Kristine Faith Roque's AP 186

In this activity, we did image enhancements in the frequency domain. In particular, we tried to eliminate repetitive patterns in an image by filtering out the frequencies associated with them via masking techniques in the frequency domain. A. Convolution To begin, we first did some exercises in Fourier transformations. Using Scilab, we generated several patterns and took their Fourier transforms (FT). These patterns include: 1. Two dots along the x-axis symmetric about the center 2.  Two circles along the x-axis symmetric about the center 3.  Two squares along the x-axis symmetric about the center 4.  Two Gaussian functions along the x-axis symmetric about the center There are several ways to produce these pattern. One is by finding the corresponding positions on the image that you want to assign a value of zero or one (depending on whether you want a white shape in a black background or vice-versa.) Another way is by convolving the shape with Dirac delta functions

IN this activity, we will try to enhance an image by manipulating its histogram. By enhance, I mean the improvement of a dark image such that features disguised by the dark areas may be revealed. The histogram of a graylevel image, when normalized to the number of pixels, gives us the probability distribution function (PDF).  For example, if we have the following color image: Figure 1a. Dark color image which will be enhanced  (taken from  http://twoleggedtripod.net/index.php?postid=3   )    Then, convert it to a graylevel image using Scilab:  Figure 1b. Grayscaled version of the image in Figure 1a We get its PDF by dividing each pixel by the total number of pixels. Figure 1c. Code for obtaining PDF of image Figure 1d. PDF of the graylevel image From the PDF, we see that the distribution is biased towards the low values. If the image has graylevels, r , with a PDF of p1(r) and a cumulative distribution function (CDF) given by, then we can map it to a new