Assign I P 050209

IP Assignment

(1)Give a single intensity transformation function for spreading the intensities of an image so the lowest intensity is 0 and the highest is L-1 (2) In some applications it is useful to model the histogram of the input images as Gaussian probability density functions (PDF) of the form p r (r ) =

1

e

−

(r −m)2 2σ 2

2 ∏σ Where m and σ are the mean and standard deviation of Gaussian PDF. What is the transformation function you would use for histogram equalization? (3)Show that subtracting the Laplacian from an image is proportional to unsharp masking (4) Laplacian with –8 in the center yields sharper results than the one with –4 in the center. Explain in detail. (5)Consider a 3x3 spatial mask that averages the four closest neighbors of point (x,y), but excludes the point itself from the average (a) Find the equivalent filter, H(u,v) in the frequency domain (b)(b) Show that the result is low pass filter (6) (a) Compute the discrete Fourier transform (DFT) of the discrete function f(x,y) =1 . (b) Compute the DFT of the discrete image function f(x, y) = sin (2Π uox+2Πvoy). (7) A continuous Gaussian low pass filter in the continuous frequency domain has transfer function H ( µ ,ν ) = Ae − that corresponding filter in spatial domain is 2 2 2 2 h(t , z ) = A2Π σ 2 e −2 Π σ ( t + z )

( µ 2 +ν 2 ) 2σ 2

. Show

(8) Explain what would happen in binary erosion and dilation if the structuring element is a single point valued 1. Give the reasons for your answer.

(9) A Binary image contains straight lines oriented horizontally, vertically, at 450, and at -450. Give a set of 3x3 masks that can be used to detect 1-pixel breaks in these lines. Assume that the intensities of lines and background are 1 and 0, respectively. (10)The image function f(x, y) = 4Cos2 (2x+2y) is to be sampled such that one can reconstruct the function from its samples without any errors. Suggest a sampling scheme. Is your sampling scheme optimal? (11)Sketch the impulse function φ(x,y) = δ(x+y-1) (12)A 4x4 gray scale original image passes through following spatial linear shift invariant filters, resulting in filtered images. Use zero padding while computing along borders (a) Compute Filtered image 1 (b) Compute Filtered image 2

1 1 2 0 1 8 0 8 6 6 4 Original

8

6

6

4

4 2 2 0 Image

0 0 0

1 0 1

0 0 0

0 1 0

1 2 1

0 1 0

½ Filter 1

1/2 Filter 2

(13) Draw the color gamut of CMY in the Rn Gn Bn chromaticity diagram. Hint: The color pure cyan has coordinates (1, 0, 0) in the CMY color coordinate system.