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## Computer and Robot Vision I

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### projection, outputs first or second argument : background ... Top-down, left-right scan: deletes edge pixels not right-boundary. DC & CV Lab. CSIE NTU ... – PowerPoint PPT presentation

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Title: Computer and Robot Vision I

1
Computer and Robot Vision I
• Chapter 6
• Neighborhood Operators

Presented by ??? ??? 0952-725532 r97944037_at_csi
e.ntu.edu.tw ???? ??? ??
2
6.1 Introduction
• neighborhood operator
• workhorse of low- level vision
• performs conditioning, labeling, grouping

3
6.1 Introduction
• The output of a neighborhood operator at a given
pixel position is a function of the position, of
the input pixel value at the position, of the
values of the input pixels in some neighborhood
around the given input position, and possibly of
some values of previously generated output pixels

4
6.1 Introduction
• numeric domain arithmetic operations
• , -, min, max
• symbolic domain Boolean operations
• AND, OR, NOT, table-look-up
• nonrecursive neighborhood operators
• output is function of input
• recursive neighborhood operators
• output depends partly on previous output

5
6.1 Introduction
• neighborhood might be small and asymmetric or
large

6
6.1 Introduction
• set of neighboring pixel positions
around position
• general nonrecursive neighborhood operator
input , output

7
6.1 Introduction
• linear operator
• one common nonrecursive neighborhood operator
• output
• possibly position-dependent linear combination of
inputs

8
6.1 Introduction
• shift-invariant position invariant
• action same regardless of position
• composition of shift-invariant operators
• shift-invariant

9
6.1 Introduction
• cross-correlation of with
• weight function kernel or mask of weights
• domain of

10
Take a break
11
6.1 Introduction
• common masks for noise cleaning, (a)
box filter

12
6.1 Introduction
• common masked for noise cleaning

13
6.1 Introduction
• application of
• mask with
• weights to image

14
6.1 Introduction
• convolution of with
• convolution
• close relative to cross-correlation
• linearshift-invariant.
• if mask symmetric, convolution and correlation
the same

15
Take a break
16
6.2 Symbolic Neighborhood Operators
• indexing of neighborhoods

17
6.2.1 Region-Growing Operator
• projection, outputs first or second argument
• background
• background pixel labeled first nonbackground label

18
6.2.1 Region-Growing Operator
• 4-connected
• output

a0 x0 a1 h(a0 , x1) a2 h(a1 , x2) a3 h(a2
, x3) a4 h(a3 , x4)
19
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20
6.2.1 Region-Growing Operator
• 8-connected
• output

21
6.2.1 Region-Growing Operator
22
6.2.1 Region-Growing Operator
23
6.2.1 Region-Growing Operator
24
6.2.1 Region-Growing Operator
25
6.2.1 Region-Growing Operator
26
6.2.2 Nearest Neighbor Sets and Influence Zones
• influence zones
• nearest neighbor sets
• iteratively region-growing

27
6.2.2 Nearest Neighbor Sets and Influence Zones
• 4-neighborhood for city-block distance
• e.g. ( i , j ), ( k , l ) ( k i )
( l j )
• 8-neighborhood for max distance (of horizontal
and vertical distances)
• e.g. ( i , j ), ( k , l ) max( k i
, l j )
• alternate 4, 8-neighborhood for Euclidean
distance

28
Take a break
29
6.2.3 Region-Shrinking Operator
• region-shrinking
• changes all border pixels to background
• can change connectivity
• can entirely delete region if repeatedly applied

30
6.2.3 Region-Shrinking Operator
• whether or not arguments identical
• background
• border has different neighbor and becomes
background

31
6.2.3 Region-Shrinking Operator
• 4-connected
• output

a0 x0 a1 h(a0 , x1) a2 h(a1 , x2) a3 h(a2
, x3) a4 h(a3 , x4)
32
a0 x0 1 a1 h(a0 , x1) a2 h(a1 , x2) a3
h(a2 , x3) a4 h(a3 , x4)
a0 x0 1 a1 h(a0 , x1) a2 h(a1 , x2) a3
h(a2 , x3) a4 h(a3 , x4)
33
6.2.3 Region-Shrinking Operator
• 8-connected
• output

34
6.2.3 Region-Shrinking Operator
• region shrinking related to binary erosion
except on labeled region

35
6.2.3 Region-Shrinking Operator
36
6.2.3 Region-Shrinking Operator
37
6.2.3 Region-Shrinking Operator
38
6.2.3 Region-Shrinking Operator
39
Take a break
40
6.2.4 Mark-Interior/Border-Pixel Operator
• mark-interior operator
• border-pixel operator
• marks all interior pixels with the label , and
all border pixels with the label

41
6.2.4 Mark-Interior/Border-Pixel Operator
• whether or not arguments identical
• recognizes whether or not its argument is
symbol

42
6.2.4 Mark-Interior/Border-Pixel Operator
• 4-connected
• output

a0 x0 a1 h(a0 , x1) a2 h(a1 , x2) a3 h(a2
, x3) a4 h(a3 , x4)
43
a0 x0 1 a1 h(a0 , x1) a2 h(a1 , x2) a3
h(a2 , x3) a4 h(a3 , x4)
a0 x0 0 a1 h(a0 , x1) a2 h(a1 , x2) a3
h(a2 , x3) a4 h(a3 , x4)
44
6.2.4 Mark-Interior/Border-Pixel Operator
• 8-connected
• output

45
Take a break
46
6.2.5 Connectivity Number Operator
• connectivity number
• nonrecursive and symbolic data domain
• classify the way pixel connected to neighbors
• six values of connectivity
• five for border, one for interior
• Border
• isolated, edge, connected, branching, crossing

47
6.2.5 Connectivity Number Operator
48
6.2.5 Connectivity Number Operator
• corner neighborhood

49
6.2.5 Connectivity Number Operator
50
Yokoi Connectivity Number
• 4-connectivity
• corner transition
• corner all , no transition
• center , neighbor , nothing will happen

51
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52
Yokoi Connectivity Number
• 5 no transition all 8 neighbors 1, thus interior
• 1 transition generates one connected
component if center removed

53
Yokoi Connectivity Number
• connectivity number

54
Yokoi Connectivity Number
55
Yokoi Connectivity Number
56
Yokoi Connectivity Number
57
Yokoi Connectivity Number
• lena.6464

58
Yokoi Connectivity Number
• lena.yokoi

59
Take a break
60
Yokoi Connectivity Number
• 8-connectivity, only slightly different
• center and corner transition
• corner no transition, all
• itself and two 4-neighbors , corner

61
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62
Yokoi Connectivity Number
63
Rutovitz Connectivity Number
• Rutovitz connectivity
• number of transitions from one symbol to another
• sometimes called crossing number

64
Take a break
65
6.2.6 Connected Shrink Operator
• connected shrink
• recursive operator, symbolic data domain
• deletes border pixels without disconnecting
regions

66
6.2.6 Connected Shrink Operator
• Top-down, left-right scan deletes edge pixels
not right-boundary

67
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68
6.2.6 Connected Shrink Operator
• determines whether corner connected

69
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70
6.2.6 Connected Shrink Operator
• background
• output symbol

71
6.2.6 Connected Shrink Operator
72
6.2.6 Connected Shrink Operator
73
6.2.6 Connected Shrink Operator
74
Take a break
75
6.2.7 Pair Relationship Operator
• pair relationship operator
• nonrecursive operator, symbolic data domain
• determines whether first argument equals
label

76
6.2.7 Pair Relationship Operator
• 4-connected mode, output
• not deletable if Yokoi number or no
neighbor
• possibly deletable if Yokoi number and
some neighbor

77
6.2.8 Thinning Operator
• thinning operator is composition of three
operators
• Yokoi connectivity
• pair relationship
• connected shrink

78
6.2.8 Thinning Operator
79
Yoloi Output
Pair relation Output
80
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81
6.2.8 Thinning Operator
• lena.thin

82
6.2.8 Thinning Operator
• lena.thin

83
Take a break
84
6.2.9 Distance Transformation Operator
• distance transformation
• produces distance to closest border pixel

85
6.2.9 Distance Transformation Operator
• nonrecursive, iterative, start with
• background
• border, because distance to border is
• interior pixels

86
6.2.9 Distance Transformation Operator
• iteration label with all with
neighbor

87
6.2.9 Distance Transformation Operator
• equivalent algorithm nonrecursive iterative
• if no neighbor labeled, still interior, leave
it alone
• self interior but
neighbor labeled
• already labeled, wont change value since
later route farther
• 4-connected output

88
6.2.9 Distance Transformation Operator
• distance transformation
• produces distance to closest background
• recursive
• two-pass

89
6.2.9 Distance Transformation Operator
• first pass left-right, top-bottom
• if background still background, since
• min min of upper and left neighbors and add
• 4-connected output

90
6.2.9 Distance Transformation Operator
• second pass right-left, bottom-up
• 4-connected output

91
6.2.9 Distance Transformation Operator
• Original

92
6.2.9 Distance Transformation Operator
• after pass 1

93
6.2.9 Distance Transformation Operator
• pass 2

94
Take a break
95
6.2.10 Radius of Fusion
• The radius of fusion for any connected component
of binary image is the radius of a disk
satisfying the condition that if the binary image
is morphologically closed with a disk of
radius , then the given connected region will
fuse with some other connected region

96
6.2.10 Radius of Fusion
97
6.2.11 Number of Shortest Paths
• number of shortest paths for each 0-pixel to
binary-1 pixel set given binary image
• can be 4-neighborhood or 8-neighborhood
• nonzero, stays unchanged since
shortest paths counted
• if zero then sum of neighboring shortest
paths

