数字图像处理期末复习资料与期末模拟试卷(含答案)

Digital Image Processing Examination1.Fourier Transform problem.1 )For an image given by the function f(x,y)=(x+y)3 where x,y are continuous varibales;evaluate f(x,y)6(x-1,y-2)and f(x,y)*6(x-1,y-2),where5 is the Dorac Delta function.2)For the optical imaging system shoen below,consisting of an image scaling and twoforward Fourier transforms show that the output image is a scale and inverted replica ofthe original image f(x,y).f(x,y)Scalingf(ax,by)FFg(x,y)一3)three binary images(with value 1 on black areas and value 0 elsewhere)are shownbelow.Sketch the continuous 2D FT of these images(don,t do this mathematically,try touse instead the convolution theorem and knowledge of FTs of common functions)2.The rate distortion function of a zero memory Gaussian source of arbitary mean andvariance a2 with respect to the mean-square error criterion isR(D)=1 ,o-2-log 2 D0forO D a2a)Plot this functionb)What is Dmaxc)If a distortion of no mor than 75%of the sources variance is allowed,what is themaximum compression that can be achieved?3.The PDF of an image is given by Pr(r)as shown below.Find the transform toconvert the images PDF to Pr(z).Assume continuity,and find the transform in terms of r andz.Explain the transformation.4.A certain inspection application gathers black&white images of parts as they travel alonga conveyor belt.It is necessary to sort the parts into two categories:parts with holes andparts with-out holes.An example of an image that might be taken by the inspectioncamera is shown at the right.Propose a method to identify and locate the objects of each category in the image so thatthey can be picked up by a robotic system and placed in different bins.Assume that theimaging system knows where each image pixel is located on the conveyor belt at everypoint in time.Provide an annotated flow chart of the algorithm you propose.5.In a given application,an averaging mask is applied to input images to reduce noise andthen a Laplacian mask is applied to enhance small details.Would mathematics predictthat the result should be the same if the order of the operations were reversed?Whatpractical issues would be encountered in computer implementation?Digital Image Processing Examination1.A preprocessing step in an application of microscopy is concerned with the issue ofisolating individual round particles from similar particles that overlap in groups of twoor more.Assuming that all particles are of the same size,propose a morphological algorithmthat will produce an image that contains only the isolated(non-overlapping)particles that are not in contact with the boundary of the image.2.An image represented by a continuous function f(x,y)is w=2 cm wide and h=3 cm high.The image is to be converted to an array of pixels by a scanner whose response is zeroabove 80 lines/centimeter in both the horizontal and vertical directions.The discrete image isrepresented by an array*f(n,m)where n and m take on integer values,0 n N-1,0 m M-1.(a)Determine suitable values for N and M.(b)Assume that 7(n,m)=f(na,mb).Determine the values of a and b.(c)Determine constants A,B,C,D,E such that the DFT o ff can be expressed as8 C z(Dun-Evm)F(u,v)=人 之 之(H,m)en=O m=O(d)Find numbers(P1,P2)such that F(u+jP1,v+kP2)=F(u,v)for any integers j,k,u,v.3.The arithmetic decoding process is the reverse of the encoding procedure.Decode themessage 0.23355 given the coding model.SymbolProbabilitya0.2e0.3i0.100.2u0.1!0.14.The gradient of a function f(x)is defined asV/=Gyaxs-f冷-Computationally,the first derivative is implemented by calculating the difference betweenadjacent pixels.(a)Is the following a linear operator?(b)State how would you implement the above operator using differences between pixels.(c)A Sobel operator uses two masks,Hx and Hy to process an image.Explain why are twomasks needed and what do they measure?(d)Write down the masks Hx and Hy,and identify them in the followingHx(u,v)Hy(U,vjlfigures:5.The three images shown were blurred using square averaging masks ofsizes n=23,25,and 45,respectively.The vertical bars on the left lower part of(a)and(c)are blurred,but a clear separation exists between them.However,the bars have merged in image(b),in spite of the fact that the mask thatproduced this image is significantly smaller than the mask that produced image(c).explain this.(b)Digital Image Processing Examination1.An image array f(m,n)of size M1 x N1 is to be convolved with a filter arrayh(m,n)of size M2 x N2 to produce a new image array g(m,n).1)Write a pseudo code program that describes a method to compute g(m,n)through the use of Fourier transforms.The result should be the same sizeas would be achieved with direct convolution.2)Modify the algorithm so that it does the correlation f-h rather than theconvolution.2.You have the job of designing an algorithm that will count the number ofobjects with holes and the number of objects without holes in images of the kindshown here.Assume that the images are binary with 0 corresponding to blackand 1 correspond