电子科技大学：《图像处理及应用 Image Processing and Application》课程教学资源（课件讲稿）Chapter 10 Image Segmentation

电子科线女学光电科学与工程学院 SCHOOL OF OPTOELECTRONIC SCIENCE AND ENGINEERING OF UESTC 4.Basic Edge Detection The image gradient and its properties The gradient of an image fx,y)at location(x,y)is defined as r-a-- Some properties about this gradient vector It points in the direction of maximum rate of change of image at (x.y) ·Magnitude:M(x,y)=mag(Vf)=√g+g? Angle: a(x,y)=tan

✓ Some properties about this gradient vector ✓ The gradient of an image f(x,y) at location (x,y) is defined as ( ) T x y g f f f grad f g x y        = = =           ( ) ( ) 2 2 , M x y mag f g g =  = +x y 4. Basic Edge Detection ◼ The image gradient and its properties ( ) 1 , tan y x g x y g  −   =     ◼ It points in the direction of maximum rate of change of image at (x,y) ◼ Magnitude: ◼ Angle:

电子科线女学光电科学与工程学院 SCHOOL OF OPTOELECTRONIC SCIENCE AND ENGINEERING OF UESTC Example:Properties of the gradient Gradient vector Gradient vector gray pixels:0 white pixels:1 《 a-90° 耳dgedirection a b c FIGURE 10.12 Using the gradient to determine edge strength and direction at a point. Note that the edge is perpendicular to the direction of the gradient vector at the point where the gradient is computed.Each square in the figure represents one pixel. 18x =-450 Note:The edge is perpendicular to the direction of the gradient vector

 2 2 , T x y g f f f g x y        = = = −           Note: The edge is perpendicular to the direction of the gradient vector. 1 0 tan 45 x y g g  −   = = −       Example: Properties of the gradient gray pixels: 0 white pixels: 1 x: ↑, y:←

电子科发女学光电科学与工程学院 SCHOOL OF OPTOELECTRONIC SCIENCE AND ENGINEERING OF UESTC 4.Basic edge detection Gradient operator ab -1 -1 FIGURE 10.13 Vf= One-dimensional masks used to gy」 implement Eqs. (10.2-12)and (10.2-13). ■Digital difference 8:=of(x,y)/ox=f(x+1,y)-f(x,y) 8,=0f(x,y)/∂y=f(x,y+1)-f(xy)

x y f g x f g f y          = =               ( , ) ( 1, ) ( , ) ( , ) ( , 1) ( , ) x y g f x y x f x y f x y g f x y y f x y f x y =   = + − =   = + − ◼ Digital difference 4. Basic edge detection ◼ Gradient operator

电子科枝女学光电科学与工程学院 "Omeo时the true fatherso时the Internet" -USA Today SCHOOL OF OPTOELECTRONIC SCIENCE AND ENGINEERING OF UESTC 4.Basic edge detection Lawrence G.Roberts(1937-) ■ Roberts operator(1963) af 0 8x =2g-25 ar gy dy 3-26 Zi Z Z3 ZA Z5 Z6 Z Zs 0← Roberts L G.Machine Perception of Three-dimention[D].Massachusetts Institute of Technology,1963

1 0 0 1   −     0 1 1 0   −     000 0 1 0 0 0 1     −       ◼ Roberts operator(1963) 0 0 0 0 0 1 0 1 0     −       4. Basic edge detection z1 z2 z3 z4 z5 z6 z7 z8 z9 9 5 8 6 x y f g z z x f g z z y  = = −   = = −  Roberts L G. Machine Perception of Three-dimention[D]. Massachusetts Institute of Technology, 1963. Lawrence G. Roberts(1937-)

电子件枝女学光电科学与工程学院 SCHOOL OF OPTOELECTRONIC SCIENCE AND ENGINEERING OF UESTC 4.Basic edge detection Prewitt operator (1970) 8= fx,》=(,++2）-(++3) Ox fx,2=(3,+6+2）-(3+24+27) ay ZI Z2 Zs -1-1-1 -1 ZA Z5 Z6 8x= 000 8 1 Z Zs Zo 1 11 Prewitt J M S.Object enhancement and extraction[J].Picture processing and Psychopictorics,1970,10(1):15-19

( ) ( ) ( ) ( ) 7 8 9 1 2 3 3 6 9 1 4 7 ( , ) ( , ) x y f x y g z z z z z z x f x y g z z z z z z y  = = + + − + +   = = + + − + +           − − − 1 1 1 0 0 0 1 1 1 1 0 1 1 0 1 1 0 1   −   −       − gx = gy = ◼ Prewitt operator (1970) 4. Basic edge detection z1 z2 z3 z4 z5 z6 z7 z8 z9 Prewitt J M S. Object enhancement and extraction[J]. Picture processing and Psychopictorics, 1970, 10(1): 15-19