Chain and Crackcodes

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Chain and Crack-codes

• Alexander Kolesnikov

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1) Vectorization of digitized curves
Raster image
Digitized curves
Vector data
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Digitized curves
Digitized curve P(x1,y1), (x2,y2), , (xn,yn)
(10,11), (11,11), (12, 12),
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8-directional chain (or Freeman) code
2
1
3
P
4
0
y1
7
5
6
x1
C01110111212111210707777767666666
Chain codes represent a digitized curve by a
connected sequence of straight-line segments of
specified length and direction Typically this
representation is based on a 4- or
8-connectivity The direction of each segment
is coded by numbers and the resulting chain code
is a sequence of numbers.
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4-directional chain (or Freeman) code
1
0
2
3
8-directional chain code 076666553321212
4-directional chain code 0033333323221211101101
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Inner border of region on binary images
4-connected inner border
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Outer border of region on binary images
(See Sonka, Hlavac, and Boyle book)
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Inner or outer borders of adjacent regions on
color images?
Inner borders Outer borders
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Border of adjacent regions on color images?
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How many regions (objects)?

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2) Vectorization of planar subdivision
Given raster image, construct vector
presentation of the planar subdivision (result
of raster image segmention).
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Raster data planar subdivision
Input image
One pixel
Fragment of the raster image
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Crack codes generation
1) Starting point (0.5, 2.5)
3 2 1 0
0
0
0
3
1
2
3
1
2
2
0 1 2 3 4
2) Crack codes for the shape 0 0 0 3 3 2 2 1 2 1
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Crack codes to vector data
x y 1) 0.5 2.5 2) 1.5 2.5 3) 2.5 2.5 4) 3.5 2.5
5) 3.5 1.5 6) 3.5 0.5 7) 2.5 0.5 8) 1.5 0.5 9) 1.5
1.5 10) 0.5 1.5 11) 0.5 2.5
3 2 1 0
0 1 2 3 4
Crack codes 0 0 0 3 3 2 2 1 2 1
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Border of adjacent regions
Inner borders Outer borders Border with

crack-codes
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Border of regions with holes
To preserve topological properties of the regions
with holes use counterclockwise order for
external border and clockwise order for internal
borders (holes).
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How many regions (objects)?How many holes?

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How many regions (objects)? How many holes?

R2, H0 R4 H1
R4 H1
1 2 4
4 4
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Digitized borders of regions
Raster image planar subdivision
Digitized borders of the regions
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Polygonal approximation of borders
Polygonal approximation of region borders
individually WRONG!
Polygonal approximation of borders from junction
point to junction point.
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Region border Example
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Region border