canny_edge_detection_digital_image_p.ppt

Canny Edge Detector 1
Canny Edge Detector
1) Smooth image with a Gaussian
• optimizes the trade-off between noise filtering
and edge localization
2) Compute the Gradient magnitude using
approximations of partial derivatives
• 2x2 filters
3) Thin edges by applying non-maxima
suppression to the gradient magnitude
4) Detect edges by double thresholding

Gradient
• At each point convolve with
• magnitude and orientation of the Gradient are
computed as
• Avoid floating point arithmetic for fast computation









1
1
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x
G 

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

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y
G
2
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]
,
[
]
,
[
]
,
[ j
i
Q
j
i
P
j
i
M 

])
,
[
],
,
[
(
tan
]
,
[ 1
j
i
P
j
i
Q
j
i 



Non-Maxima Suppression
• Thin edges by keeping large values of Gradient
– not always at the location of an edge
– there are many thick edges
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Non-Maxima Suppression (2)
• Thin the broad ridges in M[i,j] into ridges that are only one
pixel wide
• Find local maxima in M[i,j] by suppressing all values along
the line of the Gradient that are not peak values of the ridge
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gaps
false
edges

Gradient Orientation
• Reduce angle of Gradient θ[i,j] to one of the 4 sectors
• Check the 3x3 region of each M[i,j]
• If the value at the center is not greater than the 2
values along the gradient, then M[i,j] is set to 0

local
maxima
removed
depends
on condition
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• The suppressed magnitude image will contain many
false edges caused by noise or fine texture
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false edges

Thresholding
• Reduce number of false edges by applying a
threshold T
– all values below T are changed to 0
– selecting a good values for T is difficult
– some false edges will remain if T is too low
– some edges will disappear if T is too high
– some edges will disappear due to softening of the
edge contrast by shadows

Double Thresholding
• Apply two thresholds in the suppressed image
– T2 = 2T2
– two images in the output
– the image from T2 contains fewer edges but has gaps in the
contours
– the image from T1 has many false edges
– combine the results from T1 and T2
– link the edges of T2 into contours until we reach a gap
– link the edge from T2 with edge pixels from a T1 contour until
a T2 edge is found again

T2=2 T1=1
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gaps
filled
from
T1
• A T2 contour has pixels along the green arrows
• Linking: search in a 3x3 of each pixel and connect the
pixel at the center with the one having greater value
• Search in the direction of the edge (direction of Gradient)

Line Detection
• Model of a line: two edges with opposite
polarity in distance less than the size of the
smoothing filter
– edge detection filters respond to step edges
– they do not provide meaningful response to lines
• Apply nonmaxima suppression on the
smoothed output
– a line is the derivative of a step  the derivative
step of the Canny algorithm is not necessary

canny_edge_detection_digital_image_p.ppt

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