ECE468_24 - ECE 468 Digital Image Processing Lecture 23...

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ECE 468: Digital Image Processing Lecture 23 Prof. Sinisa Todorovic [email protected] 1
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Outline 2D Wavelet Transform (Textbook 7.5) 2
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2D Scaling and Wavelet Functions ϕ ( x, y ) = ϕ ( x ) ϕ ( y ) 3
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2D Scaling and Wavelet Functions ϕ ( x, y ) = ϕ ( x ) ϕ ( y ) ψ H ( x, y ) = ψ ( x ) ϕ ( y ) ψ V ( x, y ) = ϕ ( x ) ψ ( y ) ψ D ( x, y ) = ψ ( x ) ψ ( y ) 3
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2D Scaling and Wavelet Functions ϕ ( x, y ) = ϕ ( x ) ϕ ( y ) ψ H ( x, y ) = ψ ( x ) ϕ ( y ) ψ V ( x, y ) = ϕ ( x ) ψ ( y ) ψ D ( x, y ) = ψ ( x ) ψ ( y ) ϕ j,m,n ( x, y ) = 2 j 2 ϕ (2 j x - m, 2 j y - n ) ψ i j,m,n ( x, y ) = 2 j 2 ψ i (2 j x - m, 2 j y - n ) , i = H, V, D 3
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2D Discrete Wavelet Transform ϕ ( x, y ) = ϕ ( x ) ϕ ( y ) ψ H ( x, y ) = ψ ( x ) ϕ ( y ) ψ V ( x, y ) = ϕ ( x ) ψ ( y ) ψ D ( x, y ) = ψ ( x ) ψ ( y ) 4
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2D Discrete Wavelet Transform ϕ ( x, y ) = ϕ ( x ) ϕ ( y ) ψ H ( x, y ) = ψ ( x ) ϕ ( y ) ψ V ( x, y ) = ϕ ( x ) ψ ( y ) ψ D ( x, y ) = ψ ( x ) ψ ( y ) ϕ j,m,n ( x, y ) = 2 j 2 ϕ (2 j x - m, 2 j y - n ) ψ i j,m,n ( x, y ) = 2 j 2 ψ i (2 j x - m, 2 j y - n ) , i = H, V, D 4
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2D Discrete Wavelet Transform W ψ ( j, m, n ) = 1 MN M - 1 x =0 N - 1 y =0 f ( x, y ) ψ j,m,n ( x, y ) W ϕ ( j, m, n ) = 1 MN M - 1 x =0 N - 1 y =0 f ( x, y ) ϕ j,m,n ( x, y ) ϕ ( x, y ) = ϕ ( x ) ϕ ( y ) ψ H ( x, y ) = ψ ( x ) ϕ ( y ) ψ V ( x, y ) = ϕ ( x ) ψ ( y ) ψ D (
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