If an edge detector is as follows: Convolve image f(x)with go Convolve f(x)with go to...

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If an edge detector is as follows: Convolve image f(x)with go₁ Σπαξ Convolve f(x)with go₂ to form h₂(x). h₂(x)-h₁(x) Compute h₂(x) = 0₂-01 Find zero-crossings of h3 (x). e 1|X to form h₁ (x). a. Describe how h3(x) can be computed by a single convolution with some kernel g(x). What is the convolutional kernel g(x)? b. Sketch g(x). c. What is the Fourier transform G(ū) of g(x)? d. As 0₂ → 0₁, is this a good edge detector, that is, do zero-crossings of h3 occur at edges? Why or why not? Hint: Consider G(u) as d₂ → 0₁. If an edge detector is as follows: Convolve image f(x)with go₁ Σπαξ Convolve f(x)with go₂ to form h₂(x). h₂(x)-h₁(x) Compute h₂(x) = 0₂-01 Find zero-crossings of h3 (x). e 1|X to form h₁ (x). a. Describe how h3(x) can be computed by a single convolution with some kernel g(x). What is the convolutional kernel g(x)? b. Sketch g(x). c. What is the Fourier transform G(ū) of g(x)? d. As 0₂ → 0₁, is this a good edge detector, that is, do zero-crossings of h3 occur at edges? Why or why not? Hint: Consider G(u) as d₂ → 0₁.

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a To compute hx by a single convolution we can convolve fx with a kernel that is the differen... View the full answer