西安交大数字图像处理双语试题

9. Y You want to apply the L Laplacian of f a Gaussian n edge opera ator, 2G , to o an image f f(x, y) of siz ze 512x512. . Assu ume that the e edge opera ator is of siz ze 32x32, an nd that its origin o is at it ts center. De escribe in words w how to o perf form this in the frequen ncy domain.
The Fourier tran 百度文库sform equi ivalent of di ifferentiatio on is
Smo oothing follo owed by dif fferentiation n is
11. A Assume tha at the 2D Fo ourier transfo form of the M MxN image e f(x,y) is F(u (u,v). Determ mine the 2D D Fourier tran nsform of the e following functions. Y You may wi ish to refer to the prope erties of the Fourier tran nsform in th he table e on the fron nt page.
Compute the e convolutio on of the foll lowing imag ge with the filter w (ass sume that th he origin of f w is at its center). c 6. C To c compute the e result at th he border, pa ad the image with zeros s.
Image:
Result:
8. C Consider a 3x x3 spatial m mask that av verages the four f closest neighbors of o a point (x x,y) but excl ludes the po oint itsel lf from the a average. Fin nd the equiv valent filter, H (u,v) in t the frequenc cy domain. (Hint: ( Use t the translatio on prop perty of the Fourier tran nsform).
This s filter has which w of the e following p properties ( (choose two)? (a) I It adapts its window (ke ernel) size d depending on o the image e statistics. (b) I It acts like a mean filter r in areas wh here the loc cal image va ariance is clo ose to the ov verall noise e variance. (c) I It acts like a median filt ter in areas w where the lo ocal image v variance is c close to zero o. (d) I It maintains s the power spectrum of f the origina al image. (e) I It returns the e original im mage in area as where the e local imag ge variance i is high.
S Sample Test P Problem ms
The exam cove ers these sec ctions in the e Gonzalez a and Woods textbook: Chapter C 2, 3.1-3.6, 4.1-4 4.10, 5.1-5.8 8, 9.1losed book. The proble ems below a are represent tative of exa am problem ms. 9.3. It will be cl here are som me importan nt properties s and equatio ons (this will be provid ded): For reference, h
) An image is s degraded b by a Gaussia an blur who ose Fourier transform t H H(u,v) is a G Gaussian H (u, v ) e ( u v )/2 , 13. A
10. D Describe the Fourier tra ansform of a filter that performs sm moothing w with the ideal l low pass fi filter, follow wed by diffe ferentiation i in the x dire ection. Sketc ch a plot of its magnitude. es: The Fou urier transfor rm of the id deal low pas ss filter is: Note
Sket tch the gray y level transformation fo for a gamma a transforma ation that wi ill produce t the image on n the right. mera capture es a 400x400 pixel imag ge of a black and white e soccer ball l on a gray b background. The 2. A digital cam ball is 30 cm in n diameter an nd is 3 m aw way from th he camera. T The camera has a field o of field of 90 9 degrees izontally and d vertically. . hori (a) W What is the diameter of f the ball in pixels, in th he image? (i) 3 pixels (ii) 10 pixels (ii i) 20 pixels (iii) 31 pixe els (iv) 63 p pixels (b) G Give the his stogram of t the image, a assuming tha at black, wh hite, and gra ay pixels hav ve the gray levels 0, 25 55, and 128, respec ctively. Assu ume that the ere are an eq qual number r of black an nd white pix xels on the b ball. g (table tenn nis) ball is 4 40 mm in diameter. How w far away must the pin ng-pong bal ll be, to be (c) A ping-pong exac ctly the sam me apparent size as the s soccer ball i in the image e? (i) 1 10 cm (ii) 0.4 m (iii) 0.7 75 m (iv) 1 m (v) 3 m era has an im mage resolu ution of 2000 x 2000 pix xels. The in ndividual sen nsor elemen nts are squar res 3. A CCD came mea asuring 10 x 10 um, wit th no spaces s between th hem. a. If f the camera a uses a lens s with focal length = 10 00 mm, wha at is the field d of view? b. A Assume the c camera is m mounted on a an airplane, pointing str raight down n at the grou und. What he eight should d the airplane fly, so that one pix xel in the ca amera corres sponds to on ne meter on n the ground d? 4. T The histogram m of a 100x x100 image with 3 bit p pixels is give en below.
Image: :
R Result:
7. A Apply a 3x3 median filte er to the following imag ge. (You ca an disregard the outer ro ow and colu umn of the r result.)
1. T The image of f stripes below on the le eft is too da ark when dis splayed on a monitor. T To improve the display, , we appl ly a gamma transforma ation to prod duce the ima age on the ri ight.
a. C Compute the transforma ation functio on s = T(r) that t will equ ualize the histogram. b. C Compute the e histogram H H(s) of the resulting im mage, if it were transfor rmed by T. Complete the e following Matlab cod de to do a co orrelation be etween a 10x x10 templat te image T 5. C and a 100x100 image I (yo ou do not ha ave to norma alize the result).
b. f(x - 3, y + 2) ) * f(x + 3, y) (where * d denotes con nvolution)
(sele ect one)
12. T The adaptiv ve local nois se reduction n filter is def fined as: