSNACET
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Aliasing in Digital ImagesAliasing in Digital Images

22. KA – Digital Image Processing – Unit I – Jan, 2013, PSNACET
Zooming and Shrinking Digital Zooming and Shrinking Digital
ImagesImages
Zooming
Viewed as oversampling
Shrinking
Viewed as under-sampling
Zooming and shrinking are applied to a digital
image
Zooming requires two steps
Creation of new pixel locations
Assignment of gray levels to those new locations
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23. KA – Digital Image Processing – Unit I – Jan, 2013, PSNACET
Zooming and Shrinking Digital Zooming and Shrinking Digital
ImagesImages
Example
Image of size 500*500 pixels
Want to enlarge it 1.5 times to 750*750 pixels
Laying an imaginary 750*750 grid over
original image
Spacing in grid would be less than one pixel
We are fitting it over a smaller image
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24. KA – Digital Image Processing – Unit I – Jan, 2013, PSNACET
Zooming and Shrinking Digital Zooming and Shrinking Digital
ImagesImages
To perform gray-level assignment for
any point in overlay
Look for closest pixel in original image
Assign its gray level to new pixel in grid
This method of gray-level assignment is
called nearest neighbor interpolation
Pixel neighborhoods
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25. KA – Digital Image Processing – Unit I – Jan, 2013, PSNACET
Zooming and Shrinking Digital Zooming and Shrinking Digital
ImagesImages
Pixel replication
Applicable when we want to increase size of
an image an integer number of times
Double size of an image
Can duplicate each column
Doubles image size in horizontal direction
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26. KA – Digital Image Processing – Unit I – Jan, 2013, PSNACET
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Top row: images zoomed from 128*128, 64*64, and 32*32
pixels to 1024*1024 pixels, using nearest neighbor gray-level
interpolation. Bottom row: same sequence, but using bilinear
interpolation

27. KA – Digital Image Processing – Unit I – Jan, 2013, PSNACET
Zooming and Shrinking Digital Zooming and Shrinking Digital
ImagesImages
Duplicate each row of enlarged image to
double the size in vertical direction
Same procedure is used to enlarge image
by any integer number of times (triple,
quadruple, and so on)
Gray-level assignment of each pixel is
predetermined by fact that new locations are
exact duplicates of old locations
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28. KA – Digital Image Processing – Unit I – Jan, 2013, PSNACET
Zooming and ShrinkingZooming and Shrinking
Nearest neighbor interpolation is fast
Undesirable feature that it produces a checkerboard
effect
Particularly objectionable at high factors of
magnification
More sophisticated way of accomplishing gray-
level assignments
Bilinear interpolation using four nearest neighbors of
a point
To reduce possible aliasing effects
It is a good idea to blur an image slightly before
shrinking it
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29. KA – Digital Image Processing – Unit I – Jan, 2013, PSNACET
Basic Relationships between PixelsBasic Relationships between Pixels
Objective
To study relationships
between pixels in an image
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30. KA – Digital Image Processing – Unit I – Jan, 2013, PSNACET
Neighborhood of a PixelNeighborhood of a Pixel
Given a pixel p in center of 9
4-neighbors of p = b, d, e, g;
8-neighbors of p = a, b, c, d, e, f, g, h;
Diagonal neighbors of p = a, c, f, h;
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31. KA – Digital Image Processing – Unit I – Jan, 2013, PSNACET
Neighbors of a PixelNeighbors of a Pixel
There are three kinds of neighbors of a pixel
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32. KA – Digital Image Processing – Unit I – Jan, 2013, PSNACET
Neighbors of a PixelNeighbors of a Pixel
4-neighbors of p
8-neighbors of p
Diagonal neighbors of p
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33. KA – Digital Image Processing – Unit I – Jan, 2013, PSNACET
Adjacency, Connectivity, Regions, Adjacency, Connectivity, Regions,
and Boundariesand Boundaries
Connectivity between pixels is a fundamental
concept
Simplifies definition of numerous digital image
concepts
Such as regions and boundaries
If two pixels are connected it must be
determined
If they are neighbors and their gray levels satisfy
a specified criterion of similarity
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34. KA – Digital Image Processing – Unit I – Jan, 2013, PSNACET
ConnectivityConnectivity
Types
 4-connected, 8-connected
4-adjacent, 8-adjacent
Path connected
Connected component (c. c.)
For any pixel p in S , the set of pixels in S that
are connected to p is called Connected
Component
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35. KA – Digital Image Processing – Unit I – Jan, 2013, PSNACET
ConnectivityConnectivity
If it only has one connected component,
then set S is called a connected set
Let R be a subset of pixels in an image.
We call R a region of image if R is a
connected set
Boundary of a region R is set of pixels
in region that have one or more
neighbors that are not in R
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36. KA – Digital Image Processing – Unit I – Jan, 2013, PSNACET
AdjacencyAdjacency
Adjacency
Two pixels that are neighbors and have
same grey-level (or some other
specified similarity criterion) are
adjacent
Three types of adjacency
4-adjacency
8-adjacency
m-adjacency (mixed adjacency)
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37. KA – Digital Image Processing – Unit I – Jan, 2013, PSNACET
AdjacencyAdjacency
4-adjacency
Two pixels p and q with values from V are 4-
adjacent if q is in set N
4(p)
8-adjacency
Two pixels p and q with values from V are 8-
adjacent if q is in the set N
8(p)
m-adjacency (mixed adjacency)
(i).q is in N
4(p), or
(ii).p and q are diagonally adjacent and do not
have any common 4-adjacent neighbors
They cannot be both (i) and (ii)
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38. KA – Digital Image Processing – Unit I – Jan, 2013, PSNACET
AdjacencyAdjacency
Mixed adjacency is a modification of 8-
adjacency
Introduced to eliminate ambiguities that often
arise when 8-adjacency is used
For example, pixel arrangement shown in Fig
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39. KA – Digital Image Processing – Unit I – Jan, 2013, PSNACET
AdjacencyAdjacency
For V={1}
Three pixels at top show multiple (ambiguous) 8-
adjacency, as indicated by dashed lines
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40. KA – Digital Image Processing – Unit I – Jan, 2013, PSNACET
AdjacencyAdjacency
Ambiguity is removed by using m-
adjacency
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41. KA – Digital Image Processing – Unit I – Jan, 2013, PSNACET
AdjacencyAdjacency
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42. KA – Digital Image Processing – Unit I – Jan, 2013, PSNACET
Edge Edge
Edge
Found frequently in discussions
dealing with regions and
boundaries
Formed from pixels with derivative
values that exceed a preset
threshold
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43. KA – Digital Image Processing – Unit I – Jan, 2013, PSNACET
Labeling of Connected ComponentsLabeling of Connected Components
Given a pixel p with r and t as its upper and
left-hand neighbors as follows
Following algorithm labels all c.c. In an
binary image ( This algorithm is for 4-
connected)
Scan image left to right and from top to bottom
If p = 0 , continue the scan
 If p = 1 , exam r and t; if r = t = 0 assign a new
label to p
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44. KA – Digital Image Processing – Unit I – Jan, 2013, PSNACET
Region & BoundaryRegion & Boundary
(4- or 8-connected?)

