1	Announcements Mailing list: csep576@cs.washington.edu you should have received messages Project 1 out today (due in two weeks) Carpools
2	Edge Detection Today’s reading Forsyth, chapters 8, 15.1
3	Edge detection Convert a 2D image into a set of curves Extracts salient features of the scene More compact than pixels
4	Origin of Edges Edges are caused by a variety of factors
5	Edge detection How can you tell that a pixel is on an edge?
6	Image gradient The gradient of an image: The gradient points in the direction of most rapid change in intensity
7	The discrete gradient How can we differentiate a digital image F[x,y]?
8	The discrete gradient How can we differentiate a digital image F[x,y]? Option 1: reconstruct a continuous image, then take gradient Option 2: take discrete derivative (finite difference)
9	The Sobel operator Better approximations of the derivatives exist The Sobel operators below are very commonly used
10	Effects of noise Consider a single row or column of the image Plotting intensity as a function of position gives a signal
11	Solution: smooth first
12	Derivative theorem of convolution This saves us one operation:
13	Laplacian of Gaussian Consider
14	2D edge detection filters
15	The Canny edge detector original image (Lena)
16	The Canny edge detector
17	The Canny edge detector
18	Non-maximum suppression Check if pixel is local maximum along gradient direction requires checking interpolated pixels p and r
19	The Canny edge detector
20	Effect of s (Gaussian kernel spread/size)
21	Edge detection by subtraction
22	Edge detection by subtraction
23	Edge detection by subtraction
24	Gaussian - image filter
25	An edge is not a line...
26	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
27	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
28	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 (x₀, y₀) in the image space map to?
29	Hough transform algorithm Typically use a different parameterization d is the perpendicular distance from the line to the origin q is the angle this perpendicular makes with the x axis Why?
30	Hough transform algorithm Typically use a different parameterization d is the perpendicular distance from the line to the origin q is the angle this perpendicular makes with the x axis Why? Basic Hough transform algorithm Initialize H[d, q]=0 for each edge point I[x,y] in the image for q = 0 to 180 H[d, q] += 1 Find the value(s) of (d, q) where H[d, q] is maximum The detected line in the image is given by What’s the running time (measured in # votes)?
31	Extensions Extension 1: Use the image gradient same for each edge point I[x,y] in the image compute unique (d, q) based on image gradient at (x,y) H[d, q] += 1 same same What’s the running time measured in votes? Extension 2 give more votes for stronger edges Extension 3 change the sampling of (d, q) to give more/less resolution Extension 4 The same procedure can be used with circles, squares, or any other shape
32	Extensions Extension 1: Use the image gradient same for each edge point I[x,y] in the image compute unique (d, q) based on image gradient at (x,y) H[d, q] += 1 same same What’s the running time measured in votes? Extension 2 give more votes for stronger edges Extension 3 change the sampling of (d, q) to give more/less resolution Extension 4 The same procedure can be used with circles, squares, or any other shape