Canny Edge Detector
The Canny edge detector is a good approximation
of the optimal operator, i.e., the one that maximizes
the product of signal-to-noise ratio and localization.
Let I[i, j] be our input image.
First, we apply a Gaussian filter with standard
deviation  to this image to create a smoothed image
S[i, j].
Then we compute the intensity gradient. For example,
we could use the Sobel filter to obtain the vertical
derivative P[i, j] and the horizontal derivative Q[i, j].
April 21, 2016
Introduction to Artificial Intelligence
Lecture 22: Computer Vision II
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Canny Edge Detector
Once we have computed P[i, j] and Q[i, j], we can
also compute the magnitude m and orientation  of
the gradient vector at position [i, j]:
This is exactly the information that we want – it tells
us where edges are, how significant they are, and
what their orientation is.
However, this information is still very noisy.
April 21, 2016
Introduction to Artificial Intelligence
Lecture 22: Computer Vision II
2
Canny Edge Detector
The first problem is that edges in images are not
usually indicated by perfect step edges in the
brightness function.
Brightness transitions usually have a certain slope
that extends across many pixels.
As a consequence, edges typically lead to wide lines
of high gradient magnitude.
However, we would like to find thin lines that most
precisely describe the boundary between two
objects.
This can be achieved with the nonmaxima
suppression technique.
April 21, 2016
Introduction to Artificial Intelligence
Lecture 22: Computer Vision II
3
Canny Edge Detector
We first assign a sector [i, j] to each pixel according
to its associated gradient orientation [i, j].
There are four sectors with numbers 0, 1, 2, and 3:
180
225
1
0
0
1
270
135
3
3
2
2
2
2
3
315
90
1
3
0
0
1
45
0
April 21, 2016
Introduction to Artificial Intelligence
Lecture 22: Computer Vision II
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Canny Edge Detector
Then we iterate through the array m[i, j] and compare
each element to two of its 8-neighbors.
Which two neighbors we choose depends on the
value of [i, j].
In the following diagram, the numbers in the
neighboring squares of [i, j] indicate the value of [i, j]
for which these neighbors are chosen:
April 21, 2016
1
0
3
2
[i,j]
2
3
0
1
Introduction to Artificial Intelligence
Lecture 22: Computer Vision II
5
Canny Edge Detector
If the value of m[i, j] is less than either of the m-values
in these two neighboring positions, set E[i, j] = 0.
Otherwise, set E[i, j] = m[i, j].
The resulting array E[i, j] is of the same size as m[i, j]
and contains values greater than zero only at local
maxima of gradient magnitude (measured in local
gradient direction).
Notice that an edge in an image always induces an
intensity gradient that is perpendicular to the
orientation of the edge.
Thus, this nonmaxima suppression technique thins
the detected edges to a width of one pixel.
April 21, 2016
Introduction to Artificial Intelligence
Lecture 22: Computer Vision II
6
Canny Edge Detector
However, usually there will still be noise in the array
E[i, j], i.e., non-zero values that do not correspond to
any edge in the original image.
In most cases, these values will be smaller than
those indicating actual edges.
We could then simply use a threshold  to eliminate
the noise, as we did before.
However, this could still leave some isolated edge
outputs caused by strong noise and some gaps in
detected contours.
We can improve this process by using hysteresis
thresholding.
April 21, 2016
Introduction to Artificial Intelligence
Lecture 22: Computer Vision II
7
Canny Edge Detector
Hysteresis thresholding uses two thresholds - a low
threshold L and a high threshold H.
Typically, H is chosen so that 2L  H  3L.
In the first stage, we label each pixel in E[i, j] as
follows:
• If E[i, j] > H then the pixel is an edge,
• If E[i, j] < L then the pixel is no edge (deleted),
• Otherwise, the pixel is an edge candidate.
April 21, 2016
Introduction to Artificial Intelligence
Lecture 22: Computer Vision II
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Canny Edge Detector
In the second stage, we check for each edge
candidate c whether it is connected to an edge via
other candidates (8-neighborhood).
If so, we turn c into an edge.
Otherwise, we delete c, i.e., it is no edge.
This method fills gaps in contours and discards
isolated edges that are unlikely to be part of any
contour.
