An Introduction to Digital Image Processing ????????

1
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• ????????
• ??????? ??

2
??????
?? 10-1 10-2 10-3 10-4 10-5

• 10-1 ???????
• 10-2 ?????????
• 10-3 ????
• 10-4 ??????????
• 10-5 ??????????

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10-1 ???????

• ?????? (Detection of Discontinuities)
• ???????????????????????

?? 10-1 10-2 10-3 10-4 10-5
(10.1-1)
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10-1 ???????

• ??? (Point Detection)

?? 10-1 10-2 10-3 10-4 10-5
(10.1-2)
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10-1 ???????

• ??? (Line Detection)

?? 10-1 10-2 10-3 10-4 10-5
For all j ? i
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10-1 ???????

• ???? (Edge Detection)
• ?????

?? 10-1 10-2 10-3 10-4 10-5
????
??
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10-1 ???????

• ???? (Edge Detection)
• ?????

?? 10-1 10-2 10-3 10-4 10-5
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10-1 ???????

• ???? (Edge Detection)
• ?????

?? 10-1 10-2 10-3 10-4 10-5
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10-1 ???????

• ???? (Edge Detection)
• ?????? (Gradient operators)

?? 10-1 10-2 10-3 10-4 10-5
(10.1-3)
(10.1-4)
(10.1-5)
Roberts cross-gradient operators
(10.1-6)
(10.1-7)
Prewitt operators
(10.1-8)
(10.1-9)
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10-1 ???????

• ???? (Edge Detection)
• ?????? (Gradient operators)

?? 10-1 10-2 10-3 10-4 10-5
Sobel operators
(10.1-10)
(10.1-11)
(10.1-12)
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10-1 ???????

• ???? (Edge Detection)
• ????? (Gradient operators)

?? 10-1 10-2 10-3 10-4 10-5
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10-1 ???????

• ???? (Edge Detection)
• ?????? (Gradient operators)

?? 10-1 10-2 10-3 10-4 10-5
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10-1 ???????

• ???? (Edge Detection)
• ?????? (Gradient operators)

?? 10-1 10-2 10-3 10-4 10-5
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10-1 ???????

• ???? (Edge Detection)
• ????? (Gradient operators)

?? 10-1 10-2 10-3 10-4 10-5
15
10-1 ???????

• ???? (Edge Detection)
• ??????? (Laplacian operators)

?? 10-1 10-2 10-3 10-4 10-5
(10.1-13)
(10.1-14)
(10.1-15)
(10.1-16)
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10-1 ???????

• ???? (Edge Detection)
• ??????? (Laplacian operators)

?? 10-1 10-2 10-3 10-4 10-5
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10-1 ???????

• ???? (Edge Detection)

?? 10-1 10-2 10-3 10-4 10-5
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10-2 ?????????

• ???? (Local Processing)
• ???33?55?????,????f(x,y)?????????,?
• ??????f(x0,y0)?

?? 10-1 10-2 10-3 10-4 10-5
(10.2-1)
(10.2-1)
19
10-2 ?????????

• ???? (Hough Transform)
• ?XY???????(Parameter Space)

?? 10-1 10-2 10-3 10-4 10-5
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10-2 ?????????

• ???? (Hough Transform)
• ????? (Accumulator Cells)

?? 10-1 10-2 10-3 10-4 10-5
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10-2 ?????????

• ???? (Hough Transform)
• ???????????????
• ???????????????

?? 10-1 10-2 10-3 10-4 10-5
(10.2-3)
(10.2-4)
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10-2 ?????????

• ???? (Hough Transform)

?? 10-1 10-2 10-3 10-4 10-5
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10-2 ?????????

• ???? (Hough Transform)
• An approach based on the Hough Transform is as
  follows
• ? Compute the gradient of an image and threshold
  it to obtain a binary image.
• ? Specify subdivisions in the -plane.
• ?Examine the counts of the accumulator cells for
  high pixel concentrations.
• ?Examine the relationship (principally for
  continuity) between pixels in a chosen cell.

?? 10-1 10-2 10-3 10-4 10-5
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10-2 ?????????

• ???? (Hough Transform)

?? 10-1 10-2 10-3 10-4 10-5
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10-2 ?????????

• ??????????

?? 10-1 10-2 10-3 10-4 10-5
26
10-2 ?????????

• ??????????

?? 10-1 10-2 10-3 10-4 10-5
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10-2 ?????????

• ??????????
• ?Minimum-cost

?? 10-1 10-2 10-3 10-4 10-5
(10.2-6)
(10.2-7)
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10-2 ?????????

• ??????????

?? 10-1 10-2 10-3 10-4 10-5
29
10-3 ????

• ?? (Thresholding)
• ???????

?? 10-1 10-2 10-3 10-4 10-5
Based on the preceding discussion , thresholding
may be viewed as an operation that involves tests
against a function T of the form
(10.3-1)
Where f(x,y) is the gray level of point (x,y) and
p(x,y) denotes some local property of this point
For example
if
(10.3-2)
if
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10-3 ????

• ?? (Thresholding)
• ??????

?? 10-1 10-2 10-3 10-4 10-5
(10.3-3)
(10.3-4)
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10-3 ????

• ?? (Thresholding)
• ????????

?? 10-1 10-2 10-3 10-4 10-5
32
10-3 ????

• ?? (Thresholding)
• ????????
• The following algorithm can be used to
  obtain T automatically
• ?Select an initial estimate for T.
• ?Segment the image using T . This will produce
  two groups of pixels
• G1 consisting of all pixels with gray level
  values gtT and G2 consisting
• of pixels with values ?T.
• ?Compute the average gray level values µ1 and µ2
  for the pixels in
• regions G1 and G2.
• ?Compute a new threshold value
• ?Repeat step 2 through 4 until the difference in
  T in successive iterations is smaller than a
  predefined parameter T0.

