Edge Detection

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#信息技术

本章节介绍了边缘检测相关的知识，介绍了一款简单的边缘检测器，另外还介绍了我们目前使用最广泛的视觉边缘检测器canny edge detector，介绍了使用方法，操作方式，另外介绍了边缘检测的一种合适的方式RANSAC.

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1 . Lecture 5: Edge Detec.on Professor Fei-‐Fei Li Stanford Vision Lab Fei-Fei Li! Lecture 5 - !1 2-‐Oct-‐14

2 . What we will learn today •  Edge detec.on •  A simple edge detector •  Canny edge detector •  A model ﬁIng method for edge detec.on –  RANSAC Some background reading: Forsyth and Ponce, Computer Vision, Chapter 8, Chapter 15.5.2 Fei-Fei Li! Lecture 5 - !2 2-‐Oct-‐14

3 . (A)  Cave pain.ng at Chauvet, France, about 30,000 B.C.; (B)  Aerial photograph of the picture of a monkey as part of the Nazca Lines geoplyphs, Peru, about 700 – 200 B.C.; (C)  Shen Zhou (1427-‐1509 A.D.): Poet on a mountain top, ink on paper, China; (D)  Line drawing by 7-‐year old I. Lleras (2010 A.D.). Fei-Fei Li! Lecture 5 - !3 2-‐Oct-‐14

4 . We know edges are special from human (mammalian) vision studies Hubel & Wiesel, 1960s Fei-Fei Li! Lecture 5 - !4 2-‐Oct-‐14

5 . We know edges are special from human (mammalian) vision studies Fei-Fei Li! Lecture 5 - !5 2-‐Oct-‐14

6 . Walther, Chai, Caddigan, Beck & Fei-‐Fei, PNAS, 2011 Fei-Fei Li! Lecture 5 - !6 2-‐Oct-‐14

7 . Edge detec.on •  Goal: Iden.fy sudden changes (discon.nui.es) in an image –  Intui.vely, most seman.c and shape informa.on from the image can be encoded in the edges –  More compact than pixels •  Ideal: ar.st’s line drawing (but ar.st is also using object-‐level knowledge) Source: D. Lowe Fei-Fei Li! Lecture 5 - !7 2-‐Oct-‐14

8 . Why do we care about edges? •  Extract informa.on, recognize objects •  Recover geometry and Vertical vanishing point (at infinity) Vanishing viewpoint line Vanishing Vanishing point point Source: J. Hayes Fei-Fei Li! Lecture 5 - !8 2-‐Oct-‐14

9 . Origins of edges surface normal discontinuity depth discontinuity surface color discontinuity illumination discontinuity Source: D. Hoiem Fei-Fei Li! Lecture 5 - !9 2-‐Oct-‐14

10 . Closeup of edges Surface normal discon.nuity Source: D. Hoiem Fei-Fei Li! Lecture 5 - !10 2-‐Oct-‐14

11 . Closeup of edges Depth discon.nuity Source: D. Hoiem Fei-Fei Li! Lecture 5 - !11 2-‐Oct-‐14

12 . Closeup of edges Surface color discon.nuity Source: D. Hoiem Fei-Fei Li! Lecture 5 - !12 2-‐Oct-‐14

13 . What we will learn today •  Edge detec.on •  A simple edge detector •  Canny edge detector •  A model ﬁIng method for edge detec.on –  RANSAC Fei-Fei Li! Lecture 5 - !13 2-‐Oct-‐14

14 . Characterizing edges •  An edge is a place of rapid change in the image intensity func.on intensity function image (along horizontal scanline) first derivative edges correspond to extrema of derivative Fei-Fei Li! Lecture 5 - !14 2-‐Oct-‐14

15 . Image gradient •  The gradient of an image: The gradient points in the direc.on of most rapid increase in intensity The gradient direc.on is given by •  how does this relate to the direc.on of the edge? The edge strength is given by the gradient magnitude Source: Steve Seitz Fei-Fei Li! Lecture 5 - !15 2-‐Oct-‐14

16 . Finite diﬀerences: example •  Which one is the gradient in the x-‐direc.on? How about y-‐direc.on? Fei-Fei Li! Lecture 5 - !16 2-‐Oct-‐14

