image restoration & color fundamentals

8/9/2019 Image Restoration & Color Fundamentals

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Image Restoration & Color Fundamentals

Lecture 7

Sankalp [email protected]


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Constrained Least Squares Filtering

Wiener filter needs knowledge of the noise PSD as wellas the PSD of the Undegraded Image.

Estimates of the noise PSD arent always accurate.

In the least squares filter only the noise characteristicsare needed and can be gathered from the degradedimage.

The wiener filter is optimal in an average sense

the least squares filter is optimal to each image it isapplied to.


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Example of Restoration from MotionDeblurring & Additive Noise

http://www.mathworks.com/products/image/demos.html?file=

/products/demos/shipping/images/ipexwiener.html


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Geometric Transformations

They can be divided into twotypes

1) spatial transformations

2) grey level interpolations

Spatial Transformations

The geometric distortion in an image can be expressed as

),( yxrx

),( yxsy If the distortion functions are known analytical functions then theoriginal image can be reconstructed form the distorted image directly.


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Spatial Transformations

4321),( cxycycxcyxr

The distortion functions may not be known and in that case thedistortion functions are obtained by using Tie Points

The locations of the Tie Pointsis exactly known in the original and thedistorted images.

8765),( cxycycxcyxs

The value of the image over a scan is picked by passing the indices

throught the distortion function and picking the value at the output image.


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Grey Level Interpolation

The spatial transformation may lead to non integer values forthe location hence there may be need to interpolate the valuefrom the closest integer locations.

Nearest Neighbor, Cubic and Bilinear Interpolation are among

the commonly used interpolations.

Nearest Neighbor Interpolation


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Color Image Processing

Two types: Full Color andPseudo Color Processing.

Full Color is where the color isobtained from the scanner or

camera.

Pseudo Color is when thecolor is to be allotted to acertain gray scale image.

Certain gray scale methodsare directly applicable to thecolor images whereas someneed modifications.

Visible Spectrum

violet 380450 nm

blue 450495 nm

green 495570 nm

yellow 570590 nm

orange 590620 nm

red 620750 nm


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Color Basics

Green objects mostly reflect radiation in the green regionof the spectrum.

Intensity maps to gray levels

Radiance is the total amount of energy that flows fromthe light source. Measured in watts (W).

Luminance is the perceived brightness measured in

lumens (lm).

Color perception in the human eye is carried out bycones. 65% are sensitive to red 33% are sensitive togreen and 2% are sensitive to blue.


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Primary and Secondary colors

Red Green Blue primary colors

[Red+Blue] magenta

[Blue+Green] cyan secondary colors

[Red+Green] yellow

Additive Mixing Subtractive Mixing

light pigments

magenta

cyanyellow

red blue


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Color Basics

ZYX

X

x

ZYX

Yy

Brightness, hue and saturation are characteristics used todistinguish Colors.

Hue is an attribute that maps to the wavelength red orange yelloware hues.

Saturation is the amount of white light mixed with the hue.

Pure colors like red are fully saturated pink is not saturated

Tristimulus values

ZYX

Zz


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Chromaticity Diagram

Point of equal energy is white.

The colors along the boundary are theSaturated colors

A straight line joining two points on thisdiagram can show all possible shadesobtainable by mixing different proportionsof those two colors.

A line from the point of equal energy to

the boundary will show all shades ofthat hue.

A triangle with 3 fixed vertices cantEnclose the tongue shape hence 3 primaryColors arent sufficient to reproduce all colors.


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Color Models

Color Models are spatial representations of the colorpalettes, any point in the space would be representing acolor.

RGB is the most popular for cameras and monitors.

CMY and CMYK for color printing.

HSI is close to the way humans perceive color anddecouples the color and grey scale information in animage allowing application of the grey scale processingtechniques.


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RGB Color Model

The RGB color model is based on a cartesian coordinatesystem.

www.mathworks.com image processing toolbox

8 bits per color plane3 color planesResults in 16,777,216 colors

Most displays may not have theability to display all such colors

Hence a subset called Safe RGBhas been developed.


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Web Safe RGB Color Model

6 shades of each color

digit hexadecimal decimal

0 00 0

3 33 51

6 66 1029 99 153

C or (12) CC 204

F or (15) FF 255

These numbers are used todefine all the web safe colors

Each triplet is made up of 24 bits

Each color plane 8 bits.8 bits consist of 2 hex numbers.

