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# Intensity Transformations - PowerPoint PPT Presentation

Intensity Transformations. Sections 3.1-3.3 Digital Image Processing Gonzales and Woods Irina Rabaev. Representing digital image. value f(x,y) at each x, y is called intensity level or gray level. Intensity Transformations and Filters. g(x,y)=T[f(x,y)] f(x,y) – input image,

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### Intensity Transformations

Sections 3.1-3.3

Digital Image Processing

Gonzales and Woods

Irina Rabaev

value f(x,y) at each x, y is called intensity level or gray level

g(x,y)=T[f(x,y)]

f(x,y) – input image,

g(x,y) – output image

T is an operator on f defined over a neighborhood of point (x,y)

• 1 x 1 is the smallest possible neighborhood.

• In this case g depends only on value of f at a single point (x,y) and we call T an intensity (gray-level mapping) transformation and write

s = T(r)

where r and s denotes respectively the intensity of g and f at any point (x, y).

Denote [0, L-1] intensity levels of the image.

Image negative is obtained by s= L-1-r

s = clog(1+r), c – const, r ≥ 0

Maps a narrow range of low intensity values in the input into a wider range of

output levels. The opposite is true for higher values of input levels.

s = crγ, c,γ –positive constants

curve the grayscale components either to brighten the intensity (when γ < 1)

or darken the intensity (when γ > 1).

Contrast stretching is a process that expands the range of intensity levels in a image

so that it spans the full intensity range of the recording medium or display device.

Contrast-stretching transformations increase the contrast between the darks and the lights

Highlighting a specific range of gray levels in an image

The histogram of a digital image with

gray levels in the range [0, L-1] is a discrete

function h(rk)=nk, where rk is the kth gray

level and nk is the number of pixels in the

image having gray level rk.

It is common practice to normalize a

histogram by dividing each of its values by

the total number of pixels in the image,

denoted by the product MN.

Thus, a normalized histogram is given by h(rk)=nk/MN

The sum of all components of a

normalized histogram is equal to 1.

• Histogram equalization can be used to improve the visual appearance of an image.

• Histogram equalization automatically determines a transformation function that produce and output image that has a near uniform histogram

• Let rk, k[0..L-1] be intensity levels and let p(rk) be its normalized histogram function.

• The intensity transformation function for histogram equalization is

• Let f be an image with size 64x64 pixels and L=8 and let f has the intensity distribution as shown in the table

round the values to the nearest integer

Define a neighborhood and move its center from pixel to pixel. At each location, the histogram of the points in the neighborhood is computed and histogram equalization transformation is obtained.

Denote:

ri – intencity value in the range [0, L-1],

p(i) - histogram component corresponding to value ri .

The intensity variance:

Let (x, y) be the coordinates of a pixel in an image, and let Sxydenote a

neighborhood (subimage) of specified size, centered at (x, y).

The mean value of the pixels in this neighborhood is given by

where is the histogram of the pixels in region Sxy.

The variance of the pixels in the neighborhood is given by

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