CAP5415 Computer VisionSpring 2003

Khurram Hassan-Shafique

Image Filtering Modifying the pixels in an image based on

some function of a local neighborhood of the pixels

10 30 10

20 11 20

11 9 1

p

N(p)

5.7 pf

Linear Filtering The output is the linear combination of the

neighborhood pixels

The coefficients of this linear combination combine to form the “filter-kernel”

pNq

iii

qapf

1 3 02 10 24 1 1

Image

1 0 -11 0.1 -11 0 -1

Kernel

= 5

Filter Output

Convolution

k l

ljkiHlkIHIjif ,,*,

KernelImage

HI H7 H8 H9

H4 H5 H6

H1 H2 H3

H9 H8 H7

H6 H5 H4

H3 H2 H1

H1 H2 H3

H4 H5 H6

H7 H8 H9

HflipX

flipY

I1 I2 I3

I4 I5 I6

I7 I8 I9

192837

465564

738291

*

HIHIHIHIHIHIHIHIHIHI

I

Linear Filtering

0 0 00 1 00 0 0

*

Linear Filtering

0 0 00 0 10 0 0

*

Linear Filtering

1 1 11 1 11 1 1

91*

Linear Filtering

1 1 1 1 1

1 1 1 1 1

1 1 1 1 1

1 1 1 1 1

1 1 1 1 1

251*

Gaussian Filter

2

22

2 2exp

21,

yxyxG

2

22

2 211exp

21,

kjkijiH

array 1212 is , where kkjiH

Linear Filtering(Gaussian Filter)

*

Gaussian Vs Average

Gaussian Smoothing Smoothing by Averaging

Noise Filtering

Gaussian Noise

After Gaussian Smoothing

After Averaging

Noise Filtering

Salt & Pepper Noise

After Gaussian Smoothing

After Averaging

Shift Invariant Linear Systems Superposition

Scaling

Shift Invariance

gRfRgfR

fkRkfR

Fourier Transform

dxdyeyxgvuyxgF vyuxi

2,,,:Continuous

Discrete

Here u & v are larger than the previous slide

Larger than the upper example

Cheetah ImageFourier Magnitude (above)Fourier Phase (below)

Zebra ImageFourier Magnitude (above)Fourier Phase (below)

Reconstruction withZebra phase,Cheetah Magnitude

Reconstruction withCheetah phase,Zebra Magnitude

Suggested Reading Chapter 7, David A. Forsyth and Jean

Ponce, "Computer Vision: A Modern Approach"