Lecture 2 - Image Histograms

7/28/2019 Lecture 2 - Image Histograms

1/17

Image histograms

Week 2


2/17

Histogram

A histogram is simply a graph that samples a population and

shows a count of each characteristic of interest.

In an image processing context, this histogram is a graphshowing the number of pixels in an image at each differentintensity value found in that image.

For an 8-bit grayscale image there are 256 different possibleintensities.

Color histograms are three separate histograms, one each forthe Red, Green and Blue channels.


3/17

HISTOGRAMS: Thresholding

Histograms information can be used to decide what value of

threshold to use when converting a grayscale image to a

binary one by thresholding.

If the image is suitable for thresholding then the histogram

will be bi-modal--- i.e. the pixel intensities will be clustered

around two well-separated values.

A suitable threshold for separating these two groups will be

found somewhere in between the two peaks in the histogram.

If the distribution is not like this then it is unlikely that a goodsegmentation can be produced by thresholding.


4/17

Intensity histogram for the input image

One peak represents the object pixels, one

represents the background.


5/17

Thresholding

It is clear that a threshold value of around 120

should segment the picture nicely,


6/17

Thresholding (Continue)

using thresholds of 80 using thresholds of 120


7/17

Contrast stretching Vs Histogram equalization

The histogram is used and altered by many imageenhancement operators.

Two operators which are closely connected to the

histogram are contrast stretching and histogramequalization. They are based on the assumptionthat an image has to use the full intensity rangeto display the maximum contrast.

Contrast stretching takes an image in which theintensity values don't span the full intensity rangeand stretches its values linearly.


8/17

Contrast stretching

Contrast stretching (often called normalization) is a simpleimage enhancement technique that attempts to 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 that the image type concerned

allows.

For 8-bit gray level images the lower and upper limits might be 0 and 255.

Call the lower and the upper limits a and b respectively.

The simplest sort of normalization then scans the image to find the lowest and

highest pixel values currently present in the image. Call these cand d.

Then each pixel P is scaled using the following function:


9/17

Contrast stretching

each pixel P is scaled using the following function:

Scaling_factor : 255 / (High Low)

Image(i, j) = [ image(i, j) Low ] x Scaling_factor

Low and High are the lowest and highest intensity in the image.


10/17

Contrast stretching

the intensity histogram forms a tight, narrow cluster between the gray level intensity

values of 79 - 136, as shown in

After contrast stretching, using a simple linear interpolation between

c = 79 and d = 136, we obtain


11/17

Contrast stretching

most of the pixels have rather high intensity values Contrast stretching, clearly improved contrast


12/17

Contrast stretching

clc

clear all

a =imread('sample.bmp');

a=rgb2gray(a);

figure(1);

imshow(a);

[m n]=size(a);

r2=max(max(a)) %this function is used for finding the max value of a pixel in an image

r1=min(min(a)) %this function is used for finding the min value of a pixel in an image

s1=0; % this is the min and max of an image i.e. 0-255 gray levels

s2=255;

for i=1:m %here we use 2 for loops for traversing the image in x & y coordinate

for j=1:n

s(i,j) = (a(i,j)-r1)* (255/(r2 - r1));

end end

figure(2);

imshow(s);


13/17

Histogram equalization The idea of histogram equalization is that the pixels should be

distributed evenly over the whole intensity range, i.e. the aim isto transform the image so that the output image has aflat

histogram.


14/17

Histogram equalization

The 8-bit greyscale image shown has the following values:

Pixel values that have a zero count are excluded for the sake of brevity.


15/17


the minimum value in the subimage is 52 and the maximum value is 154. The cdf of

64 for value 154 coincides with the number of pixels in the image. The cdf must benormalized to [0, 255] . The general histogram equalization formula is:

Where cdfmin is the minimum value of the cumulative distribution function (in this case 1),M N gives the image's number of pixels (for the example above 64, where M is width and

N the height) and L is the number of grey levels used (in most cases, like this one, 256).

The equalization formula for this particular example is:

For example, the cdf of 78 is 46. (The value of 78 is used in the bottom row of the 7th column.)

The normalized value becomes


16/17


Notice that the minimum value (52) is now 0 and the maximum value (154) is now 255


17/17


Documents

Lecture 2 - Image Histograms