LAPLACE OPERATOR.ppt [Lecture seule]

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Laplace operator• Sensitive to high-frequency noise.• Notice the Fourier transform pairs:⎧ ∂ ⎫I ⎨ f(x,y) ⎬ = j 2 π u F(u,v)⎩∂x⎭{ }2 2 2 2I∇ f(x,y) = − 4 π (u + v) F(u,v)

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Laplace operator⎡0 −1 0 ⎤⎢−1 4 −1⎥⎢ ⎥⎢⎣0 −1 0 ⎥⎦⎡−1 −1 −1⎤⎢1 8 1⎥⎢− −⎥⎢⎣−1 −1 −1⎥⎦

Laplace operator• Sensitive to high-frequency noise.• Notice the Fourier transform pairs:⎧ ∂ ⎫I ⎨ f(x,y) ⎬ = j 2 π u F(u,v)⎩∂x⎭{ }2 2 2 2I∇ f(x,y) = − 4 π (u + v) F(u,v)

Page 1 and 2: LAPLACE OPERATOR
Page 3 and 4: It follows that:Laplace operator[ ]
Page 5: Laplace operatorThe Laplace operato
Page 9 and 10: LOG filter (Laplacian of Gaussian)
Page 11 and 12: LOG filter (Laplacian of Gaussian)G
Page 13 and 14: LOG filter (Laplacian of Gaussian)r
Page 15: LOG filter (Laplacian of Gaussian)G

LAPLACE OPERATOR.ppt [Lecture seule]

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