Image%20Editing%20by%20Point%20Operatons

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Image Editing by Point Operatons

• Fall 2001
• Martin Jagersand

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3D reality -gt captured 2D image
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Pinhole cameras
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Examples of image sources

• Analog cameras
• Digital cameras
• Optic Scanners (linear image sensors)
• Laser scanners (2 and 3D images)
• Radar
• X-ray
• NMRI

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Image display

• VDU
• Raster
• Vector
• LCD
• Printer
• Photo process
• Plotter (x-y table type)

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THE ORGANIZATION OF A 2D IMAGE
Pixel Binary 1 bit Grey 1 byte Color 3 bytes
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Mathematical / Computationalimage models

• Continuous mathematical
• I f(x,y)
• Discrete (in computer) adressable 2D array
• I matrix(i,j)
• Discrete (in file) e.g. ascii or binary sequence
• 023 233 132 232
• 125 134 134 212

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Image representation for display

• True color, RGB, .

(R,G,B) (R,G,B) (R,G,B) (R,G,B)
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Image representation for display

• Indexed image

(I) (I) (I) (I)
(R,G,B) (R,G,B) (R,G,B)
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Point operations on images

• Point operations perform some operation on one
  pixel at a time (independent on the neighboring
  pixels)
• For each (x,y)
• I2(x,y) f(I(x,y))
• Contrast to image transforms (later in course)
  perform operations on the whole image

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Common point operations

• Brightness adjustment
• Contrast adjustment
• Dynamic range compression
• Gray level slicing
• Histogram equalization
• Image (sequence) averaging
• Background subtraction

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Linear brightness and contrast adjustment

• As seen on TV!
• Brightness
• For each (x,y)
• I2(x,y) I(x,y)const
• Contrast
• I2(x,y) constI(x,y)

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Contrast adjustment example
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Special purpose contrast adjustments

• Dynamic range limitation
• I2(x,y) sqrt(I(x,y))
• I2(x,y) log(I(x,y))
• Inverted image
• I2(x,y) 1-I(x,y)
• Gray level slicing

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Image histogram

• For a discrete image quantized e.g. on 0..255
• Let n total number of pixels
• Let nk number of pixels with value k
• Histogram pk nk / n
• Analogy Consider the image a sample of a random
  variable. Then pk is probability of a pixel
  having value k

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Histogram examples

• Dark image Light image

narrow contrast Wide contrast
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Histogram equalization

• Let p(k) image histogram on k 0..1
• Goal find a contrast stretching transform T(k)
  so that I2 T(I) and p2 1(uniform)

p2
p(k)
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Histogram eq.

• Consider
• Then

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Discrete histogram equalization

• Compute discrete histogram summing bins
• Compute cumulative sum
• Map image intensities through cumulative
  histogram
• Question is discrete histogram uniform?

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Background subtraction

• Subtract out static background to capture changes

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What process actually happened?
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Image averaging

• Average several images of the same scene
• Is(x,y) sum(I(x,y))/n
• Can remove noise