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.
November 18, 2014
Computer Vision
Lecture 18: Object Recognition II
1
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.
November 18, 2014
Computer Vision
Lecture 18: Object Recognition II
2
Corner Detection with FAST
November 18, 2014
Computer Vision
Lecture 18: Object Recognition II
3
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.
November 18, 2014
Computer Vision
Lecture 18: Object Recognition II
4
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.
November 18, 2014
Computer Vision
Lecture 18: Object Recognition II
5
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.
November 18, 2014
Computer Vision
Lecture 18: Object Recognition II
6
Key Point Description with BRIEF
November 18, 2014
Computer Vision
Lecture 18: Object Recognition II
7
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.
November 18, 2014
Computer Vision
Lecture 18: Object Recognition II
8
Key Point Matching with BRIEF
November 18, 2014
Computer Vision
Lecture 18: Object Recognition II
9
How do Neural Networks (NNs) work?
• NNs are able to learn by adapting their
connectivity patterns so that the organism
improves its behavior in terms of reaching certain
(evolutionary) goals.
• The strength of a connection, or whether it is
excitatory or inhibitory, depends on the state of a
receiving neuron’s synapses.
• The NN achieves learning by appropriately
adapting the states of its synapses.
November 18, 2014
Computer Vision
Lecture 18: Object Recognition II
10
Supervised Function Approximation
In supervised learning, we train an artificial NN (ANN)
with a set of vector pairs, so-called exemplars.
Each pair (x, y) consists of an input vector x and a
corresponding output vector y.
Whenever the network receives input x, we would like
it to provide output y.
The exemplars thus describe the function that we
want to “teach” our network.
Besides learning the exemplars, we would like our
network to generalize, that is, give plausible output
for inputs that the network had not been trained with.
November 18, 2014
Computer Vision
Lecture 18: Object Recognition II
11
An Artificial Neuron
synapses
x1
neuron i
x2
Wi,1
Wi,2
…
…
xi
Wi,n
xn
n
net input signal
net i (t )   wi , j (t ) x j (t )
j 1
output
November 18, 2014
x i (t )  f i (neti (t ))
Computer Vision
Lecture 18: Object Recognition II
12
Linear Separability
n
w x
f ( x1 , x2 ,..., xn )  1, if
i i
i 1

 0, otherwise
Input space in the two-dimensional case (n = 2):
x2
-3 -2 -1
0
3
2
1
1
1
-1
-2
-3
2
1
3
x1
w1 = 1, w2 = 2,
=2
November 18, 2014
x2
-3 -2 -1
3
2
1
1
1
-1
-2
-3
2
0
3
x1
w1 = -2, w2 = 1,
=2
Computer Vision
Lecture 18: Object Recognition II
x2
-3 -2 -1
3
2
1
1
-1
-2
-3
2
0
3
x1
w1 = -2, w2 = 1,
=1
13