Activity 4 – Enhancement by Histogram Manipulation

This activity involves the manipulation of image histograms to enhance the quality of low contrast images. The histogram of an image is equivalent to the Probability Distribution Function taking into account that the whole image is normalized with the total number of pixels. Taking the cumulative sum of this PDF, a CDF or Cumulative Distribution function can be obtained. Using this CDF, one can backproject the gray values of a poor-contrast image to this CDF and in turn enhancing the image.

Presented in this activity are the different types of CDF to enhance poor-contrast images. Below are the plots of these desired CDFs.

The blue plot represents the CDF of an original image, yellow corresponds to a linear CDF, green is from a non-linear CDF specifically an arctan function and red plot, also a non-linear CDF is a parabolic CDF.

Displayed below are the corresponding images of the CDFs above. The first image is the original image, 2nd is the enhanced image via backprojection of a linear CDF, 3rd is by using the arctan function and the last set of images are for the parabolic CDF.

It can be observed that there is a significant visual difference among the set of processed images. There is a good visual contrast enhancement for both the linear and arctan CDF application. It is observed that compared from the original image, there is good shading and is pleasing to the eye the reconstructions using these CDFs. However for the parabolic CDF, it seems that the image was saturated because this CDF increases the value of each pixel being backprojected as observed.

Shown above are the histograms of sample- set of images. From the orginal histogram, there is a concentration of low value pixels whereas when compared with the linear and arctan - enhanced images, there is a good distribution of pixel values both in the high and low pixel values. For the parabolic CDF, there is a lump of pixel value at the high value pixel range making the image look saturated.

When the CDF of histograms of these images are obtained, the result is the applied CDF in to the image.

Non-linear CDFs mimic that non-linear human eye response. The results are shown above where there are good enhancements using the arctan and linear CDFs rather than the parabolic CDF.

I give myself 9 points for finishing and understanding the activity but posted late.

References:
images are taken from

http://z.about.com/d/geology/1/0/u/E/1/sutbutaerialorig.jpg
http://static.photo.net/attachments/bboard/00F/00FzkU-29347284.jpg
http://myweb.lsbu.ac.uk/dirt/museum/margaret/08--452-1000120.jpg
http://www.dphclub.com/learn-photoshop/images/war-time-1.jpg