l13 - 1 CMPEN/EE455 Lecture 13 Topics today 1 2-D...

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Unformatted text preview: 1 CMPEN/EE455 Lecture 13 Topics today: 1. 2-D Discrete (Linear) Convolution - G&W Ch. 4.4.1, 4.6.6 2. 2-D Discrete (Circular) Convolution/Filtering using the DFT- G&W Ch. 4.7.3 2-D Discrete (Linear) Convolution h ( x, y ) = f ( x, y ) * g ( x, y ) = ∞ X m =-∞ ∞ X n =-∞ f ( m, n ) g ( x- m, y- n ) Suppose: f ( x, y ) = 0 outside 0 ≤ x ≤ A- 1, 0 ≤ y ≤ B- 1 ↑ nonzero only in an A × B rectangle g ( x, y ) = 0 outside 0 ≤ x ≤ C- 1, 0 ≤ y ≤ D- 1 ↑ nonzero only in an C × D rectangle Then, for filtered image: h ( x, y ) = 0 outside 0 ≤ x ≤ A + C- 2, 0 ≤ y ≤ B + D- 2 ↑ nonzero only in an ( A + C- 1) × ( B + D- 1) rectangle CMPEN/EE455 – Lect 13 2 Let M = A + C- 1 and N = B + D- 1 CMPEN/EE455 – Lect 13 3 Often g ( x, y ) may be a small “mask” (3 × 3) operator. → brute-force computation of convolution fine! But, if f ( x, y ) and g ( x, y ) comparable in spatial support, then, brute-force computation is Very Intense!...
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l13 - 1 CMPEN/EE455 Lecture 13 Topics today 1 2-D...

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