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# old-exam-homework2 - (11(11 pts(all(El{fl(si Figure 1 Image...

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Unformatted text preview: (11] (11] pts} (all (El {fl (si Figure 1: Image patch For the image patch in Figure 1 at the pixel at the center [1 that is the pixel marked by; the hlack square] apply; the following ﬁlters and round to the nearest integer t-‘alue: 1 2 1 i. a 3 x 3 Gaussian ﬁlter 1115 2 =1 2 1 2 1 ii. a 3 x 3 Box ﬁlter (that is averaging in a 3 x 3 neighl’mrhmd]. lCompute the edge direction and strength [: that is the direction and ahsolute value of the image gradient-l at the center pixel using the masks of the Sohel edge detector. 1 —1 £1 1 1 1 2 1 31: E —2 U 2 52 = E U I] I] k —1 U 1 k —1 —2 —1 Apply; a median ﬁlter to the center pixel. Explain for what kind of noise median ﬁltering 1will work hest. 1ill-Thy is the Gaussian ﬁlter a good smoothing ﬁlter? [:How' can it he implemented fast? How can we implement repeated Gaussian ﬁltering in one operation?) 1iill-"hat happens to the two edges at the boundaries of a dark line on a white hackground it the image is smoothed with a Gaussian with kernel size larger than the width of the line? Explain why Box ﬁltering (that is averaging] attenuates the noise. Explain the concept of aliasing and give an example. (2] (11] pts} lConsider the cube 1writ-h points P1. P2. P3. P4. P5.PG.PT. P8 and 3D coordinates in the world coordinate system as given in Figure 2. A. Pil-I:.D.-1.'2.1: 33—:1; 1'11: F?-[1.1.'2.1] P5-|IZI.1-‘2.EI:- PE--:1.1.'2.E-: Figure 2: calihrated camera with focal length f = 1 whose origin is at (ﬁll. —3]I and which has a rotation of —¢L-'3“' around the Y—axis with respect to the world coordinate system takes an image of the cube. The image ccoor— dinates of the corners of the cube are labeled 331. p2. p3. pl. p5. 3313. pT. pd Remember a rotation of angle o: around the Y—axis can he expressed cos (I: 1] sin or hv the rotation matrix R = [l 1 [l _. aud cosi—zl-Ero} = —sino 1] cos n- %u’§. and EDIE—45'") = —%u’§. (a) Derive the projection matrix mapping homogeneous world coor— dinates to homogeneous image coordinates. [hi] ICompute the homogeneous and the non—homogenous image coor— dinates of points 335. 30-5. pT. 338. (c) Derive the non—homogenous coordinates of the 3 vanishing points, corresponding to the 3 parallel lines. {d} ICompute the vanishing point of the line PIS—PT {e} How would the camera need to he positioned with respect to the cuhe. such that 2 of the vanishing points are ideal [that is are at inﬁnith 7.’ [3:] {5pm} Describe the Emmy edge detector. Exlain its three modules. Figure =1: Image patches at two instances in time 5:] (Epts) {a} lIC‘onsider the cube with a stripe pattern in front of a plane with a stripe pattern shown in Figure 3. The scene is observed by a moving camera which translates to the right [: parallel to the X—aXlSl. Draw the optical ﬂow ﬁeld and draw the normal ﬂow ﬁeld. [hi] At time t5. and time t1 the camera observes the image patches shown in Figure :1 [i the image patch at to is the same as the one in problem 1). lC‘-n:+1'.n1:rute the normal ﬂow vector at the center of the patch. Estimate the spatial derivative If and Iy by averaging the derivatives computed with the Sohel operator at the two time instances. lCompute the time derivative I; as difference between the intensity; at the center pixels. ...
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old-exam-homework2 - (11(11 pts(all(El{fl(si Figure 1 Image...

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