1) Goal: Given an image corrupted by acquisition noise, locate the edges most likely to be generated by scene elements not by noise.
2) Operations required in edge detection
Sx (a2 ca3 a4 ) (a0 ca7 a6 ) S y (a0 ca1 a2 ) (a6 ca5 a4 )
where c is constant,
a0 a7 a6
e.g., c = 2
-1 0 1
Sx= -2 0 2
-1 0 1
And,
M
S
2 x
S
2 y
a1 a2 [i,j] a3 a5 a4
121
Sy= 0 0 0
-1 -2 -1
3. LapLacian Operator
----Second derivative of a smoothed step edge gives a function that crosses zero at the location of the edge. The second derivative of a 2D function is Laplacian.
the edge. In computation, gradient is approximated
by:
Gx f [i, j 1] f [i, j]
Gy f [i, j] f [i 1, j]
GX = -1 1 for symmetry,
1 GY = -1
-1 1 GX = -1 1
11 GY = -1 -1
2 f
2 f
2 f
x 2 y 2
In discrete computation:
f 2 f [i, j 1] 2 f [i, j] f [i, j 1]
x 2 f 2
f [i 1, j] 2 f [i, j] f [i 1, j] y 2
iii) Edge Location: Decide which local maximum in the filter’s output are edges and which are just caused by noise.
3) Edge descriptions:
edge normal: the direction (unit vector) of the maximum intensity variation at edge pixels. Edge normal is perpendicular to the edge.
Usually, edges are classified as ： step edge, ridge edge roof edge.
We will emphasize on step edge detection in our discussions.
1. Edge detection:
2) Roberts Operator
Gx f [i, j] f [i 1, j 1] Gy f [i 1, j] f [i, j 1] G( f [i, j]) G x G y ;
3) Sobel Operator: — avoid having the gradient calculated about an interpolated point between pixels.
Course 5 Edge Detection
Course 5 Edge Detection
Image Features: local, meaningful, detectable parts of an image.
edge corner texture …
Edges: Edges points, or simply edges, are pixels at or around which the image values undergo a sharp variation.
ii) Edge Enhancement: Design a filter corresponding to edges; that is, the filter’s output is large at edge pixel and low elsewhere, so edge an be located as the maximum in filter’s output.
2. Gradient Based Edge Detection:
1) Gradient:
f fຫໍສະໝຸດ (x,y)G[
f
(
x,
y)]
Gx G y
fx
y
Magnitude
G(x, y)
G
2 x
G
2 y
Direction
(x,
y)
tan
1
G (
y
)
Gx
Note:
The direction of edge normal is perpendicular to
edge direction: perpendicular to edge normal, and therefore tangent to the contour.
edge position: the pixel position where the edge is located.
edge strength: the measurement of local image contrast, e.g., intensity variation along an edge normal.
i) Noise smoothing: suppress as much of the image noise as possible, without destroying the edges. In the absence of specific information of image, assume the noise white and Gaussian.