17 . Intensity proﬁle Intensity Gradient Source: D. Hoiem Fei-Fei Li! Lecture 5 - !17 2-‐Oct-‐14

18 . Eﬀects of noise •  Consider a single row or column of the image –  PloIng intensity as a func.on of posi.on gives a signal Where is the edge? Source: S. Seitz Fei-Fei Li! Lecture 5 - !18 2-‐Oct-‐14

19 . Eﬀects of noise •  Finite diﬀerence ﬁlters respond strongly to noise –  Image noise results in pixels that look very diﬀerent from their neighbors –  Generally, the larger the noise the stronger the response •  What is to be done? –  Smoothing the image should help, by forcing pixels diﬀerent to their neighbors (=noise pixels?) to look more like neighbors Source: D. Forsyth Fei-Fei Li! Lecture 5 - !19 2-‐Oct-‐14

20 . Eﬀects of noise •  Finite diﬀerence ﬁlters respond strongly to noise –  Image noise results in pixels that look very diﬀerent from their neighbors –  Generally, the larger the noise the stronger the response •  What is to be done? –  Smoothing the image should help, by forcing pixels diﬀerent to their neighbors (=noise pixels?) to look more like neighbors Source: D. Forsyth Fei-Fei Li! Lecture 5 - !20 2-‐Oct-‐14

21 . Solu.on: smooth ﬁrst f g f*g d ( f ∗ g) dx d •  To ﬁnd edges, look for peaks in ( f ∗ g) dx Source: S. Seitz Fei-Fei Li! Lecture 5 - !21 2-‐Oct-‐14

22 . Deriva.ve theorem of convolu.on •  Diﬀeren.a.on is convolu.on, and convolu.on is associa.ve: d ( f ∗ g ) = f ∗ d g dx dx •  This saves us one opera.on: f d g dx d f∗ g dx Source: S. Seitz Fei-Fei Li! Lecture 5 - !22 2-‐Oct-‐14

23 . Deriva.ve of Gaussian ﬁlter * [1 -1] = •  Is this ﬁlter separable? Fei-Fei Li! Lecture 5 - !23 2-‐Oct-‐14

24 . Deriva.ve of Gaussian ﬁlter x-direction y-direction Fei-Fei Li! Lecture 5 - !24 2-‐Oct-‐14

25 . Tradeoﬀ between smoothing and localiza.on 1 pixel 3 pixels 7 pixels •  Smoothed deriva.ve removes noise, but blurs edge. Also ﬁnds edges at diﬀerent “scales”. Source: D. Forsyth Fei-Fei Li! Lecture 5 - !25 2-‐Oct-‐14

26 . Implementa.on issues •  The gradient magnitude is large along a thick “trail” Source: D. Forsyth or “ridge,” so how do we iden.fy the actual edge points? •  How do we link the edge points to form curves? Fei-Fei Li! Lecture 5 - !26 2-‐Oct-‐14

27 . Designing an edge detector •  Criteria for an “op.mal” edge detector: –  Good detec,on: the op.mal detector must minimize the probability of false posi.ves (detec.ng spurious edges caused by noise), as well as that of false nega.ves (missing real edges) –  Good localiza,on: the edges detected must be as close as possible to the true edges –  Single response: the detector must return one point only for each true edge point; that is, minimize the number of local maxima around the true edge Fei-Fei Li! Lecture 5 - !27 2-‐Oct-‐14

28 . What we will learn today •  Edge detec.on •  A simple edge detector •  Canny edge detector •  A model ﬁIng method for edge detec.on –  RANSAC Fei-Fei Li! Lecture 5 - !28 2-‐Oct-‐14

29 . Canny edge detector •  This is probably the most widely used edge detector in computer vision •  Theore.cal model: step-‐edges corrupted by addi.ve Gaussian noise •  Canny has shown that the ﬁrst deriva.ve of the Gaussian closely approximates the operator that op.mizes the product of signal-‐to-‐noise ra7o and localiza.on J. Canny, A Computa*onal Approach To Edge Detec*on, IEEE Trans. Pamern Analysis and Machine Intelligence, 8:679-‐714, 1986. Fei-Fei Li! Lecture 5 - !29 2-‐Oct-‐14

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