ImageProcessing

CosimoDistante

Lecture6:MonochromeandColorprocessing

Pointwise operator: algorithms that execute simple operation on the single pixel without involving neighboring pixels

I0(i,j)=Opointwise[II(i,j)]

If II(i,j) > 150 then IO(i,j)=1 else IO(i,j)=0

Local Operator: algorithms that define the new value of a pixel based on the intensity values of the neighboring pixels II input image, F(i,j) a window defined over the analysing pixel I0 output image

I0(i,j)=Olocale{II(ik,jl); (ik,jl)∈F(i,j)}

Median filter with window size 3×3

Global Operator: algorithms that extract global information from the image They use all pixels of the image

R=Oglobal[II(i,j)]

Histogram H(x) is the frequency of intensity value x The histogram HI(x) can be seen as the results of the global operatorfor the input image I With the histogram we loose spacial information

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Original Dark Light

Contrast manipulation Given: x gray level of input image II(i,j), y gray level of output image I0(i,j), T(x) the gray level transform (manipulation)

y=T(x)

Linear

y=β(x-xa)

with xa≤x≤xb and the stretching coefficient obtained by the ratio of the output gray level range and input gray level range Δx=xb-xa.

β =Δ

Δ

yx

Example: the interval of the most frequent levels in the image is [50..100] Then Δx=50 different levels That can be stretched to 256 levels (Δy) to have a better quality

Linear

stretching

Linear with multiple paths

α =yxa

a ab

ab

xxyy

−

−=β

)()(

max

max

b

b

xxLyyL

−

−=δ

ya and yb are constants used to increase or decrease the global illumination

Linear with multiple paths – special case

If α=0 and δ=0 Then stretching is related to interval (xa,xb) While are excluded (clipping) gray levels less than xa and greater than xb

This is useful when we know the object is in (xa,xb) in order to segment it. IF xa=xb≡xT, the output image is named Binary Image.

background object

Quadratic transformation:

y=x2 Expand high gray level and compress lower gray level Square root transf. Opposite behavior as previous transf. Log transform Applied when the range of gray levels in input image is much wider than the wanted range in output image (in Fourier representation)

Non Linear

xy =

yxx

e

e

=+

+

log ( )log [ max( )]

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Negative

Complementing with respect to the maximum gray level of the input image Inverse Useful to visualize very dark details of an image

y = 1x

with x > 0

xLy −= max

Imm. Original Negative Inverse

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HistogramEqualizaGon•  ThehistogramequalizaGontransformaGongenerates

animagewithequallylikelyintensityvalues•  Theintensityvaluesintheoutputimagecoverthefull

range,[01]•  TheresulGngimagehashigherdynamicrange•  Recallthevaluesinthenormalizedhistogramare

approximatelytheprobabilityofoccurrenceofthosevalues

•  ThehistogramequalizaGontransformisthecumulaGvedistribuGonfuncGon(CDF)

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Histogram CDF

CUMULATIVEDISTRIBUTIONFUNCTION

Histogram equalization

Histogram equalization

Histogram equalization Algorithm

GivenNxMthaimagesizeandLmaxthemaximumgraylevelsFirststepistocreatethehistogramoftheimageHI

ThenbuildthecumulaGvehistogramHc

ThencomputethemappingfuncGon

andremapeverypixel

Hc(x)

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InputImage OutputImage

HistogramEqualizaGon

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HistogramEqualizaGonExample

•  g=histeq(f,nlev)wherefistheoriginalimageandnlevnumberofintensitylevelsinoutputimage

Adaptive Histogram Equalization (AHE)

SinceoureyesadapttolocalregionsinsteadofenGreimage,itisusefultoopGmizeimageenhancementlocallyTheimageisdividedinagridofnon-overlappingregions

histogramequalizaGonappliedineachregion

Contrast Limited Adaptive Histogram Equalization (CLAHE)

OperateaclipontheequalizedhistogramComputethecumulaGvehistogram

ßisthecliplimitandαclipfactor

smaxmaximumallowedslopeForX-rayimagessmax=4PerformhistogramequalizaGonlocallyandoperateaclippingredistribuGngthepixels

Nota%onchangeNisthenumberofgraylevelsMthetotalnumberofpixelsinImage

Contrast Limited Adaptive Histogram Equalization (CLAHE)

h(n)

n

β h(n)-β Nota%onchangeNisthenumberofgraylevelsMthetotalnumberofpixelsinImage

Contrast Limited Adaptive Histogram Equalization (CLAHE)

Original Image

CLAHE

Histogram Equalization