l06-07 interpolation geometry
TRANSCRIPT
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19922008 R. C. Gonzalez & R. E. Woods
5-06%&)6 7 8--3/
Chapter 2
Digital Image Fundamentals
Chapter 2
Digital Image Fundamentals
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19922008 R. C. Gonzalez & R. E. Woods
5-06%&)6 7 8--3/
Chapter 2
Digital Image Fundamentals
Chapter 2
Digital Image Fundamentals
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19922008 R. C. Gonzalez & R. E. Woods
5-06%&)6 7 8--3/
Chapter 2
Digital Image Fundamentals
Chapter 2
Digital Image Fundamentals
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19922008 R. C. Gonzalez & R. E. Woods
5-06%&)6 7 8--3/
Chapter 2
Digital Image Fundamentals
Chapter 2
Digital Image Fundamentals
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19922008 R. C. Gonzalez & R. E. Woods
5-06%&)6 7 8--3/
Chapter 2
Digital Image Fundamentals
Chapter 2
Digital Image Fundamentals
) C/,0" C1$"&234,$-31 9O334=
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19922008 R. C. Gonzalez & R. E. Woods
5-06%&)6 7 8--3/
Chapter 2
Digital Image Fundamentals
Chapter 2
Digital Image Fundamentals
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Low-Res.
High-Res.
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19922008 R. C. Gonzalez & R. E. Woods
5-06%&)6 7 8--3/
Chapter 2
Digital Image Fundamentals
Chapter 2
Digital Image Fundamentals
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Non-damaged Damaged
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19922008 R. C. Gonzalez & R. E. Woods
5-06%&)6 7 8--3/
Chapter 2
Digital Image Fundamentals
Chapter 2
Digital Image Fundamentals
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19922008 R. C. Gonzalez & R. E. Woods
5-06%&)6 7 8--3/
Chapter 2
Digital Image Fundamentals
Chapter 2
Digital Image Fundamentals
Concept
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19922008 R. C. Gonzalez & R. E. Woods
5-06%&)6 7 8--3/
Chapter 2
Digital Image Fundamentals
Chapter 2
Digital Image Fundamentals
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19922008 R. C. Gonzalez & R. E. Woods
5-06%&)6 7 8--3/
Chapter 2
Digital Image Fundamentals
Chapter 2
Digital Image Fundamentals
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f(n)=[0,120,180,120,0]
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f(x)=[0,20,40,60,80,100,120,130,140,150,160,170,180, ], x=n/6
Interpolate at 1/2-pixel
Interpolate at 1/3-pixel
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19922008 R. C. Gonzalez & R. E. Woods
5-06%&)6 7 8--3/
Chapter 2
Digital Image Fundamentals
Chapter 2
Digital Image Fundamentals
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spline;sinc; lanczos; "$#?
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19922008 R. C. Gonzalez & R. E. Woods
5-06%&)6 7 8--3/
Chapter 2
Digital Image Fundamentals
Chapter 2
Digital Image Fundamentals
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19922008 R. C. Gonzalez & R. E. Woods
5-06%&)6 7 8--3/
Chapter 2
Digital Image Fundamentals
Chapter 2
Digital Image Fundamentals
) Bilinear Interpolation
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19922008 R. C. Gonzalez & R. E. Woods
5-06%&)6 7 8--3/
Chapter 2
Digital Image Fundamentals
Chapter 2
Digital Image Fundamentals
) Bilinear Interpolation
CXW;]\?Y ^
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19922008 R. C. Gonzalez & R. E. Woods
5-06%&)6 7 8--3/
Chapter 2
Digital Image Fundamentals
Chapter 2
Digital Image Fundamentals
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19922008 R. C. Gonzalez & R. E. Woods
5-06%&)6 7 8--3/
Chapter 2
Digital Image Fundamentals
Chapter 2
Digital Image Fundamentals
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19922008 R. C. Gonzalez & R. E. Woods
5-06%&)6 7 8--3/
Chapter 2
Digital Image Fundamentals
Chapter 2
Digital Image Fundamentals
) Bilinear Interpolation
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19922008 R. C. Gonzalez & R. E. Woods
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Chapter 2
Digital Image Fundamentals
Chapter 2
Digital Image Fundamentals
) Bicubic Interpolation
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19922008 R. C. Gonzalez & R. E. Woods
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Chapter 2
Digital Image Fundamentals
Chapter 2
Digital Image Fundamentals
) Bicubic Interpolation (Discrete)
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19922008 R. C. Gonzalez & R. E. Woods
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Chapter 2
Digital Image Fundamentals
Chapter 2
Digital Image Fundamentals
) Interpolation Comparative
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19922008 R. C. Gonzalez & R. E. Woods
5-06%&)6 7 8--3/
Chapter 2
Digital Image Fundamentals
Chapter 2
Digital Image Fundamentals
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19922008 R. C. Gonzalez & R. E. Woods
5-06%&)6 7 8--3/
Chapter 2
Digital Image Fundamentals
Chapter 2
Digital Image Fundamentals
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19922008 R. C. Gonzalez & R. E. Woods
5-06%&)6 7 8--3/
Chapter 2
Digital Image Fundamentals
Chapter 2
Digital Image Fundamentals
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X
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19922008 R. C. Gonzalez & R. E. Woods
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Chapter 2
Digital Image Fundamentals
Chapter 2
Digital Image Fundamentals
Edge-Sensitive Interpolation
Step 1: interpolate the missing pixels along the diagonal
black or white?
