1

Vladimir Botchko,

Jussi Parkkinen, Heikki Kälviäinen

2

3

http://www.techexpo.com/www/opto-knowledge/ for previous picture site.

http://stargate.jpl.nasa.gov/lctf/ for this picture site.

4

Image Model

where

f X D X( ) ( )

f X f X f X

D diag

X X X

T

nT

n

nT

v nT

( ) ( ( ), , ( ))

( , , )

( , , )

( ) ( ( ), , ( ))

( , , )

1 2

1

1

1

1

5

Image Model

K

k K k K k K

k K k K k K

k K k K k K

f

n n

n n

n n n n nn n

F

H

GGGG

I

K

JJJJ

11 12

12 1 2 1 1

21 2 1 22 22

2 2

1 1 2 22

6

Image Model

k

k k k

k k k

k k k

n

n

n n nn

F

H

GGGG

I

K

JJJJ

11 12 1

21 22 2

1 2

k

n

n

n n

F

H

GGGG

I

K

JJJJ

1

1

1

1

2

1 2

7

Statistical Analysis of Natural Images

8

Statistical Analysis of Natural Images

9

Statistical Analysis of Natural Images

v c

( )1

0 1

0 1

10

Synthetic texture coloring algorithm

Synthesizes the vector field Sets the mean vector according to the given spectrum Sets the standard deviation vector Computes the vector field Reproduces the color image through the multispectral image Enhances texture contrast

( )X

v

f X( )

11

Synthetic texture coloring

12

Gray level texture image coloring algorithm

Normalizes the gray level image Copies the normalized image several times to get a vector field Sets the mean vector according to the given spectrum Sets the standard deviation vector Computes the vector field Reproduces the color image through the multispectral image Enhances texture contrast

( )X

v

f X( )

13

Gray level texture image coloring

14

Gray level texture image coloring

15

Gray level texture image coloring

const v const

16

Gray level texture image coloring

v c ( )1

1 0 8.

0 5. 0

17

The ”Water Lily Pond”, Claude Monet

18

Gray level composed image coloring

b f s ( )1 0 1 0 55.

19

Final coloring results

.

20

High order statistics role in color reproduction

21

Color reproduced through the only HOS !