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cs440-lec6-vision-hough - CS 440 ECE 448 Introduction to...

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CS440 / ECE 448 – Spring 2008 Lecture #6 CS 440 / ECE 448 Introduction to Artificial Intelligence Spring 2008 Instructor: Eyal Amir TAs: Li-Lun Wang, Mark Richards
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CS440 / ECE 448 – Spring 2008 Lecture #6 Edge detection Convert a 2D image into a set of curves Extracts salient features of the scene More compact than pixels
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CS440 / ECE 448 – Spring 2008 Lecture #6 Origin of Edges Edges are caused by a variety of factors depth discontinuity surface color discontinuity illumination discontinuity surface normal discontinuity
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CS440 / ECE 448 – Spring 2008 Lecture #6 Last Time: Detecting Local Features Convolution : Slide a window over the image, creating an image of dot products Detect Line Edge / Edgel Corners Direction of the above
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CS440 / ECE 448 – Spring 2008 Lecture #6 Effect of σ (Gaussian kernel size) Canny with Canny with original The choice of depends on desired behavior large detects large scale edges small detects fine features
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CS440 / ECE 448 – Spring 2008 Lecture #6 Edge detection by subtraction original
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CS440 / ECE 448 – Spring 2008 Lecture #6 Edge detection by subtraction smoothed (5x5 Gaussian)
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CS440 / ECE 448 – Spring 2008 Lecture #6 Edge detection by subtraction smoothed – original (scaled by 4, offset +128) Why does this work? filter demo
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CS440 / ECE 448 – Spring 2008 Lecture #6 Gaussian - image filter Laplacian of Gaussian Gaussian delta function
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CS440 / ECE 448 – Spring 2008 Lecture #6 An edge is not a line... How can we detect lines ?
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CS440 / ECE 448 – Spring 2008 Lecture #6 Finding lines in an image Option 1: Search for the line at every possible position/orientation What is the cost of this operation? Option 2: Use a voting scheme: Hough transform
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CS440 / ECE 448 – Spring 2008 Lecture #6 Finding lines in an image Connection between image (x,y) and Hough (m,b) spaces A line in the image corresponds to a point in Hough space To go from image space to Hough space: given a set of points (x,y), find all (m,b) such that y = mx + b x y m b m 0 b 0 image space Hough space
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CS440 / ECE 448 – Spring 2008 Lecture #6 Finding lines in an image Connection between image (x,y) and Hough (m,b) spaces A line in the image corresponds to a point in Hough space To go from image space to Hough space: given a set of points (x,y), find all (m,b) such that y = mx + b What does a point (x 0 , y 0 ) in the image space map to? x y m b image space Hough space A: the solutions of b = -x 0 m + y 0 this is a line in Hough space x 0 y 0
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CS440 / ECE 448 – Spring 2008 Lecture #6 Hough transform algorithm Typically use a different parameterization d is the perpendicular distance from the line to the origin θ is the angle this perpendicular makes with the x axis Why? Basic Hough transform algorithm 1. Initialize H[d, θ ]=0 2. for each edge point I[x,y] in the image for θ = 0 to 180 H[d, θ ] += 1 1. Find the value(s) of (d, θ ) where H[d, θ ] is maximum 2. The detected line in the image is given by What’s the running time (measured in # votes)?
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CS440 / ECE 448 – Spring 2008 Lecture #6 Extensions Extension 1: Use the image gradient 1. same 2.
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