Edge Detection
by
Scale Multiplication
Vahid Rezaei
Professor William Hoff
Course Project for Computer Vision
Department of Electrical Engineering and Computer Science
Spring 2012
Outline
• Review of Edge Detection methods
• Scale Multiplication approach
 1D signals
 The discrimination of singularity and noise.
 The scale multiplication.
 The thresholding.
 2D images
• Simulations
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Outline
• Review of Edge Detection methods
• Scale Multiplication approach
 1D signals
 The discrimination of singularity and noise.
 The scale multiplication.
 The thresholding.
 2D images
• Simulations
3
Review – Why Edge Detection?


Edges are used to show considerable change
in some physical aspect of the image such as
intensity changes in a neighborhood.
Applications are in object recognition, image
registration, image segmentation, data
compression, and image reconstruction .
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Review – Classical Approaches



For example: The Laplacian operators
compute some quantity
related to the
Laplacian of the underlying image gray tone
intensity surface.
The zero-crossing operators determine
whether there is a zero-crossing within the
pixel or not.
A threshold value is used for gradient to find
the edges.
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Review – Classical Approaches
The major drawbacks of such operators are:
A. It is difficult to find the actual location of
the edge.
B. The choice of threshold value (and other
parameters) is based on trial and error
which may leads in meaningless edges.
C. dealing with noisy images is another
challenge for classical approaches.

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Review – Canny Edge Detector



Canny’s work on edge detection is based on
three
criteria:), and
good
n(x)~N(0,
G(x) isdetection,
a step edge withgood
of A.
localization, magnitude
low
spurious
response.
(Optimal edge detector)
Consider the 1D-signal W(x)=G(x)+n(x) and
assume
is a FIR filter on [-T,T] (edgedetector filter).
The response of f toW :
.
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Review – Canny Edge Detector

Canny assumed the edges are the local maxima
of
and introduced the following criteria:
1. Good detection: It simply means to keep the
2. Good Localization: It means the detected edge
SNR at x=0 as high as possible.
should be as close as possible to x=0.
3. Low Spurious Response: Since input is single
step, it is not allowed to have multiple maxima.
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Outline
• Review of Edge Detection methods
• Scale Multiplication approach
 1D signals
 The discrimination of noise.
 The scale multiplication.
 The thresholding.
 2D images
• Simulations
9
The idea of Scale-Multiplication
An important issue is the scale of detection filter
where: small-scaled filter is sensetive to noise
and large-scaled filter filters some useful
details.
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Assumptions
∗

2

2
2

∗θ
1.4
1.2
1
0.8
0.6
0.4
0.2
0
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
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Edge vs Noise


Local regularity can be measured by Lipschitz
exponent.
A function f(x) is Lipschitz
at
iff there
exists a constant such that in the neighborhood
of


=0 for Step Edge & =-0.5 for White Noise.
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Scale Multiplication

13
Thresholding
.

for
c
.
Where
1
2
.
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2D Image

,

,





,
,
.
.
15
2D Image

,
,
,

,
,
.
,
,
.
,
arctan
0.8
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Outline
• Review of Edge Detection methods
• Scale Multiplication approach
 1D signals
 The discrimination of singularity and noise.
 The scale multiplication.
 The thresholding.
 2D images
• Performance evaluation
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Performance evaluation
Figure of Merrit
(The greater the F,
better detection )


MS of Distance
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Performance evaluation

Noisy cameraman with SNR=16.5278 dB [Canny vs
SMED]
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Performance evaluation

LoG vs SMED
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Performance evaluation

Canny vs SMED
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Conclusion


While the classic methods are sensitive to
“noise”, the proposed method is able to
handle the effect of the noise on detected
edges.
Tuning of different parameters is a concern
in other methods while the proposed method
is almost 100% automatic.
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References
1.
2.
Zhang, Bao; “Edge Detection by Scale
Multiplication in Wavelet Domain”; Pattern
Recognition Letters; pp. 1771-1784; Vol 23;
2002.
Bao, Zhang, Wu; “Canny Edge Detection
Enhancement by Scale Multiplication”; IEEE
Trans. On Pattern Analysis and Machine
Intelligence; pp. 1485-1490; Vol 27 No 9; 2005
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