SD475 Digital Image Processing – Midterm Examination October 25, 2012 9:45am – 11:15am

Prof. D. A. Clausi Aids: calculator, crib sheet (both sides of standard paper, no solutions to problems). Submit crib sheet with

solution booklet. Total Marks: 45 1. [Total: 15 marks] SMOOTHING. A Gaussian low pass filter (LPF) h1(x) can be used to smooth high frequency noise in

an image. Consider its 1-d implementation:

h1(x) =

25.0

1

1

21

−

σ

πσ

x

e

(a) [1 mark] What is the primary drawback to using any LPF for smoothing high frequency noise? (b) [2 marks] Would an ideal “box” spatial filter be more appropriate for smoothing an image? Why or why not? (c) [2 marks] Sketch a continuous input signal f(x) = 1 + 5u(x) plus additive Gaussian noise with σn = 0.2, where u(x)

is the unit step. (d) [4 marks] Sketch the outputs when f(x) is filtered using h1(x) for (i) σ1 = 0.1 and (ii) σ1 = 3. (e) [2 marks] Does h1(x) retain the DC gain in the image? Why or why not? (f) [4 marks] Is h1(x) (i) a linear filter? (ii) a causal filter? For each case, provide an explanation.

2. [10 marks] POINT OPERATIONS. Assume an image has a distribution pf(r) = 1 - cos(2πr), 0