Lab 6/7 Exercise 1 Using pyMi to read certain image shapes and obtain the Fourier transformations Figure 1: circle image     Fourier Transformation of circle                                                                   Figure 2: rectangle image  Fourier transformation of rectangle                                                                Figure 3: square image     Fourier transformation of square                                                                   Figure 4: stripes          Fourier transformation of stripes                                                                   Variety of sine waves can be combined to form all kinds of shapes and images. Fourier transformation is instrumental in breaking down of the image into various sine waves that combines to form it. Moreover, it can plot frequencies which merge to make up that shape or image. For instance, when a circular image is cut into two similar halves and then flipped in order to appear like a square wave, several sine waves can then be utilized to reform it. In this case, majority of that image (square) can be demonstrated by use of a single low frequency sine wave. On the other hand, high frequency sine waves can be used to fill extra spaces. The figures below illustrate this: low freq high freq which can be plotted as From the results, it can be observed that there is high intensity of lower frequencies since the shapes were made from low frequency waves which are large. The small points observed shows extra frequencies (high frequencies) utilized to fill that square. This is clearly shown in the second graph above (2D graph), where large points represent large sine waves with lower frequencies. Moreover, the first graph above is in one dimension (x-axis). In case the image is cut in all planes, for instance x, y axis, at 45 0 , it would give numerous points, which are plotted in all the planes. This will happen irrespective of the point of cut since a circle is symmetrical. It gives a frequency graphs that seems to rotate about an axis. Therefore in case numerous points are cut (thousands), the resultant image would appear like rings as shown in the first figure (circle image-Fourier transformation). It can also be observed that a cut in x axis for a rectangular image produces higher frequency than that made on y axis of the same image. This is as illustrated below: This results in clustering of low frequencies towards the centre in y axis and dispersal of high frequencies on the x axis. It is also quite important to note that when this is done on a square image, it produces similar plots on both axes. Moreover, when stripes are used, edges that run parallel will not be detected. Instead, Fourier transformations only detect frequencies of edges that are perpendicular to the image. This is mainly because Fourier transformations give lines which run in opposite directions. In addition, majority of information is usually in low frequency. This is because it is at the centre. Exercise 2 Irregular images        The images are predominated by Low frequencies. In fact, transformation of a rectangular image is similar to that of a train image. Moreover, high frequency sine waves are found near the edges. This is mainly because the sine waves are usually utilized at the edges of the train to fill it along its sharp ends. The Fourier transformation that results from a rectangular image is similar to tha