EXAMINATION QUESTION PAPER

Transcription

1 Faculty of Science and Technology EXAMINATION QUESTION PAPER Exam in: FYS-2010 Digital Image Processing Date: Monday 26 September 2016 Time: Place: Approved aids: Administrasjonsbygget, Aud.Max. One sheet of paper (that is, two written A4 pages) with notes, printed or hand-written, and calculator with empty memory card Type of sheets (sqares/lines): Number of pages incl. cover page: Contact person during the exam: Squares 5 Stian Normann Anfinsen ( ) / Michael Kampffmeyer ( ) Phone: NB! It is not allowed to submit rough paper along with the answer sheets PO Box 6050 Langnes, NO-9037 Tromsø / / postmottak@uit.no / uit.no

2 General Remark In problems requiring Matlab (or equivalent) code, you may use built-in commands if you wish. You should strive to comment any code and make the code understandable by explanations, also with respect to the underlying theory, for the generally knowledgeable digital image processing person. All answers must be argued for and explained. All subproblems are equally important when grading the exams. Problem 1 Fig. 1. Intensity transformation (a) Given the image I and the intensity transformation T (I) shown in Figure 1, indicate: 2

3 (i) which among the images in the middle row of the figure is T(I), and (ii) which among the histograms in the bottom row corresponds to I. (b) Describe the motivation for use of thresholding based segmentation techniques and give a brief overview of the approaches belonging to this field. Include a discussion of the role of noise in this context and possible actions to reduce its impact. (c) Describe the fundamental concepts behind and the applications of histogram based intensity transformations. (d) An image array f(m, n) of size M N is to be convolved with a filter array h(m, n) of size P Q to produce a new image array g(m, n). Write a pseudocode program which computes g(m, n) by use of the Fourier transforms. The result should be the same size as would be achieved with direct convolution. (e) Modify the algorithm so that it computes the correlation between functions f and h instead of the convolution. Problem 2 We will in this problem study image restoration and reconstruction. (a) Two degraded images are shown in Figure 2(a) and 2(b), whereas Figure 2(c) displays the Fourier spectrum of the image in 2(b). Name and describe two filters (one for each image) that can be used to remove the noise. Explain for both cases why your chosen filter is appropriate. (b) Give the equations that describe the degradation/restoration process in the spatial and frequency domain for both images. (c) The adaptive, local noise reduction filter is given by ˆf(x, y) = g(x, y) σ2 η [g(x, y) m σl 2 L ]. Define the terms in the equation and explain how this filter, given an image which is degraded by additive noise, will allow noise removal also in areas with edges. 3

4 (a) (b) (c) Fig. 2. Degraded images (d) Explain why the ideal lowpass filter (ILPF) and the ideal highpass filter (IHPF) are commonly not used for image processing tasks. Problem 3 We start this exercise by looking at the three image masks with size 3x3, named W a, W b and W c, given as W a = , W b = 2 0 2, W c = (a) Characterize the three masks by looking at their coefficients. Also describe what the individual masks will do to an image f and the applications they normally have. (b) We will use the mask W a further as part of a highboost filter to create an image g which appears sharper than f. Give a graphical illustration of the individual steps in a highboost filter when it is applied to the intensity profile shown in Figure 3. (c) Show that the entire highboost filter based on W a can be represented by 4

5 the mask where k is a highboost constant. Fig. 3. Intensity profile W hb = 1 0 k 0 6 k 6 + 4k k. 0 k 0 (d) Show that the respective discrete Fourier transforms F and G of images f and g can be related as for a general highboost filter. G(u, v) = [1 + kh hp (u, v)]f (u, v) (1) (e) Find an expression for the filter H hp which corresponds to the mask W a. Hint: You may want to use the shift identity of the discrete Fourier transform: { ( ux0 f(x x 0, y y 0 ) F (u, v) exp j2π M + vy )} 0 N where M and N are the respective number of samples in x and y direction. (f) Describe problems that will arise in a practical situation when we want to implement a filter like (1) in the Fourier domain. Also suggest how these problems might be solved. 5