9th August 1999

Due Monday, 23rd August 1999

* READ CHAPTER 3

in Digital Image Processing by Gonzalez and Woods

* Solve the following problems:

  1. Let f[x,y], for x=0,1,2,....,M-1 and y=0,1,2,....,N-1 be a discrete sequence and F[m,n] for m=0,1,2,....,M-1 and n=0,1,2,....,N-1, be its two-dimensional Fourier transform. Write a program for computing the two-dimensional discrete Fourier transform of a possibly complex sequence f[x,y] using the row-column method. Assume that M and N are powers of two, which are <=256.

    For the images square.pgm, line.pgm which I have sent you by email do the following:

    a) Compute the Fourier spectrum of the images. The Fourier spectrum should be shifted to the centre of the frequency square (see page 95 of the text). Appropriately scale the intensity values in the spectrum (see page 92 of the text) to obtain a good display on the computer screen.

    b) Blur the spacial domain images by averaging over a 7x7 window and then compute its Fourier spectrum image. View as suggested above.

    c) Rotate the spatial domain images by 45 degrees and then compute its Fourier spectrum image. View as above.

  2. Write a description of any relations between the image forms and Fourier Transforms that you observe.

  3. Problem 3.23 in the text.

    For this assignment submit your results as follows:

    + email me the final versions of your programs (computing the DFT, blurring, rotating and scaling the intensity values to obtain a good display)

    + Can you get printouts without hassles? In that case submit the resulting images with your descriptions in Problem 3. Otherwise email me any one Fourier spectrum image of your choice. For the rest explain by roughly drawing what you see on the screen.


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