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Bài giảng Nhập môn thị giác máy tính - Chapter 7: Edge detection - Lê Thanh Hải

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Chapter 7 – Edge Detection  
7-1  
Chapter 7  
Edge Detection  
Prof. Fei-Fei Li, Stanford Univers ity  
Department of Mechatronics  
Chapter 7 – Edge Detection  
7-2  
Contents  
Edge detection  
• Canny edge detector  
Department of Mechatronics  
ge Detection  
7-3  
(A) Cave painting 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.).  
Department of Mechatronics  
Chapter 7 – Edge Detection  
7-4  
We know edges are special from human  
(mammalian) vision studies  
Department of Mechatronics  
Chapter 7 – Edge Detection  
7-5  
Walther, Chai, Caddigan, Beck & Fei-‐Fei, PNAS, 2011  
Department of Mechatronics  
Chapter 7 – Edge Detection  
7-6  
Edge detection  
• Goal: Identify sudden changes  
(discontinuities) in an image  
– Intuitively, most semantic and shape  
information from the image can be  
encoded in the edges  
– More compact than pixels  
• Ideal: artist’s line drawing (but  
artist is also using object ‐ level  
knowledge)  
Source: D. Lowe  
Department of Mechatronics  
Chapter 7 – Edge Detection  
7-7  
Origin of Edges  
surface normal discontinuity  
depth discontinuity surface  
color discontinuity  
illumination discontinuity  
• Edges are caused by a variety of factors  
Department of Mechatronics  
Chapter 7 – Edge Detection  
7-8  
Characterizing edges  
• An edge is a place of rapid change in the image intensity  
function  
intensity function  
image  
(along horizontal scanline)  
first derivative  
edges correspond to  
extrema of derivative  
Department of Mechatronics  
Chapter 7 – Edge Detection  
7-9  
Image gradient  
• The gradient of an image:  
The gradient points in the direction of most rapid increase in intensity. The  
gradient direction is given by  
• How does this relate to the direction of the edge?  
The edge strength is given by the gradient magnitude  
Source: Steve  
Seitz  
Department of Mechatronics  
Chapter 7 – Edge Detection  
7-10  
Differentiation and convolution  
• We could approximate this  
• Recall, for 2D function,  
as  
f(x,y):  
f x , y f x, y   
f x , y f x , y   
   
   
f  
x  
f  
x  
n1  
n
lim  
0   
x  
• (which is obviously a  
convolution)  
• This is linear and shift  
invariant, so must be the result  
of a convolution.  
-1  
1
Source: D. Forsyth, D. Lowe  
Department of Mechatronics  
Chapter 7 – Edge Detection  
7-11  
Finite difference filters  
• Other approximations of derivative filters  
Department of Mechatronics  
Chapter 7 – Edge Detection  
7-12  
Finite differences: example  
Which one is the gradient in the x-direction? How about y‐direction?  
Department of Mechatronics  
14  
Chapter 7 – Edge Detection  
7-13  
Effects of noise  
• Consider a single row or column of the image  
– Plotting intensity as a function of position gives a signal  
Where is the edge?  
Department of Mechatronics  
Chapter 7 – Edge Detection  
7-14  
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?  
Department of Mechatronics  
Chapter 7 – Edge Detection  
7-15  
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  
Department of Mechatronics  
Chapter 7 – Edge Detection  
7-16  
Solution: smooth first  
f
g
f * g  
d
f * g  
dx  
d
• To find edges, look for peaks in  
f * g  
Source: S.  
Seitz  
dx  
Department of Mechatronics  
Chapter 7 – Edge Detection  
7-17  
Derivative theorem of convolution  
• Differentiation is convolution, and convolution is associative:  
d
d
f * g f * g  
dx  
dx  
• This saves us one operation:  
f
g
풅
풇 ∗ 품  
풅풙  
Source: S. Seitz  
Department of Mechatronics  
19  
Chapter 7 – Edge Detection  
7-18  
Derivative of Gaussian filter  
* [1 -1] =  
• Is this filter separable?  
Department of Mechatronics  
Chapter 7 – Edge Detection  
7-19  
Derivative of Gaussian filter  
y-direction  
x-direction  
• Which one finds horizontal/vertical edges?  
Department of Mechatronics  
Chapter 7 – Edge Detection  
7-20  
Tradeoff between smoothing and localization  
1 pixel  
3 pixels  
7 pixels  
• Smoothed derivative removes noise, but blurs edge.  
Also finds edges at different “scales”.  
Department of Mechatronics  
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