Binary Images

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Binary Images Region Representation
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Binary Images Region Representation -
Boundary Representation - Region Representation
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Boundary Representation Techniques - Chain
Codes - Polygonal Approximations -
Signatures - Boundary Segments Region
Representation Techniques - Skeletons -
Fractal Representation
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Boundary Representation Techniques -
translational invariance - rotational
invariance - scale invariance
Invariance, why is it important?
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Chain Codes
OBJECT
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Chain Codes
OBJECT
BOUNDARY
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Chain Codes
OBJECT
BOUNDARY (4 - CONNECTED)
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Chain Codes
OBJECT
BOUNDARY (8 - CONNECTED)
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Chain Codes
4-CONNECTED
8-CONNECTED
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0
Chain Code
0
BOUNDARY
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0
0
Chain Code
0, 0
BOUNDARY
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0
0
7
Chain Code
0, 0, 7
BOUNDARY
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0
0
7
2
7
1
2
Chain Code
5
2
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0, 0, 7, 7, 5, 6, 5, 5 4, 3, 2, 2, 2, 1, 2
2
5
5
3
4
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First Difference Chain Code
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First Difference Chain Code
Direction codes are given relative to the
direction of the previous movement (rotational
invariance)
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First Difference Chain Code
Direction codes are given relative to the
direction of the previous movement (rotational
invariance) Resulting code may be circularly
shifted to form an integer of minimum magnitude
(implementation invariance)
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First Difference Chain Code
Direction codes are given relative to the
direction of the previous movement (rotational
invariance) Resulting code may be circularly
shifted to form an integer of minimum magnitude
(implementation invariance) Sampling grid may be
adjusted (scale invariance)
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First Difference Chain Code
0, 0, 7, 7, 5, 6, 5, 5, 4, 3, 2, 2, 2, 1, 2
0
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First Difference Chain Code
0, 0, 7, 7, 5, 6, 5, 5, 4, 3, 2, 2, 2, 1, 2
0, 7
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First Difference Chain Code
0, 0, 7, 7, 5, 6, 5, 5, 4, 3, 2, 2, 2, 1, 2
0, 7, 0
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First Difference Chain Code
0, 0, 7, 7, 5, 6, 5, 5, 4, 3, 2, 2, 2, 1, 2
0, 7, 0, 6
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First Difference Chain Code
0, 0, 7, 7, 5, 6, 5, 5, 4, 3, 2, 2, 2, 1, 2
0, 7, 0, 6, 1
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First Difference Chain Code
0, 0, 7, 7, 5, 6, 5, 5, 4, 3, 2, 2, 2, 1, 2
0, 7, 0, 6, 1, 7
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First Difference Chain Code
0, 0, 7, 7, 5, 6, 5, 5, 4, 3, 2, 2, 2, 1, 2
0, 7, 0, 6, 1, 7, 0, 7, 7, 7, 0, 0, 7, 1
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First Difference Chain Code
0, 0, 7, 7, 5, 6, 5, 5, 4, 3, 2, 2, 2, 1, 2
0, 7, 0, 6, 1, 7, 0, 7, 7, 7, 0, 0, 7, 1, 6
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Chain code 0, 0, 7, 7, 5, 6, 5, 5, 4, 3, 2, 2,
2, 1, 2
First difference Chain Code 0, 7, 0, 6, 1, 7, 0,
7, 7, 7, 0, 0, 7, 1, 6
Minimum magnitude 0, 0, 7, 1, 6, 0, 7, 0, 6, 1,
7, 0, 7, 7, 7,
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Polygonal Approximation a digital boundary can
be approximated with a polygon
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Polygonal Approximation a digital boundary can
be approximated with a polygon approximation is
exact when of points in polygon points
in boundary
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Polygonal Approximation a digital boundary can
be approximated with a polygon approximation is
exact when of points in polygon points
in boundary goal is to capture the essence of
the shape with the fewest possible segments
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Polygonal Approximation Minimal perimeter
polygon
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Polygonal Approximation Minimal perimeter
polygon
Fit a rubberband about the corners of the border
pixels
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Polygonal Approximation Boundary Splitting
Subdivide the boundary about its two farthest
points
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Polygonal Approximation Boundary Splitting
Subdivide each resulting region. Find point with
greatest perpendicular distance.
Continue until perpendicular distance is less
than some threshold.
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Polygonal Approximation Boundary Splitting
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Polygonal Approximation Boundary Splitting
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Signatures 1-D representation of a
boundary plot distance from the centroid to the
boundary as a function of angle
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Signatures plot distance from the centroid to
the boundary as a function of angle
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Signatures translation invariant signature may
be started at point which is farthest from
centroid (rotational invariance) amplitude of
function may be scaled to the range 0, 1 (scale
invariance)
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Boundary Segments
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Boundary Segments
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Boundary Segments
Use a smoothed version of the boundary
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Skeletons
Medial Axis Transform
For each point P in the region, we find its
closest neighbor on the border B. If more than
one closest neighbor, then it is part of the
medial axis.
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Skeletons
Thinning 1) does not remove endpoints 2) does not
break connectedness 3) does not cause excessive
erosion of the region