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1 Written test Tuesday 19th of December Aids allowed : All usual aids Weighting : All questions are equally weighted. NAME : Signature : Desk no. : Question Answer Question Answer Possible answers to each question are numbered from 1 to 6. The chosen number of the answer must be entered in the table above. In case you enter an incorrect number in the table this may be corrected by "inking out" the wrong number and instead placing the correct number below. Should there be any doubts in connection with a correction, the question will be considered as not answered. ONLY THE FRONT PAGE IS TO BE HANDED-IN. If you decide to make a blank hand-in or leave the examination prematurely the front page must in all circumstances be handed-in. Rough drafts, calculations and comments will not be included in the evaluation. Only numbers included in the above table will be registered. A correct answer will be equivalent to 5 points. An incorrect answer will be equivalent to -1 points. Questions unanswered as well as answer number six (equivalent to "do not know") will not produce points. The number of points required for a satisfactorily answered exam is finally determined by teacher and external examiner. Please don't forget to state your name, signature and desk number on the paper.

2 QUESTION 00.1 A digital camera with a camera constant of mm gives sharp images at a distance of 1 m. Find the smallest of the following aperture stops that gives a field of depth from 0.5 m to 5 m. A circle of confusion diameter of maximum 7 µm is accepted

3 QUESTION 00.2 We want to classify a pixel in a satellite image of the earth surface. For the pixel we have a set of reflection measurements for different wave lengths collected in a feature vector X. The classification problem has 5 classes characterized by Class Name Prior Probability Class Conditional Density for X 1 Wheat field Barley Field Sugar Beet Field Forest Road The loss function is Chosen Class True Class which class will a Bayes classifier assign to X? 1. Class 1 2. Class 2 3. Class 3 4. Class 4 5. Class 5

4 QUESTION 00.3 A SAR image is shown below with 2 areas indicated. The mean intensity for area I is 0.20, and for area II it is In the original 1-look SAR image, the variance of the intensity in the two areas are I: 0.05 and II: 0.01, respectively. The speckle is now reduced by a filter that fully preserves the edge content in the image, and the mean intensity of the two areas is therefore the same as before filtering. The variance is, however, reduced, and after the speckle reduction the variance in the two areas are I: 0.005, and II: 0.001, respectively. I I II What is the equivalent number of looks for the image after speckle reduction?

5 QUESTION What is the value of the marked pixel after a 5 x 5 median filter?

6 QUESTION 00.5 A digital satellite image is rectified using a polynomial transformation and least squares optimization. Polynomials of 1 st to 5 th order are computed from the same ground control points. For each polynomial the quality of the rectification is estimated from the residuals in the ground control points and the residuals in a number of independent control points. The table below shows the standard deviations for each polynomial: Polynomial Ground control points σ in m Control points σ in m 1 st order nd order rd order th order th order Which polynomial would you recommend for the rectification? 1. 1 st order 2. 2 nd order 3. 3 rd order 4. 4 th order 5. 5 th order

7 QUESTION 00.6 A camera is built with a CCD-chip. The chip has the following data: Resolution: 512 pixels * 512 pixels Pixel size: a * a Pixel placement: a (centre to centre) Also Diagonal field of view: 57.0 o. Focal length: 8.0 mm. Find the pixel size a: 1. a = 11.0 µm 2. a = 12.0 µm 3. a = 13.0 µm 4. a = 14.0 µm 5. a = 15.0 µm

8 QUESTION 00.7 Maps and other graphic images on the Internet often have a high probability of neighboring pixels having the same color (i.e. pixel value). This question considers a coding method where the first step for each pixel, f(i,j) is to code the binary decision, whether or not the pixel, f(i,j) has the same value as the previous pixel, f(i,j-1). For a typical map the neighboring values are equal (f(i,j) = f(i,j-1)) for 7 out of 8 pixels. Assume these values to be consistent with the expected values. What is the (lower bound on the) expected code length (per pixel) for coding the binary decision? 1. 0,54 bits per pixel 2. 1 bit per pixel 3. 0,12 bits per pixel 4. 3 bits per pixel 5. 0,88 bits per pixel

9 QUESTION 00.8 In an RGB-image we want the stretch the intensity with a gamma mapping (γ = 2) and leave the hue and saturation unchanged. Which RGB-value should (0.5, 0.3, 0.4) be mapped into? 1. (0.2, 0.71, 0.16) 2. (0.82, 0.34, 0.43) 3. (0.2, 0.5, 0.4) 4. (0.4, 0.61, 0.32) 5. (0.26, 0.06, 0.16)

10 QUESTION 00.9 On the set of black pixels X in this image we perform the morphological operation (( A) X U ( X B )) \ ( X C ) where A= B= C= 1 * * * 1 * 1 * * * 1 * 1 * * How many black pixels are left in the result?

