l06-07 interpolation geometry

7/23/2019 L06-07 Interpolation Geometry

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www.ImageProcessingPlace.com

19922008 R. C. Gonzalez & R. E. Woods

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Chapter 2

Digital Image Fundamentals

Chapter 2


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Chapter 2


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Chapter 2


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Chapter 2


Chapter 2


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Chapter 2


Chapter 2


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Chapter 2


Chapter 2


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Low-Res.

High-Res.


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Chapter 2


Chapter 2


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Chapter 2


Chapter 2


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Chapter 2


Chapter 2


Concept

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Chapter 2


Chapter 2


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a 1-a

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f(n+1)f(n+a)

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Chapter 2


Chapter 2


D%/"&-#,4 F:,/24".

f(n)=[0,120,180,120,0]

f(x)=[0,60,120,150,180,150,120,60,0], x=n/2

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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Chapter 2


Chapter 2


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Chapter 2


Chapter 2


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Chapter 2


Chapter 2


) Bilinear Interpolation

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Chapter 2


Chapter 2



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Chapter 2


Chapter 2


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Chapter 2


Chapter 2



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Chapter 2


Chapter 2




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Chapter 2


Chapter 2


) Bicubic Interpolation

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Chapter 2


Chapter 2


) Bicubic Interpolation (Discrete)

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Chapter 2


Chapter 2


) Interpolation Comparative


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Chapter 2


Chapter 2



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Chapter 2


Chapter 2



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Chapter 2


Chapter 2


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Jagged artifacts

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Edge blurring


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Chapter 2


Chapter 2


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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Chapter 2


Chapter 2


A common confusion


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Chapter 2


Chapter 2


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Chapter 2


Chapter 2


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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Chapter 2


Chapter 2


Rotation

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x

y

x

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f

x

y

x

y


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Chapter 2


Chapter 2


Scale

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x

a

a

y

x

d]W

W

f

f

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Chapter 2


Chapter 2


Affine Transform

y

x

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yx

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Chapter 2


Chapter 2


Affine TransformExample

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XY?

]Y?

f

f

y

x

y

x


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Chapter 2


Chapter 2


Shear

y

x

d

d

y

x

sy

x

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Chapter 2


Chapter 2


Shear Example

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Chapter 2


Chapter 2


Extend you imagination


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Chapter 2


Chapter 2


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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Chapter 2


Chapter 2


Application into Image Metamorphosis


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Chapter 2


Chapter 2


Which is good?

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Chapter 2


Chapter 2


Which is good? (contd.)

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Chapter 2


Chapter 2


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l06-07 interpolation geometry

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