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Unformatted text preview: CMPEN/EE455 – Lect 10 4 2D Convolution h ( x,y ) = f ( x,y ) * g ( x,y ) = Z ∞∞ Z ∞∞ f ( α,β ) g ( xα,yβ ) dαdβ Also, h ( x,y ) = g ( x,y ) * f ( x,y ) Image f ( x,y ) is put through a linear spaceinvariant ﬁlter g ( x,y ) → h ( x,y ) is ﬁltered image. Comments: 1. 2D convolution often denoted as f ( x,y ) * * g ( x,y ) 2. Mask operations are often 2D convolutions. 3. Hard to draw examples! CMPEN/EE455 – Lect 10 5 Convolution Property: f ( x,y ) * g ( x,y ) ↔ F ( u,v ) G ( u,v ) Convolution in one domain ↔ Multiplication in other domain....
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 Fall '08
 staff
 2D Fourier transform, 2d convolution, rotated frequency variables

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