11 QUESTION What is the difference energy for the gray level difference histogram for h = (1,1) in the texture ?

12 QUESTION A camera calibration has given the following related values for the camera constant and the radial symmetric distortion: c = 40.0 a a a a = 0 = 8 10 = = Give the camera constant that results in a radial symmetric distortion of 0 along a circle in the image plane with orego in the principal point and a radius of

13 QUESTION Given two normally distrubuted populations Population 1: N 1 2, Population2: N 3 2, The prior probabilities are 0.8 for population 1 and 0.2 for population 2. We assume a symmetric loss function. X 1 Given an observation X =, what will be the Bayes classifier decision X 2 rule for assigning it to class 1? 1. -x 1 + x log x 1 + x log x 1 + 4x 2-2 log x 1 + 4x 2-2 log x 1 + 4x 2-3 log 4 1

14 QUESTION In the image we see an object consisting of 9 black pixels. What is the λ - ratio, R λ, for this object?

15 QUESTION Which of the statements about CCD based cameras below are true (T) and which are false (F): a) It is better to use frames than fields in scenes with motion when using an interlaced camera. b) CCD-chips with electronic shutter have a fixed integration time. c) The charge in a pixel is proportional to the light intensity and the integration time. d) Most CCD-chips has the largest spectral sensitivity in the infrared area. 1. (a,b,c,d) = (T,T,F,F) 2. (a,b,c,d) = (T,T,F,T) 3. (a,b,c,d) = (F,F,T,T) 4. (a,b,c,d) = (F,T,T,T) 5. (a,b,c,d) = (T,F,T,T)

16 QUESTION Which of the following statements is false? 1. The Euclidean distance transform can be performed using 4 masks 2. min ( x - u, y - v ) can be used as a distance metric between the points ( x,y ) and (u,v) 3. The chessboard distance transform can be implemented using the Chamfer algorithm 4. The city-block distance transform uses the d 4 metric 5. The Euclidian distance transform results in a vector distance map

17 QUESTION In a robot system guidemarks filling 4 * 4 pixels in the image are used. The guidemark has 4 fields, two black and two white. Two algorithms for detection of the guidemark are to be analysed. Algorithm 1: The image is convoluted with the kernel: The guidemark is detected if the center value is greater than 200. Algorithm 2: The four fields are numered as shown in the figure. S i means the sum of the values in field i The guidemark is detected if: S 1 - S 2 > 30 and S 1 - S 3 > 30 and S 4 - S 3 > 30 and S 4 - S 2 > 30 Show as d means detected and nd means not detected how the two algorithms work on the guidemarks below, the guidemarks are in the order (a,b,c). a b

18 QUESTION CONTINUED c Algorithm 1 = (d, nd, d), Algorithm 2 = (d, d, d). 2. Algorithm 1 = (d, nd, d), Algorithm 2 = (d, d, nd). 3. Algorithm 1 = (d, d, nd), Algorithm 2 = (d, d, nd). 4. Algorithm 1 = (d, nd, d), Algorithm 2 = (d, nd, nd). 5. Algorithm 1 = (d, nd, d), Algorithm 2 = (d, d, d).

19 QUESTION Which one of the following 5 statements is wrong? 1. Homologous points lie in the same epipolar plane. 2. The direct linear transformation (DLT) does not model the radial symmetric lens distortion. 3. At least 5 coplanarity equations are needed to compute the relative orientation between stereoscopic images. 4. The radial symmetric lens distortion is corrected by the colinearity equations. 5. The absolute orientation of a stereoscopic model is described by 7 parameters.

20 QUESTION X is the set of black pixels in this binary image. X is morphologically opened using the structuring element X How many black pixels are left in the result?

21 QUESTION Three binary images shown in part below are coded using run-length (RL-) coding and JBIG. The run-length code is based on applying Huffman coding to the run-lengths of the image. The Huffman code is optimized for text images (as in the early FAX standards). JBIG uses coding based on probabilities conditioned on a 10 pixel template. (We may assume JBIG codes close to the conditional entropy.) A. Text B. Halftone C. Random (enlarged) Which of the following statements is correct? (The part of image C is enlarged so the individual pixels can be seen.) 1. JBIG gives a high compression rate for all three images. RL-coding gives a low compression rate for the images B and C. 2. RL-coding compresses the images A and B better than JBIG, while JBIG compresses image C better. 3. RL-coding can only code image A, while JBIG can code all three images. 4. The compression rates (C R ) for the three images are ordered for each method. For RL-coding the highest C R is achieved for image A, then C, and lowest for B. For JBIG the order is: B highest, then A, and lowest for C. 5. JBIG codes the images efficiently compared with the entropy of the images. RL-coding codes image A fairly efficiently compared with the entropy, but not B and C.

22 QUESTION We consider a digital image that has a peak in the Fourier power spectrum for the frequency (a,b) = (27,3). The value of the Fourier transform in the peak is 6+2i. The image is convolved with an unknown lowpass convolution filter, whereby the value of the Fourier transform in the peak is changed to 4-2i. What is the value of the Fourier transform of the filter in the point (27,3)? i i i 5. i + 0.2i

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