Unformatted text preview: )? (b) What is the special name for this ﬁltering operation? (c) You can achieve the same result via iterated convolution with a 2-tap ﬁlter. What is that ﬁlter? 3. (6 pts) Consider the M × N image f ( x,y ) = (-1) x for x = 0 ,...,N-1 and y = 0 ,...,M-1. (a) Describe what f ( x,y ) looks like as an image. (b) Put f ( x,y ) into the form e j 2 π u o · x , where x = ( x,y ) > and u o = ( u o ,v o ) > . (c) What is the Fourier transform F ( u,v )? Write it down for the case of M = N = 4. 4. (10 pts) Consider the 1D continuous kernel h ( x ) = e-x 2 / 2 σ 2 . (a) Give the name of this kernel and write the expression for its Fourier transform H ( u ). (b) Sketch h ( x ) and H ( u ) for two cases: large σ and small σ . (c) Calculate g ( x ) = dh ( x ) dx and its Fourier transform G ( u ). (d) Sketch g ( x ) and G ( u ) for two cases: large σ and small σ ....
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- Fall '06
- Image processing, Prof. Serge Belongie