Question 2
1.4
Question 3
(b) (15 marks)
Determine the discrete-time Fourier transform of the Laplacian filter L(u,v). x and u are horizontal position and frequency, respectively, whereas y and v are vertical position and frequency, respectively. Plot the magnitude of the 1D profiles L(u,0) and L(0,v). Is L(u,v) a highpass or a lowpass filter? Explain your answer
(c)
Question 4
(a) (b)
The original image shown in Fig. 4(a) was filtered by a Gaussian lowpass filter, resulting in the output image shown in Fig. 4(b).
Explain why there is a black streak on the top edge and a white streak at the bottom edge of Fig. 4(b). Also explain why the streak only appears on the top and bottom edges but not the left and right edges.
Question 5
The histograms of two example images are shown in fig. 5(a) and (b). Sketch the point operations required to flatten the histogram. Provide qualitative explanations of your plots. Note that a full mathematical derivation is not required as the purpose of this question is to assess your intuitive understanding of histogram equalization.
(a) (b)
Question 6
Image A is an 8-bit image shown in Fig. 5a and has a histogram denoted by . Image B shown in Fig. 5b is formed by swapping the top and the bottom halves of Image A and has a histogram denoted by . What is the mathematical relationship between and ? Justify your answer.
Fig. 5a Fig. 5b
Fig. 5 Histograms of two example images.