The 6 numbers yield (6)3 = 216colors

For Example pure bright redwould be FF0000

RGB safe color cube


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Web Safe RGB Color Model

Web-Safe Colors

*000* 300 600 900 C00 *F00* *003* 303 603 903 C03 *F03*

006 306 606 906 C06 F06 009 309 609 909 C09 F09

00C 30C 60C 90C C0C F0C *00F* 30F 60F 90F C0F *F0F*

030 330 630 930 C30 F30 033 333 633 933 C33 F33

036 336 636 936 C36 F36 039 339 639 939 C39 F39

03C 33C 63C 93C C3C F3C 03F 33F 63F 93F C3F F3F

060 360 660 960 C60 F60 063 363 663 963 C63 F63

066 366 666 966 C66 F66 069 369 669 969 C69 F69


090 390 690 990 C90 F90 093 393 693 993 C93 F93

096 396 696 996 C96 F96 099 399 699 999 C99 F99


0C0 3C0 6C0 9C0 CC0 FC0 0C3 3C3 6C3 9C3 CC3 FC3

0C6 3C6 6C6 9C6 CC6 FC6 0C9 3C9 6C9 9C9 CC9 FC9

0CC 3CC 6CC 9CC CCC FCC 0CF 3CF 6CF 9CF CCF FCF

*0F0* 3F0 *6F0* 9F0 CF0 *FF0* 0F3 *3F3* *6F3* 9F3 CF3 *FF3*

*0F6* *3F6* 6F6 9F6 *CF6* *FF6* 0F9 3F9 6F9 9F9 CF9 FF9

*0FC* *3FC* 6FC 9FC CFC FFC *0FF* *3FF* *6FF* 9FF CFF *FFF*


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CMY and CMYK model

The color printers use a model which is subtractive. i.e

a Cyan pigment will not reflect any Red light whenilluminated by white light.

B

G

R

Y

M

C

1

1

1

The printing devices internally do a RGB to CMY conversion .

The black obtained by mixing all the CMY components looks

muddy hence an additional black component is added tomake the CMYK model.


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HSI Color Map

The human color perception is closer to the HSI model.

We describe objects as light or dark and having a certaincolor.

RGB color model

black

blue red

cyan yellow

white

Intensity [gray scale] is along the line from blackto white saturation is perpendicular distance from

this intensity axis


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HSI Color Model

Usually Red is considered zero degrees


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Pseudocolor Image Processing

Pseudocolor Image Processing is used to assign colors to grey

scale images.

The reason is that an instant the human eye can discern

thousands of colors and intensities but only a few grey levels.

Intensity Slicing

The grey level images are

quantized into several levels

where each level is mappedto a particular color.


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Grey Level to Color Transformations

Red Transformation

Green Transformation

Blue Transformation

fr(x,y)

fg(xy)

fb(x,y)

Transformation T1

Transformation T2

Transformation T3

g1(x,y)

g2(xy)

gk(x,y)

f1(x,y)

f2(x,y)

fk(x,y)

AdditionalProcessing

hr(xy)

hb(xy)

hg(xy)


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Color Image Processing

Histograms [some may be only on the Icomponent of HSI]

Smoothing/Sharpening

Complements and Slicing

Segmentation

Compression


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Tone and Color Corrections

The different print media as well as monitors of different typesshould be able to correctly display color gamut.

A device independent color model is used.

The most common being CIELAB

The L* a* b* color components are given by

16116

wY

YhL

ww Y

Yh

X

Xha 500

ww Z

Zh

Y

Yhb 200

)(qh3 q

116/16787.7 q

008856.0q

008856.0q{


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Xw, Yw and Zw are the white tristimulus valueswhich match with the white of the CIEchromaticity diagram.

L* a* b* colorimetric, perceptually uniform anddevice independent.

It is not a directly displayable format.

Decouples intensity from color useful in imagemanipulation and compression.


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Saturation is corrected after correcting the tonalrange.

Tonal range is also called the images key type.Which could be high low or medium.

The transformations can be carried out

individually in any of the color planes.

The transformations are similar to the grey levelpiecewise linear and power law transformations


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Mid Terms next week

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Pencils eraser scale

Closed book exam

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