a b
c d
xSince |a-c|=|b-d|
x has equal probabilityof being black or white
c
Step 2: interpolate the other half missing pixelsa
bdSince |a-c|>|b-d|
x=(b+d)/2=black
x
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19922008 R. C. Gonzalez & R. E. Woods
5-06%&)6 7 8--3/
Chapter 2
Digital Image Fundamentals
Chapter 2
Digital Image Fundamentals
A common confusion
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19922008 R. C. Gonzalez & R. E. Woods
5-06%&)6 7 8--3/
Chapter 2
Digital Image Fundamentals
Chapter 2
Digital Image Fundamentals
!"#$%&" `
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19922008 R. C. Gonzalez & R. E. Woods
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Chapter 2
Digital Image Fundamentals
Chapter 2
Digital Image Fundamentals
Geometric Transformation
In the virtual space, you can have any kind of apple you want!
MATLAB functions: griddata, interp2, maketform, imtransform
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19922008 R. C. Gonzalez & R. E. Woods
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Chapter 2
Digital Image Fundamentals
Chapter 2
Digital Image Fundamentals
Rotation
y
x
y
x
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y
x
y
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19922008 R. C. Gonzalez & R. E. Woods
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Chapter 2
Digital Image Fundamentals
Chapter 2
Digital Image Fundamentals
Scale
y
x
a
a
y
x
d]W
W
f
f
,^]dX
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19922008 R. C. Gonzalez & R. E. Woods
5-06%&)6 7 8--3/
Chapter 2
Digital Image Fundamentals
Chapter 2
Digital Image Fundamentals
Affine Transform
y
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19922008 R. C. Gonzalez & R. E. Woods
5-06%&)6 7 8--3/
Chapter 2
Digital Image Fundamentals
Chapter 2
Digital Image Fundamentals
Affine TransformExample
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XY?
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f
f
y
x
y
x
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19922008 R. C. Gonzalez & R. E. Woods
5-06%&)6 7 8--3/
Chapter 2
Digital Image Fundamentals
Chapter 2
Digital Image Fundamentals
Shear
y
x
d
d
y
x
sy
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f
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19922008 R. C. Gonzalez & R. E. Woods
5-06%&)6 7 8--3/
Chapter 2
Digital Image Fundamentals
Chapter 2
Digital Image Fundamentals
Shear Example
]
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f
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y
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y
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19922008 R. C. Gonzalez & R. E. Woods
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Chapter 2
Digital Image Fundamentals
Chapter 2
Digital Image Fundamentals
Extend you imagination
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19922008 R. C. Gonzalez & R. E. Woods
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Chapter 2
Digital Image Fundamentals
Chapter 2
Digital Image Fundamentals
Free Form Deformation
Seung-Yong Lee et al., Image Metamorphosis Using Snakes and Free-Form Deformations,
SIGGRAPH 1985, Pages 439-448
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19922008 R. C. Gonzalez & R. E. Woods
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Chapter 2
Digital Image Fundamentals
Chapter 2
Digital Image Fundamentals
Application into Image Metamorphosis
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19922008 R. C. Gonzalez & R. E. Woods
5-06%&)6 7 8--3/
Chapter 2
Digital Image Fundamentals
Chapter 2
Digital Image Fundamentals
Which is good?
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9\=Edge Preservation: O+" /"$+3A .+3%4A 2&"."&>" "A0". ,1A B3%1A,&-".;
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19922008 R. C. Gonzalez & R. E. Woods
5-06%&)6 7 8--3/
Chapter 2
Digital Image Fundamentals
Chapter 2
Digital Image Fundamentals
Which is good? (contd.)
9(= Texture Preservation: O+" /"$+3A .+3%4A 13$ B4%& 3& ./33$+ $":$%&"A &"0-31.?
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19922008 R. C. Gonzalez & R. E. Woods
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Chapter 2
Digital Image Fundamentals
Chapter 2
Digital Image Fundamentals
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