<Introduction Line detection I circle detection I irregular shape detection Least squares energy minimization (seehttp://mathworld.wolframcom/leastsquarEsfittinghtml) Given: Many(i,yi)pairs (x2y) y=mx+c Find: Parameters(m, c) ☆ Minimize: Average square distance: ★☆ (y2-mx-c)2 y nx.-c E N Using aE aE 0 y=mx am C ∑(x1-x)y-y) Note ∑y∑ ∑(x-x N Hough transforIntroduction | Line detection | circle detection | irregular shape detection Least Squares energy minimization (see http://mathworld.wolfram.com/LeastSquaresFitting.html) Hough transform v0.b 4 y = mx+c y mx c i − i − ( , ) i i x y y x Given: Many pairs Find: Parameters Minimize: Average square distance: Using: Note: ( , ) i i x y (m,c)  − − = i i i N y mx c E 2 ( ) 0 & = 0   =   c E m E c = y − m x   − − − = i i i i i x x x x y y m 2 ( ) ( )( ) N y y i  i = N x x i  i =