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(ELEC317)98_Spring_exam.pdf
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ELEC 317 Exam (Spring 1998) Name:________________________
Student No.:___________________ Signature:_____________________
This paper contains 6 questions with unequal weights. Answer all questions.
1. Matlab Programming and Halftoning, 10%
a. (10%) Write a Matlab program dither.m to performs 4 bit quantization with dithering
function y=halftone(x) where x is the input image with unknown image size, and y is the output image. Determine for yourself how large the noise mask should be and explain why. Note that the Matlab com-mand, rand(M,N) generates an MxN matrix of random entries, chosen from a uniform distri-bution on the interval (0, 1).
2. Image Transforms, 30%
a.
(4%) An NxN image u can be considered as a column-ordered N2x1 vector x. How is x de-fined in terms of elements of u? What are the corresponding basis images? (Hint: the basis images can be expressed in terms of ei, the ith Nx1 basis vector.)
b.
(10%) Show that any linear transformation v=T(u), or NN
vm, n) = ui) ij(,( (, jmn)
i =1 j =1
(such as DST, DCT, DFT) on an image u can be written in the form of y=T(x)=Ax, where x and y are the column-ordered N2x1 image vectors corresponding to u and v respectively, and A is an N2xN2 matrix. What special meaning is associated with the columns or rows of A?
c.
(8%) Images are known to be highly correlated, but it is desirable to decorrelate the image completely in image compression. Prove that the KL transform decorrelates the image.
d.
(8%) What is the definition of a separable transform? The computation of y=Ax in part (b) requires N4 multiplications which is too large. How can the computation be simplied (using u and v instead of x and y) for separable transforms? How many multiplications are needed now? What are the new basis images?
P. 1 of 6
3. Fourier Feature Recognitions (10%)
Here are 12 possible 2D FFT.
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A1B1 C1
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A4B4 D4
P. 2 of 6
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a) ___________
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d) ___________
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g) __________
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j) __________
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b) ___________
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