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Lec15.SfAR-CVF-Lecture

# example g x y e x2 y2 2 2 x 1

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Unformatted text preview: smoothing ﬁlter ﬁrst Enhances edge areas Stage 3: Detec-on }༇  Produces a binary output, with edges marked by 1, other areas as zero Smoothing Masks 1 g ( x, y ) = ce 1 1 1 1 1 5 21 35 21 5 21 94 155 94 21 35 155 255 155 35 21 94 155 94 21 5 21 35 21 5 1/9 x }༇  − 1 1 Mean Filter }༇  Gaussian Filter 1 ( x2 + y2 ) 2σ 2 Filtering Gaussian Filter }༇  Pixel weight is inversely propor-onal to distance from origin }༇  g ( x, y ) = e }༇  ( x2 + y2 ) − 2σ 2 Value of σ has to be speciﬁed Gaussian Filtering }༇  Example g ( x, y ) = e }༇  − ( x2 + y2 ) 2σ 2 x = - 1, y = - 1, σ = 1 g (−1,−1) = e ( −1) 2 + ( −1) 2 − 2 0.367 ≈ 0.367 Gaussian Filtering }༇  Implementa-on problem }༇  }༇  Float mul-plica-ons are slow Solu-on }༇  }༇  Mul-ply mask with 255, round to nearest integer Scale answer by sum of all weights Gaussian Filtering 94 155 94 1 155 255 155 94 155 94 5 21 35 21 5 21 94 155 94 21 35 155 255 155 35 21 94 155 94 21 5 21 35 21 5 ≈ 2 1 2 4 2 1 2 1 Round(g/70) Gaussian Filtering Continuous Gaussian Function }༇  1- D Gaussian x2 −2 2σ 1 g ( x) = e 2π σ }༇  Non zero from - ∞ to ∞ }༇  Width is controlled by σ }༇  Symmetric }༇  Area under curve = 1 ∞ ∫ −∞ x2 −2 1 e 2σ = 1 2π σ Continuous Gaussian Function 2- D Gaussian Function g ( x, y ) = 1 2πσ e ( x2 + y2 ) − 2σ 2 Gaussian Filter ⊗ = Derivative Masks From deﬁni-on of deriva-ves -1 1 -1 1 Prewi[ Operator -1 0 1 -1 -1 -1 -1 0 1 0 0 0 -1 0 1 1 1 1 }༇  Sobel Operator -1 1 -1 -2 -1 -2 0 2 0 0 0 -1 }༇  0 0 1 1 2 1 Robert’s Operator 1 0 0 1 0 -1 -1 0 Properties of Masks }༇  Filtering Masks }༇  }༇  }༇  }༇  }༇  All values are +ve Sum to 1 Output on smooth region is unchanged Blurs areas of high contrast Larger mask - > more smoothing }༇  Deriva-ve Masks }༇  }༇  }༇  }༇  }༇  opposite signs Sum to zero Output on smooth region is zero Gives high output in areas of high contrast Larger mask - > more edges detected Application of 2- D Masks If fx is deriva-ve in x- direc-on, fy is deriva-ve...
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