Manipulating contrast/point operations. Examples of point operations: Threshold (demo) Threshold...

Manipulating Manipulating contrast/point contrast/point

operationsoperations

Examples of point operations:Examples of point operations:

Threshold (demo)Threshold (demo) Invert (demo)Invert (demo)

Out[x,y] = max – In[x,y]Out[x,y] = max – In[x,y]RGB RGB gray conversion gray conversionGamma correctionGamma correctionOther methodsOther methods

histogram equalizationhistogram equalizationcolor to graycolor to grayscalingscaling

Gray to binaryGray to binary

ThresholdingThresholding G G B B

const int t=200;const int t=200;

if (G[r][c]>t)if (G[r][c]>t) B[r][c]=1;B[r][c]=1;

elseelse B[r][c]=0;B[r][c]=0;

How do we choose t?How do we choose t?1.1. InteractivelyInteractively

2.2. AutomaticallyAutomatically

Gamma correctionGamma correction

HISTOGRAM HISTOGRAM EQUALIZATIONEQUALIZATION

Histogram equalizationHistogram equalization

For many images we observe that it For many images we observe that it only uses a few different gray only uses a few different gray values.values.

Often these gray values are close Often these gray values are close together.together.


Histogram equalization goals:Histogram equalization goals:1.1. Output image should use all gray Output image should use all gray

values.values.

2.2. Output image has same number of Output image has same number of pixels of each gray value.pixels of each gray value.

Which distribution is then preferred? Which distribution is then preferred? (normal or uniform)(normal or uniform)

3.3. (While maintaining the relationship (While maintaining the relationship (order) among gray values. - George’s (order) among gray values. - George’s rule.)rule.)


from from http://en.wikipedia.org/wiki/Histogram_equalizationhttp://en.wikipedia.org/wiki/Histogram_equalization

Histo eq exampleHisto eq example(from (from

http://www.cs.utah.edu/~jfishbau/improc/project2/images/crowd_hist_compare.png)http://www.cs.utah.edu/~jfishbau/improc/project2/images/crowd_hist_compare.png)


Histogram equalization attempts to Histogram equalization attempts to remap the input gray values to remap the input gray values to output gray values s.t. the histogram output gray values s.t. the histogram of the output achieves goals 1 and 2 of the output achieves goals 1 and 2 (and 3) as best as possible.(and 3) as best as possible.

Histo eq exampleHisto eq example(from http://web2.clarkson.edu/class/image_process/qa1/Histogram%20Equalization(from http://web2.clarkson.edu/class/image_process/qa1/Histogram%20Equalization

%20Example_files/img92.gif)%20Example_files/img92.gif)

HistogramHistogram

Step 1: Estimate probability of a given Step 1: Estimate probability of a given gray value in an image.gray value in an image.

h(g) = count of pixels w/ gray value h(g) = count of pixels w/ gray value equal to g.equal to g.histogramhistogram

p(g) = h(g) / (w*h)p(g) = h(g) / (w*h)w*h = # of pixels in entire imagew*h = # of pixels in entire image

Demo histogram.Demo histogram.

1..0 :Note gp


Step 2: Estimate c.d.f. (cumulative Step 2: Estimate c.d.f. (cumulative distribution function).distribution function).

g

i

gpgcdf0

1..0 :Note gcdf


Step 3: Use c.d.f. to map an input gray Step 3: Use c.d.f. to map an input gray value g to “equalized” gray value, g’.value g to “equalized” gray value, g’.

Note: Since cdf(g) is in [0..1], we need to Note: Since cdf(g) is in [0..1], we need to multiply by the max gray value so the result multiply by the max gray value so the result is in [0..max].is in [0..max].

Note: Calculate above only once for each Note: Calculate above only once for each gray value, save in a (lookup) table, and gray value, save in a (lookup) table, and then let g’=lut[g].then let g’=lut[g].

max*' gcdfg


Only gray eq discussed so far.Only gray eq discussed so far.What about color?What about color?

1.1. Create 3 separate histograms for R, G, Create 3 separate histograms for R, G, and B, and then equalize each and B, and then equalize each individually (same as gray).individually (same as gray).

2.2. Better way is to convert RGB to color Better way is to convert RGB to color space with luminance (e.g., CIE Xspace with luminance (e.g., CIE XYYZ, Z, YYIQ, YUV, HSIQ, YUV, HSLL, or HS, or HSVV), equalize ), equalize luminance (same as gray), then convert luminance (same as gray), then convert back to RGB.back to RGB.

Histogram equalization Histogram equalization algorithmalgorithm

Do Exercise 5.2 for homework.Do Exercise 5.2 for homework.

SCALING A RANGE OF SCALING A RANGE OF GRAY VALUESGRAY VALUES

What about gray data that is What about gray data that is less than 8 bits? less than 8 bits?

Linearly map input [0,K] to [0,255].Linearly map input [0,K] to [0,255].

in

inout

out

out

in

in

max

255gg

max

g

max

g

What about gray data that is What about gray data that is less than 8 bits? less than 8 bits?

What if our minimum input value is What if our minimum input value is something other than 0?something other than 0?

inin

ininout

out

out

inin

inin

minmax

ming255g

max

g

minmax

ming

What about gray data that is What about gray data that is more than 8 bits? more than 8 bits?

Linearly map input min to 0 and Linearly map input min to 0 and input max to 255.input max to 255.But we then compress (lose) our But we then compress (lose) our

dynamic range, i.e., lose details.dynamic range, i.e., lose details.

Map subranges of gray data to Map subranges of gray data to [0..255].[0..255].A.K.A. window width and level.A.K.A. window width and level.

from http://www.netterimages.com/images/vpv/000/000/061/61653-from http://www.netterimages.com/images/vpv/000/000/061/61653-0550x0475.jpg0550x0475.jpg

Window width and levelWindow width and level


useruser

userinout

out

out

useruser

userin

minmax

ming255g

max

g

minmax

ming

Window width and levelWindow width and level


255g 255g

0g 0g

minmax

ming255g

outout

outout

useruser

userinout

if

if

from from https://www.imt.liu.se/people/dafor/visualization_files/image001.pnghttps://www.imt.liu.se/people/dafor/visualization_files/image001.png

COLOR TO GRAY COLOR TO GRAY CONVERSIONCONVERSION

Standard conversion from rStandard conversion from rggb to b to ggrayray

NTSC luminanceNTSC luminance

int luminance = (int)(0.30*r + 0.59*g + 0.11*b + int luminance = (int)(0.30*r + 0.59*g + 0.11*b + 0.5);0.5);

if (luminance<0)if (luminance<0) luminance = 0;luminance = 0;if (luminance>255)if (luminance>255) luminance = 255;luminance = 255;

http://www.tektronix.com/Measurement/cgi-http://www.tektronix.com/Measurement/cgi-bin/framed.pl?Document=/Measurement/bin/framed.pl?Document=/Measurement/App_Notes/NTSC_Video_Msmt/App_Notes/NTSC_Video_Msmt/colorbars.html&FrameSet=televisioncolorbars.html&FrameSet=television

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