4. Detection Of Discontinuities
• There are three basic types of grey level discontinuities that
we tend to look for in digital images:
– Points
– Lines
– Edges
• We typically find discontinuities using masks and
correlation
5. Point Detection
• Point detection can be achieved simply using the mask below:
• Points are detected at those pixels in the subsequent filtered image
that are above a set threshold
-1 -1 1
-1 8 -1
-1 -1 -1
7. Line Detection
• The next level of complexity is to try to detect lines
• The masks below will extract lines that are one pixel thick and running
in a particular direction
8. Line Detection
Binary image of a
wire bond mask
After processing
with -45° line
detector
Result of
thresholding
filtering result
9. Edge Detection
• An edge is a set of connected pixels that lie on the
boundary between two regions
10. Edges & Derivatives
• We have already spoken
about how derivatives
are used to find
discontinuities
• 1st derivative tells us
where an edge is
• 2nd derivative can
be used to show
edge direction
11. Derivatives & Noise
• Derivative based edge detectors are extremely sensitive to noise
• We need to keep this in mind
12. Common Edge Detectors
• Given a 3*3 region of an image the following edge detection filters
can be used
14. Edge Detection Problems
• Often, problems arise in edge detection in that there are is too much
detail
• For example, the brickwork in the previous example
• One way to overcome this is to smooth images prior to edge
detection
15. Edge Detection With Smoothing
Original Image Horizontal Gradient Component
Vertical Gradient Component Combined Edge Image
16. Designing “Optimal”
Edge Detector
Criteria for an “optimal” edge detector:
• Good detection: the optimal detector must minimize the probability
of false positives (detecting spurious edges caused by noise), as well
as that of false negatives (missing real edges)
• Good localization: the edges detected must be as close as possible to
the true edges
• Single response: the detector must return one point only for each true
edge point; that is, minimize the number of local maxima around the
true edge
17. Canny Edge Detector
• This is probably the most widely used edge detector in computer
vision
• Theoretical model: step-edges corrupted by additive Gaussian noise
• Canny has shown that the first derivative of the Gaussian closely
approximates the operator that optimizes the product of signal- to-
noise ratio and localization
18. Canny Edge Detector
1. Filter image with derivative of Gaussian
2. Find magnitude and orientation of gradient
3. Non-maximum suppression:
Thin multi-pixel wide “ridges” down to single pixel width
4. Linking and thresholding (hysteresis):
Define two thresholds: low and high
Use the high threshold to start edge curves and the low threshold to
continue them
21. Interest Points
• Feature detection and matching are an essential component of many
computer vision applications
• For example, we are going to align following images so they can be
seamlessly stitched into composite mosaic
22. Interest Points
• What kinds of features should you detect and then match in order to
establish such an alignment?
• The first kind of feature that we may notice are specific locations in
the images, such as mountain peaks, or interestingly shaped patches
of snow
• These kinds of localized feature are often called keypoint features or
interest points and are often described by the appearance of patches
of pixels surrounding the point location
23. Applications
Interest points are used for:
• Image alignment
• 3D reconstruction
• Motion tracking
• Robot navigation
• Indexing and database
retrieval
• Object recognition
25. Characteristics of good features
• Repeatability
– The same feature can be found in several images despite
geometric and photometric transformations
• Saliency
– Each feature is distinctive
• Compactness and efficiency
– Many fewer features than image pixels
• Locality
– A feature occupies a relatively small area of the image; robust to
clutter and occlusion
26. Corner Detection: Basic Idea
• We should easily recognize the point by looking through a small window
• Shifting a window in any direction should give a large change in intensity
“edge”:
no change along the
edge direction
“corner”:
significant change in
all directions
“flat” region:
no change in all
directions
27. Finding Corners
• Key property: in the region around a corner, image gradient has two
or more dominant directions
• Corners are repeatable and distinctive
28. Harris Corner Detector
1. Compute x and y derivatives of image
1. Compute products of derivatives at every pixel
2. Compute the sums of the products of derivatives at each
pixel
I
G
I x
x
I
G
I y
y
x
x
x
I
I
I
2 y
y
y
I
I
I
2 y
x
xy I
I
I
2
2 ' x
x
I
G
S
2
2 ' y
y
I
G
S
xy
xy I
G
S
'
29. Harris Corner Detector
4. Define the matrix at each pixel
5. Compute the response of the detector at each pixel
6. Threshold on value of R; compute non-max suppression
25-Jun-21 Image Processing and Multimedia Retrieval 29
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,
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y
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M
y
xy
xy
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trace
det M
k
M
R
= g(Ix
2
)g(Iy
2
)-[g(IxIy )]2
-a[g(Ix
2
)+g(Iy
2
)]2
35. Invariance and covariance
• Corner locations should be invariant to photometric transformations and
covariant to geometric transformations
– Invariance: image is transformed and corner locations do not change
– Covariance: if we have two transformed versions of the same image,
features should be detected in corresponding locations
36. Acknowledgment
Some of slides in this PowerPoint presentation are adaptation from
various slides, many thanks to:
1. Dr. Brian Mac Namee, School of Computing at the Dublin Institute
of Technology (http://www.comp.dit.ie/bmacnamee/gaip.htm)
2. James Hays, Computer Science Department, Brown University,
(http://cs.brown.edu/~hays/)
