Unformatted text preview: f linear? Is it shift invariant? (b) Writing this operation in the form g = f * h , what choice of h will produce the desired g ? (c) Let f represent an image of a white disk on a black background. Sketch f and k g k . 3. (8 pts) Let W=dftmtx(4) . (a) Explain in words what each column of W represents. (b) Write down the result of the operation (1/4)*W*W’ . What property of W does this illus-trate? 4. (8 pts) Recall that the chi-squared distance between a pair of K-bin histograms h i ( k ) and h j ( k ) is given by: χ 2 ( i, j ) = 1 2 K X k =1 [ h i ( k )-h j ( k )] 2 h i ( k ) + h j ( k ) (a) For the use of this distance to be valid, what two conditions must each histogram satisfy? (b) What is the chi-squared distance between two identical histograms? Show that χ 2 ( i, j ) cannot be smaller than this value. (c) What is the largest possible chi-squared distance between two histograms? Show that χ 2 ( i, j ) cannot exceed this value. 1...
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- Fall '06
- Image processing, Low-pass filter