98
6.2.11 Number of Shortest Paths
99
6.2.11 Number of Shortest Paths
100
6.2.11 Number of Shortest Paths
101
Take a break
102
6.3 Extremum-Related Neighborhood Operators
103
6.3.1 Non-Minima-Maxima Operator
• non-minima-maxima
• nonrecursive operator
• symbolic output

104
6.3.1 Non-Minima-Maxima Operator
• a pixel can be neighborhood maximum not relative
maximum

105
6.3.1 Non-Minima-Maxima Operator
106
6.3.1 Non-Minima-Maxima Operator
• 4-connected
• output pixel

107
6.3.2 Relative Extrema Operator
• relative extrema operators
• relative maximum and minimum operators
• relative extrema
• recursive operator, numeric data domain
• relative extrema
• input not changedoutput modified
• top-down, left-right scan
• then bottom-up, right-left scan
• until no change

108
6.3.2 Relative Extrema Operator
• output value of highest extrema reachable by
monotonic path
• relative extrema pixels output same as input
pixels

109
6.3.2 Relative Extrema Operator
• pixel designations for the normal and reverse
scans

110
6.3.2 Relative Extrema Operator
111
6.3.2 Relative Extrema Operator
• two primitive functions and
• use new maximum value when
ascending
• keep original maximum when descending

112
6.3.2 Relative Extrema Operator
• 4-connected, output

top-down , left-right
bottom-up , right-left
113
6.3.2 Relative Extrema Operator
a0 l0 a1 h (x0, x1, a0, l1) a2 h (x0, x2,
a1, l2)
114
6.3.2 Relative Extrema Operator
a0 l0 a1 h (x0, x1, a0, l1) a2 h (x0, x2,
a1, l2)
115
6.3.2 Relative Extrema Operator
a0 l0 a1 h (x0, x1, a0, l1) a2 h (x0, x2,
a1, l2)
116
6.3.2 Relative Extrema Operator
a0 l0 a1 h (x0, x1, a0, l1) a2 h (x0, x2,
a1, l2)
117
6.3.2 Relative Extrema Operator
a0 l0 a1 h (x0, x1, a0, l1) a2 h (x0, x2,
a1, l2)
118
6.3.2 Relative Extrema Operator
a0 l0 a1 h (x0, x1, a0, l1) a2 h (x0, x2,
a1, l2)
119
6.3.2 Relative Extrema Operator
a0 l0 a1 h (x0, x1, a0, l1) a2 h (x0, x2,
a1, l2)
120
6.3.2 Relative Extrema Operator
a0 l0 a1 h (x0, x1, a0, l1) a2 h (x0, x2,
a1, l2)
121
6.3.2 Relative Extrema Operator
a0 l0 a1 h (x0, x1, a0, l1) a2 h (x0, x2,
a1, l2)
122
Take a break
123
6.3.3 Reachability Operator
• successively propagating labels that can reach by
monotonic paths descending reachability operator
employs

124
6.3.3 Reachability Operator
• g pixels that are not relative extrema labeled
background
• a unchanged when neighbor is g or the same with
neighbor
• b become first propagated label if originally g
• c common region more than one extremum can reach
it by monotonic path
• c already labeled and neighbor has different
label, then two extrema reach
• a propagate from extremum

125
6.3.3 Reachability Operator
• 4-connected, output

a0 l0 a1 h (a0 , l1 , x0 , x1) a2 h (a1 ,
l2 , x0 , x2)
126
6.3.3 Reachability Operator
127
6.3.3 Reachability Operator
128
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129
6.3.3 Reachability Operator
130
Take a break
131
6.4 Linear Shift-Invariant Neighborhood Operators
• Convolution
• Commutative
• Associative
• distributor over sums
• homogeneous

132
6.4.1 Convolution and Correlation
• convolution of an image f with kernel w

133
6.4.1 Convolution and Correlation
134
6.4.1 Convolution and Correlation
Convolution
135
6.4.1 Convolution and Correlation
136
6.4.1 Convolution and Correlation
137
6.4.1 Convolution and Correlation
138
6.4.1 Convolution and Correlation
139
6.4.1 Convolution and Correlation
140
6.4.1 Convolution and Correlation
141
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142
6.4.2 Separability
143
6.4.2 Separability
144
Project due Nov. 18 ??
• Write a program to generate Yokoi connectivity
number
• You can down sample lena.bmp from 512512 to
6464 first.
• Sample pixels positions at (r, c) (0,0), (0,8)
, so everyone will get the same answer .

145
Project due Nov. 25
• Write a program to generate thinned image.
• You can down sample lena.bmp from 512512 to
6464 first.
• Sample pixels positions at (r, c) (0,0), (0,8)
, so everyone will get the same answer .
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