?? 10-1 10-2 10-3 10-4 10-5
33
10-3 ????

• ?? (Thresholding)
• ????????

?? 10-1 10-2 10-3 10-4 10-5
34
10-3 ????

• ?? (Thresholding)
• ????????

?? 10-1 10-2 10-3 10-4 10-5
35
10-3 ????

• ?? (Thresholding)
• ????????

?? 10-1 10-2 10-3 10-4 10-5
36
10-3 ????

• ?? (Thresholding)
• ??????????

?? 10-1 10-2 10-3 10-4 10-5
?????Histrogram??????????,?????????????????????T??
(10.3-5)
(10.3-6)
37
10-3 ????

• ?? (Thresholding)
• ??????????
• The probability of erroneously classifying a
  background point as an object point is

?? 10-1 10-2 10-3 10-4 10-5
(10.3-7)
(10.3-8)
(10.3-9)
To find the threshold value for which this error
is minimal requires differentiating E(T) with
respect to T and equating the result to 0.The
result is
(10.3-10)
????????-????
(10.3-11)
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10-3 ????

• ?? (Thresholding)
• ??????????

?? 10-1 10-2 10-3 10-4 10-5
?(10.3-10)?(10.3-11)????T?
(10.3-12)
??
(10.3-13)
??????, ?,?
(10.3-14)
p(z)??????????????????????
(10.3-15)
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10-3 ????

• ?? (Thresholding)
• ??????????

?? 10-1 10-2 10-3 10-4 10-5
40
10-3 ????

• ?? (Thresholding)
• ??????????

?? 10-1 10-2 10-3 10-4 10-5
41
10-3 ????

• ?? (Thresholding)
• ??????????????

?? 10-1 10-2 10-3 10-4 10-5
????Histrogram???????????
(10.3-16)
42
10-3 ????

• ?? (Thresholding)
• ??????????????

?? 10-1 10-2 10-3 10-4 10-5
43
10-3 ????

• ?? (Thresholding)
• ?????????

?? 10-1 10-2 10-3 10-4 10-5
44
10-4 ??????????

• Basic Formulation

?? 10-1 10-2 10-3 10-4 10-5
Let R represent the entire image region. We may
view segmentation as a process that partitions R
into n subregions , R1 , R2 ,,Rn ,such that
?
? Ri is a connected region , i1,2,,n
? for all I and j , i ? j
? for i 1,2,.,n
? for i ? j
Here , P(Ri) is a logical predicate defined over
the points in set Ri and is f the null set.
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10-4 ??????????

• ???? (Region Growing)

?? 10-1 10-2 10-3 10-4 10-5
46
10-4 ??????????

• ???? (Region Growing)

?? 10-1 10-2 10-3 10-4 10-5
47
10-4 ??????????

• ???? (Region Growing)
• ? ???????(Region Splitting and Merging)

?? 10-1 10-2 10-3 10-4 10-5
? Split into four disjoint quadrants any region
Ri for which P(Ri)FALSE.
? Merge any adjacent regions Rj and Rk for which
.
? Stop when no further merging or splitting is
possible.
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10-4 ??????????

• ???? (Region Growing)

?? 10-1 10-2 10-3 10-4 10-5
49
10-5 ??????????

• ???? (Spatial Techniques)

?? 10-1 10-2 10-3 10-4 10-5
? ???? (Difference Image)
(10.6-1)
? ???? (Accumulative Difference)
? AADI
(10.6-2)
? PADI
(10.6-3)
? NADI
(10.6-4)
50
10-5 ??????????

• ???? (Spatial Techniques)

?? 10-1 10-2 10-3 10-4 10-5
51
10-5 ??????????

• ???? (Spatial Techniques)
• ? ??????(Establishing a reference image)

?? 10-1 10-2 10-3 10-4 10-5
? ?????
? ??PADI?????????????????
? ??????????,??????????????? ???????
52
10-5 ??????????

• ???? (Frequency Domain Techniques)
• ? ???

?? 10-1 10-2 10-3 10-4 10-5
? timet ?
????? ??? frame ??? V1 pixels (x??),????
53
10-5 ??????????

• ???? (Frequency Domain Techniques)
• ? ????????( x , y???????? )

?? 10-1 10-2 10-3 10-4 10-5
? For a sequence of K digital images of size
MN,the sum of the weighted projections
onto the x axis at any integer instant of time is
(10.6-6)
(10.6-7)
Where,as noted already ,a1 and a2 are
positive integers.
? The 1-D Fourier transforms of Eqs.(10.6-6) and
(10.6-7),respectively,are
(10.6-8)
(10.6-9)
? The frequency-velocity relationship is
(10.6-10)
(10.6-11)
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10-5 ??????????

• ???? (Frequency Domain Techniques)
• ? ????

?? 10-1 10-2 10-3 10-4 10-5
(10.6-12)
(10.6-13)
? ?S1x?S2x???,?V1????
? ?S1x?S2x???,?V1????
? ?S1x?S2x????,??? ? gx?
55
10-5 ??????????

• ???? (Frequency Domain Techniques)

?? 10-1 10-2 10-3 10-4 10-5
56
10-5 ??????????

• ???? (Frequency Domain Techniques)

?? 10-1 10-2 10-3 10-4 10-5
57
10-5 ??????????

• ???? (Frequency Domain Techniques)

?? 10-1 10-2 10-3 10-4 10-5
58
10-5 ??????????

• ???? (Frequency Domain Techniques)

?? 10-1 10-2 10-3 10-4 10-5