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,
Digital Image Processing
Gonzales and Woods
value f(x,y) at each x, y is called intensity level or gray level
f(x,y) – input image,
g(x,y) – output image
T is an operator on f defined over a neighborhood of point (x,y)
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.
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.
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