Intensity of image processing PowerPoint Presentation

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1 Digital Image Processing Chapter # 3 Image Transformations and Spatial Filtering PART B

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2 Histogram of a Grayscale Image Let I be a 1-band (grayscale) image. I(r,c) is an 8-bit integer between 0 and 255. Histogram, hI, of I: a 256-element array, hI hI (g) = number of pixels in I that have value g. for g = 0,1, 2, 3, …, 255

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3 Histogram of a Grayscale Image Histogram of a digital image with gray levels in the range [0,L-1] is a discrete function Where rk = kth gray level nk = number of pixels in the image having gray level rk h(rk) = histogram of an image having rk gray levels

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4 Normalized Histogram Dividing each of histogram at gray level rk by the total number of pixels in the image, n p(rk) gives an estimate of the probability of occurrence of gray level rk The sum of all components of a normalized histogram is equal to 1

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5 Histogram of a Grayscale Image 16-level (4-bit) image black marks pixels with intensity g lower RHC: number of pixels with intensity g

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6 Histogram of a Grayscale Image Plot of histogram: number of pixels with intensity g Black marks pixels with intensity g

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7 Histogram of a Grayscale Image Plot of histogram: number of pixels with intensity g Black marks pixels with intensity g

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8 Histogram of a Grayscale Image

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9 Histogram of a Color Image If I is a 3-band image then I(r,c,b) is an integer between 0 and 255. I has 3 histograms: hR(g) = # of pixels in I(:,:,1) with intensity value g hG(g) = # of pixels in I(:,:,2) with intensity value g hB(g) = # of pixels in I(:,:,3) with intensity value g

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10 Histogram of a Color Image There is one histo-gram per color band R, G, & B. Luminosity histogram is from 1 band = (R+G+B)/3

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11 Histogram of a Color Image

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12 Histogram of a Color Image

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13 Histogram: Example How would the histograms of these images look like? Dark Image Bright Image

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14 Histogram: Example Dark image Components of histogram are concentrated on the low side of the gray scale Bright image Components of histogram are concentrated on the high side of the gray scale

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15 Histogram: Example How would the histograms of these images look like? Low Contrast Image High Contrast Image

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16 Histogram: Example Low contrast image Histogram is narrow and centered toward the middle of the gray scale High contrast image Histogram covers broad range of the gray scale and the distribution of pixels is not too far from uniform with very few vertical lines being much higher than the others

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17 Contrast Stretching Improve the contrast in an image by `stretching' the range of intensity values it contains to span a desired range of values, e.g. the the full range of pixel values

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18 Contrast Stretching If rmax and rmin are the maximum and minimum gray level of the input image and L is the total gray levels of output image, the transformation function for contrast stretch will be rmin L rmax

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19 Contrast Stretching

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20 Histogram Equalization Histogram equalization re-assigns the intensity values of pixels in the input image such that the output image contains a uniform distribution of intensities

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21 The Probability Distribution Function of an Image This is the probability that an arbitrary pixel from I has value g.

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22 The Probability Distribution Function of an Image p(g) is the fraction of pixels in an image that have intensity value g. p(g) is the probability that a pixel randomly selected from the given image has intensity value g. Whereas the sum of the histogram h(g) over all g from 0 to 255 is equal to the number of pixels in the image, the sum of p(g) over all g is 1. p is the normalized histogram of the image

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23 The Cumulative Distribution Function of an Image This is the probability that any given pixel from I has value less than or equal to g. Let q = I(r,c) be the value of a randomly selected pixel from I. Let g be a specific gray level. The probability that q ≤ g is given by where hI(γ ) is the histogram of image I.

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24 The Cumulative Distribution Function of an Image This is the probability that any given pixel from I has value less than or equal to g. Let q = I(r,c) be the value of a randomly selected pixel from I. Let g be a specific gray level. The probability that q ≤ g is given by where hI(γ ) is the histogram of image I. Also called CDF for “Cumulative Distribution Function”.

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25 The Cumulative Distribution Function of an Image P(g) is the fraction of pixels in an image that have intensity values less than or equal to g. P(g) is the probability that a pixel randomly selected from the given band has an intensity value less than or equal to g. P(g) is the cumulative (or running) sum of p(g) from 0 through g inclusive. P(0) = p(0) and P(255) = 1;

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26 Histogram Equalization The CDF itself is used as the LUT. be the cumulative (probability) distribution function of I. Task: remap image I so that its histogram is as close to constant as possible

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27 Histogram Equalization pdf The CDF (cumulative distribution) is the LUT for remapping. CDF

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28 Histogram Equalization pdf The CDF (cumulative distribution) is the LUT for remapping. LUT

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29 Histogram Equalization pdf The CDF (cumulative distribution) is the LUT for remapping. LUT

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30 Histogram Equalization

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31 Histogram Equalization after before Luminosity

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32 Histogram Equalization: Example An 8x8 image

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33 Histogram Equalization: Example Image Histogram (Non-zero values) Fill in the following table/histogram

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34 Histogram Equalization: Example Image Histogram (Non-zero values shown)

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35 Histogram Equalization: Example

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36 Histogram Equalization: Example Cumulative Distribution Function (cdf) Image Histogram/Prob Mass Function

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37 Histogram Equalization: Example Cumulative Distribution Function (cdf)

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38 Histogram Equalization: Example Cumulative Distribution Function (cdf)

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39 Histogram Equalization: Example Normalized Cumulative Distribution Function (cdf) Divide each value by total number of pixels (64) to get the normalized cdf

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40 Histogram Equalization: Example Original Image If cdf is normalized If cdf is NOT normalized

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41 Histogram Equalization: Example

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42 Histogram Equalization: Example Original Image Corresponding histogram (red) and cumulative histogram (black) Image after histogram equalization Corresponding histogram (red) and cumulative histogram (black)

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43 Histogram Equalization: Example Dark image Bright image Equalized Histogram Equalized Histogram

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44 Histogram Equalization: Example Low contrast High Contrast Equalized Histogram Equalized Histogram

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Histogram Equalization vs. Contrast Stretching Histogram equalization is sophisticated version of contrast stretching Contrast Stretching – Enhancement is less harsh

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Original Image Contrast Stretching Histogram Equalization Dramatic Enhancement - Artificial look Histogram Equalization vs. Contrast Stretching

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Original Image Contrast Stretching Histogram Equalization Histogram Equalization vs. Contrast Stretching

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48 Acknowledgements Digital Image Processing”, Rafael C. Gonzalez & Richard E. Woods, Addison-Wesley, 2002 Peters, Richard Alan, II, Lectures on Image Processing, Vanderbilt University, Nashville, TN, April 2008 Brian Mac Namee, Digitial Image Processing, School of Computing, Dublin Institute of Technology Computer Vision for Computer Graphics, Mark Borg Material in these slides has been taken from, the following resources