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Edge Linking Problem Edge points/pixels/segments seldom characterize an edge completely (e.g., noise, breaks in the edge from non-uniform illumination) Edge points are linked to become a boundary by using either local processing, or global processing (based on Hough transform ) COMP344 Edge Linking
Local Processing Idea All edge points that are similar are linked/connected Question What is “ similar ”? COMP344 Edge Linking

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Defining “Similar” Gradient operator used to produce an edge pixel f ( x , y ) magnitude f = G 2 x + G 2 y direction α ( x , y ) = tan - 1 G y G x ( x 0 , y 0 ): current pixel coordinates; ( x , y ): neighbor pixel coordinates 1 Similar strengths of the responses of the gradient operator | ∇ f ( x , y ) - f ( x 0 , y 0 ) | ≤ E E : non-negative magnitude threshold 2 Similar directions of the gradient operators | α ( x , y ) - α ( x 0 , y 0 ) | ≤ A A : non-negative angle threshold 3 Close distance between current and neighbor pixel points ( x - x 0 ) 2 + ( y - y 0 ) 2 D D : non-negative distance threshold COMP344 Edge Linking

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Global Processing Objective Assume that there are n points in an image and we want to find subsets of these points that lie on straight lines COMP344 Edge Linking
Hough Transform For a point ( x i , y i ), straight line equation: y i = ax i + b a : slope ;

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