April 21, 2016
Introduction to Artificial Intelligence
Lecture 22: Computer Vision II
9
Canny Edge Detector - Example
April 21, 2016
Introduction to Artificial Intelligence
Lecture 22: Computer Vision II
10
Canny Edge Detector - Example
0
2
3
2
3
0
0
1
1
1
1
0
0
1
1
2
3
0
0
1
1
2
2
0
0
0
2
3
1
0
0
0
0
0
0
0
Remember the
directions:
1
0
3
2
[i,j]
2
3
0
1
[i, j]
April 21, 2016
Introduction to Artificial Intelligence
Lecture 22: Computer Vision II
11
Canny Edge Detector - Example
April 21, 2016
Introduction to Artificial Intelligence
Lecture 22: Computer Vision II
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Canny Edge Detector - Example
Key Points
Often we are unable to detect the complete contour of
an object or characterize the details of its shape.
In such cases, we can still represent shape
information in an implicit way.
The idea is to find key points in the image of the
object that can be used to identify the objects and
that do not change dramatically when the orientation
or lighting of the object change.
A good choice for this purpose are corners in the
image.
April 21, 2016
Introduction to Artificial Intelligence
Lecture 22: Computer Vision II
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Corner Detection with FAST
A very efficient algorithm for corner detection is called
FAST (Features from Accelerated Segment Test).
For any given point c in the image, we can test whether
it is a corner by:
• Considering the 16 pixels at a radius of 3 pixels
around c and
• finding the longest run (i.e., uninterrupted sequence)
of pixels whose intensity is either
• greater than that of c plus a threshold or
• less that that of c minus the same threshold.
• If the run is at least 12 pixels long, then c is a corner.
April 21, 2016
Introduction to Artificial Intelligence
Lecture 22: Computer Vision II
15
Corner Detection with FAST
April 21, 2016
Introduction to Artificial Intelligence
Lecture 22: Computer Vision II
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Corner Detection with FAST
The FAST algorithm can be made even faster by first
checking only pixels 1, 5, 9, and 13. If not at least three
of them fulfill the intensity condition, we can
immediately rule out that the given point is a corner.
In order to avoid detecting multiple corners near the
same pixel, we can require a minimum distance
between corners.
If two corners are too close, we only keep the one with
the higher corner score.
Such a score can be computed as the sum of intensity
differences between c and the pixels in the run.
April 21, 2016
Introduction to Artificial Intelligence
Lecture 22: Computer Vision II
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Key Point Description with BRIEF
Now that we have identified interesting points in the
image, how can we describe them so that we can
detect them in other images?
A very efficient method is to use BRIEF (Binary Robust
Independent Elementary Features) descriptors.
They can be described with minimal memory
requirement (32 bytes per point).
Their comparison only requires 256 binary operations.
April 21, 2016
Introduction to Artificial Intelligence
Lecture 22: Computer Vision II
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Key Point Description with BRIEF
First, smooth the input image with a 9×9 Gaussian filter.
Then choose 256 pairs of points within a 35×35 pixel
area, following a Gaussian distribution with  = 7 pixels.
Center the resulting mask on a corner c.
For every pair of points, if intensity at the first point is
greater than at the second one, add a 0 to the bitstring,
otherwise add a 1.
The resulting bit string of length 256 is the descriptor for
point c.
April 21, 2016
Introduction to Artificial Intelligence
Lecture 22: Computer Vision II
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Key Point Description with BRIEF
April 21, 2016
Introduction to Artificial Intelligence
Lecture 22: Computer Vision II
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Key Point Matching with BRIEF
In order to compute the matching distance between the
descriptors of two different points, we can simply count
the number of mismatching bits in their description
(Hamming distance).
For example, the bit strings 100110 and 110100 have a
Hamming distance of 2, because they differ in their
second and fifth bits.
In order to find the match for point c in another image,
we can find the pixel in that image whose descriptor
has the smallest Hamming distance to the one for c.
April 21, 2016
Introduction to Artificial Intelligence
Lecture 22: Computer Vision II
21
Key Point Matching with BRIEF
April 21, 2016
Introduction to Artificial Intelligence
Lecture 22: Computer Vision II
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