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Image Editing by Point Operatons

Image Editing by Point Operatons. Fall 2001 Martin Jagersand. 3D reality -> captured 2D image. x. z. y. y. x. z. y. x. Pinhole cameras. Examples of image sources:. Analog cameras Digital cameras Optic Scanners (linear image sensors) Laser scanners (2 and 3D images) Radar X-ray

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Image Editing by Point Operatons

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  1. Image Editing by Point Operatons Fall 2001 Martin Jagersand

  2. 3D reality -> captured 2D image x z y y x z y x

  3. Pinhole cameras

  4. Examples of image sources: • Analog cameras • Digital cameras • Optic Scanners (linear image sensors) • Laser scanners (2 and 3D images) • Radar • X-ray • NMRI

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

  6. THE ORGANIZATION OF A 2D IMAGE Pixel Binary 1 bit Grey 1 byte Color 3 bytes

  7. 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

  8. Image representation for display • True color, RGB, …. (R,G,B)(R,G,B) … (R,G,B) : (R,G,B)

  9. Image representation for display • Indexed image (I)(I) … (I) : (I) (R,G,B) (R,G,B) : (R,G,B)

  10. 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

  11. Common point operations • Brightness adjustment • Contrast adjustment • Dynamic range compression • Gray level slicing • Histogram equalization • Image (sequence) averaging • Background subtraction

  12. 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) = const*I(x,y)

  13. Contrast adjustment example

  14. 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

  15. 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

  16. Histogram examples Dark image Light image narrow contrast Wide contrast

  17. 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)

  18. Histogram eq. • Consider: • Then:

  19. Discrete histogram equalization • Compute discrete histogram summing bins • Compute cumulative sum • Map image intensities through cumulative histogram • Question: is discrete histogram uniform?

  20. Background subtraction • Subtract out static background to capture changes - = What process actually happened?

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

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