Lec15.SfAR-CVF-Lecture

# A line that passes through 1 point gets one vote find

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Unformatted text preview: odel }༇  }༇  }༇  }༇  }༇  Equa-on of line: y = mx + c Error induced by ith point: ei = mxi + c - yi Error for whole data: E = Σi ei2 E = Σi (mxi + c – yi)2 Step 3: Diﬀeren-ate Error w.r.t. parameters, put equal to zero and solve for minimum point Line Fitting: Least Squared Error Solution 2 E = ∑ (mxi + c − yi ) i ∂E = ∑ (mxi + c − yi )xi = 0 ∂m i ∂E = ∑ (mxi + c − yi ) = 0 ∂c i ⎡ྎ∑ xi2 ⎢ྎ i ⎢ྎ∑ xi ⎢ྎ i ⎣ྏ ∑ x ⎤ྏ ⎡ྎm⎤ྏ ⎡ྎ∑ x y ⎤ྏ ⎥ྏ ⎢ྎ ⎥ྏ ⎢ྎ c ⎥ྏ = ⎢ྎ ∑1 ⎥ྏ ⎣ྏ ⎦ྏ ⎢ྎ ∑ y ⎥ྏ ⎥ྏ ⎥ྏ ⎣ྏ ⎦ྏ ⎦ྏ i i i i x y 1.3 5.7 2.4 7.3 3.4 10.5 4.6 11.8 5.3 13.9 6.6 16.3 6.4 15.3 8.0 17.9 8.9 20.8 9.2 20.9 i i i i 380.63 56.1 56.1 10 m c 914.68 = 140.4 Solu-on: m = 1.9274 c = 3.227 Line Fitting: Least Squared Error Solution Least Squared Error Solution }༇  Disadvantages? }༇  }༇  }༇  Mul-ple Lines… Not robust to noise Example Finding Lines Problem Deﬁni-on: }༇  Given a binary image, ﬁnd all signiﬁcant lines }༇  Line: y = mx + c }༇  Es-mate m,c parameters of all signiﬁcant lines in presence of noise }༇  Hough Transform Method to ﬁnd any type of shape that can be represented in parametric form }༇  E.g. lines, circles, parabolas, ellipses… }༇  Generalized Hough Transform }༇  }༇  For arbitrary shapes Hough Transform for Lines }༇  General Idea: }༇  Search for the best possible m and c parameters given the data Consider all possible...
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