45. KA – Digital Image Processing – Unit I – Jan, 2013, PSNACET
Distance MeasuresDistance Measures
For pixels p, q, and z, with coordinates (x, y),
(s, t), and (v, w), respectively
D is a distance function or metric if
D(p, q) ≥= 0
D(p, q)=0 if f p=q,
D (p, q) = D (q, p)
D(p, z) ≤ = D(p, q)+D(q, z)
Euclidean distance between p and q is defined
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46. KA – Digital Image Processing – Unit I – Jan, 2013, PSNACET
Distance MeasuresDistance Measures
Pixels having a distance less than or
equal to some value r from (x, y) are
points contained in a disk of radius r
centered at (x, y)
City-block distance between p and q
Pixels with D
4 =
1 are 4-neighbors of (x, y)
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47. KA – Digital Image Processing – Unit I – Jan, 2013, PSNACET
Distance MeasuresDistance Measures
Pixels with D
4 distance ≤ 2 from (x, y)
(center point) form following contours of
constant distance
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48. KA – Digital Image Processing – Unit I – Jan, 2013, PSNACET
Distance MeasuresDistance Measures
D
8distance (also called chessboard distance)
between p and q
Pixels with D
8
=1 to a pixel p are 8 neighbors
of p
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49. KA – Digital Image Processing – Unit I – Jan, 2013, PSNACET
Distance MeasureDistance Measure
• L
1, City-block, or D
4 distance
• L
, Chessboard, Chebyshev, or D
8 distance
• L
2
, or Euclidean distance
2 1 2
1 0 1
2 1 2
2 1 2
1 0 1
2 1 2
1 1 1
1 0 1
1 1 1

50. KA – Digital Image Processing – Unit I – Jan, 2013, PSNACET
Distance MeasuresDistance Measures
D4 and D8 distances between p and q are
independent of any paths that might exist
between points
Because these distances involve only
coordinates of points
D
m distance between two points is defined
as shortest m-path between point
Distance between two pixels will depend on
values of pixels along path
As well as values of their neighbors
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51. KA – Digital Image Processing – Unit I – Jan, 2013, PSNACET
Distance MeasuresDistance Measures
Following arrangement of pixels
Assume that p, p
2 and p
4 have value 1
p
1and p
3 can have a value of 0 or 1
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52. KA – Digital Image Processing – Unit I – Jan, 2013, PSNACET
Distance MeasuresDistance Measures
Suppose that we consider adjacency of
pixels valued 1 (i.e., V={1})
Case 1
If p
1 and p
3 = 0
Length of shortest path between p and p
4 = 2
Case 2
If p
1 = 1 and p
3 = 0
Length of shortest path between p and p
4 = 3
Path p p
1 p
2 p
4
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53. KA – Digital Image Processing – Unit I – Jan, 2013, PSNACET
Distance MeasuresDistance Measures
Case 3
If p
1 = 0 and p
3 = 1
Length of shortest path between p and p
4
= 3
Path p p
2 p
3 p
4
Case 4
If p
1
= 1 and p
3
= 1
Length of shortest path between p and p
4 = 4
Path p p
1 p
2 p
3 p
4
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54. KA – Digital Image Processing – Unit I – Jan, 2013, PSNACET
Problem Problem
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55. KA – Digital Image Processing – Unit I – Jan, 2013, PSNACET
Solution Solution
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56. KA – Digital Image Processing – Unit I – Jan, 2013, PSNACET
Problem 2Problem 2
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