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6_2DConvolution

# 6_2DConvolution - EE 211A Fall Quarter 2011 Instructor John...

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1 EE 211A Digital Image Processing I Fall Quarter, 2011 Handout 6 Instructor: John Villasenor 2D Convolution as an Array Multiplication: Example Find ) , ( ) , ( n m h n m x where , 1 2 1 3 4 0 ) , ( m n n m x = m n n m h = 1 1 1 2 0 3 ) , ( Step 1: Write x , h as matrices , 3 4 0 1 2 1 2 columns X Υ Υ Υ Φ Τ ΢ ΢ ΢ Σ Ρ = ʹ′     columns h 3 0 1 1 3 2 1 Υ Φ Τ ΢ Σ Ρ = h x y = will have 2 + 3 – 1 = 4 columns, 3 + 2 – 1 = 4 rows. Step 2: Express ) , ( n m x as column-oriented vector Υ Υ Υ Υ Υ Υ Υ Υ Φ Τ ΢ ΢ ΢ ΢ ΢ ΢ ΢ ΢ Σ Ρ = Υ Υ Φ Τ ΢ ΢ Σ Ρ = 3 4 0 1 2 1 1 0 X X X Step 3: Form matrices : n H Each n H contains the elements from the column n of h . Number of columns of n H = Number of rows of x . Number of rows of n H = Number of rows of y .

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6_2DConvolution - EE 211A Fall Quarter 2011 Instructor John...

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