Image Resizing and Warping

Image Resizing and Warping

Yao Wang Tandon School of Engineering, New York University

Samping and Resizing

? Nyquist sampling and interpolation theorem ? Common sampling and interpolation filters ? Sampling rate conversion of discrete images (image

resizing)

? Yao Wang, 2016

EL-GY 6123

2

Illustration of Image Sampling and Interpolation

dx=dy=2mm

16 mm dx=dy=1mm

? Yao Wang, 2016

EL-GY 6123

3

Uniform Sampling

?

f(x,y) represents the the sampled image,

aonridginfa^(lx,cyo) ntintuhoeurseicmoangster,ufcst(emd,n)

image.

? Uniform sampling

fs (m, n) = f (mx, ny), m = 0,..., M -1; n = 0,..., N -1.

? x and y are vertical and horizontal sampling intervals. fs,x=1/ x, fs,y=1/ y are vertical and horizontal sampling frequencies.

? Yao Wang, 2016

EL-GY 6123

4

Image Sampling as Product with Impulse Train

? Periodic impulse

M -1N -1

p(x, y) =

(x - mx , y - n y )

sequence

m=0 n=0

~

f

s (x, y)

=

f

(x,

y)?

p(x,

y)

=

M -1 N -1

f

(mx , n y ) (x - mx , y - n y )

m=0 n=0

M -1N -1

=

fs (m, n) (x - mx , y - n y )

m=0 n=0

m = 0

1

x

p(x,y)

...

M - 1 x

? Yao Wang, 2016

y n= 0 1 2

EL-GY 6123

y N-1

5

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