CS 440 / ECE 448
Introduction to Artificial Intelligence
Fall 2006
Instructor: Eyal Amir
TAs: Deepak Ramachandran (head TA),
Jaesik Choi
CS440 / ECE 448 – Fall 2006
Lecture #2
Today: Computer Vision
• Vision tasks
– Given an image or a set of images formed by
a camera or another sensor (e.g., laser)
– Identify objects
– Identify scene
– Identify actions
– Localize the above
• Vision seems deceptively easy
CS440 / ECE 448 – Fall 2006
Lecture #2
Bug
Face
Human/Felix
Barbara
Steele
Joe Camel
Problem:
Recognizing instances
Recognizing categories
CS440 / ECE 448 – Fall 2006
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CS440 / ECE 448 – Fall 2006
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Variability: Camera position
Illumination
Internal parameters
Within-class variations
CS440 / ECE 448 – Fall 2006
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Object Recognition
• How to detect the class of object and its
identity mechanically?
– Canonical, invariant representation? Eliminate
most of the parameters that govern
appearance?
– Work with the raw pixels?
• How do we use prior knowledge about the
domain?
– Scale, location, possible objects, texture
CS440 / ECE 448 – Fall 2006
Lecture #2
Processing an Image
Image:
array
of pixels
Localizing
matching against
prototype/class
Transformation
to real-world, 3D
coordinates
Segmentation,
aggregation
CS440 / ECE 448 – Fall 2006
Lecture #2
Features:
lines, shapes,
invariants,
colors, positions,
histograms
Today: Detecting Features
Image:
array
of pixels
matching against
prototype/class
Segmentation,
aggregation
CS440 / ECE 448 – Fall 2006
Lecture #2
Features:
lines, shapes,
invariants,
colors, positions,
histograms
Detecting Local Features
• Slide a window over the image
• Detect
– Line
– Edge / Edgel
– Corners
– Direction of the above
CS440 / ECE 448 – Fall 2006
Lecture #2
Edge detection
• Convert a 2D image into a set of curves
– Extracts salient features of the scene
– More compact than
pixels
CS440 / ECE 448 – Fall 2006
Lecture #2
Edge is Where Change Occurs
• Change is measured by derivative in 1D
• Biggest change, derivative has maximum
magnitude
• Or 2nd derivative is zero.
CS440 / ECE 448 – Fall 2006
Lecture #2
Image gradient
• The gradient of an image:
• The gradient points in the direction of most rapid
change in intensity
• The gradient direction is given by:
– how does this relate to the direction of the edge?
• The edge strength is given by the gradient magnitude
CS440 / ECE 448 – Fall 2006
Lecture #2
The discrete gradient
• How can we differentiate a digital image
f[x,y]?
– take discrete derivative (finite difference)
• How would you implement this as a crosscorrelation?
CS440 / ECE 448 – Fall 2006
Lecture #2
The Sobel operator
• Better approximations of the derivatives
– The Sobel operators below are very
commonly used
-1 0 1
1 2 1
-2 0 2
0 0 0
-1 0 1
-1 -2 -1
– The standard defn. of the Sobel operator
omits the 1/8 term
• doesn’t make a difference for edge detection
• the 1/8 term is needed to get the right gradient
value, however
CS440 / ECE 448 – Fall 2006
Lecture #2
Gradient operators
(a): Roberts’ cross operator (b): 3x3 Prewitt operator
(c): Sobel operator (d) 4x4 Prewitt operator
CS440 / ECE 448 – Fall 2006
Lecture #2
Effects of noise
• Consider a single row or column of the image
– Plotting intensity as a function of position gives a signal
• Where is the edge?
CS440 / ECE 448 – Fall 2006
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Solution: smooth first
CS440 / ECE 448 – Fall 2006
Where is the edge?
Peaks in
Lecture #2
Derivative theorem of convolution
• This saves us one operation:
CS440 / ECE 448 – Fall 2006
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Laplacian of Gaussian
Laplacian of Gaussian
operator
• Where is the edge?
• Zero-crossings of
CS440 / ECE 448 – Fall 2006
Lecture #2
bottom graph
2D edge detection filters
Laplacian of Gaussian
Gaussian
•
derivative of Gaussian
is the Laplacian operator:
CS440 / ECE 448 – Fall 2006
Lecture #2
Exercise
• Write an algorithm for detecting edges
• Congratulations! You now know how to
detect edges in computer images!
• … what now?
• A little more edge detection
• Detecting lines and other shapes from
edges
CS440 / ECE 448 – Fall 2006
Lecture #2
Optimal Edge Detection: Canny
• Assume:
– Linear filtering
– Additive iid Gaussian noise
• Edge detector should have:
– Good Detection. Filter responds to edge,
not noise.
– Good Localization: detected edge near true
edge.
– Single Response: one per edge.
CS440 / ECE 448 – Fall 2006
Lecture #2
Optimal Edge Detection: Canny
(continued)
• Optimal Detector is approximately
Derivative of Gaussian.
• Detection/Localization trade-off
– More smoothing improves detection
– And hurts localization.
• This is what you might guess from (detect
change) + (remove noise)
CS440 / ECE 448 – Fall 2006
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The Canny edge detector
• original image
CS440 / ECE 448 – Fall 2006
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The Canny edge detector
• norm of the gradient
CS440 / ECE 448 – Fall 2006
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The Canny edge detector
• thresholding
CS440 / ECE 448 – Fall 2006
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The Canny edge detector
• Thinning (non-maximum suppression)
CS440 / ECE 448 – Fall 2006
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Non-maximum suppression
• Check if pixel is local maximum along
gradient direction
CS440 / ECE 448 – Fall 2006
– requires checking
interpolated
pixels p and r
Lecture
#2
Predicting
the next
edge point
Assume the
marked point is an
edge point. Then
we construct the
tangent to the edge
curve (which is
normal to the
gradient at that
point) and use this
to predict the next
points (here either
r or s).
CS440 / ECE 448 – Fall 2006
Lecture #2
(Forsyth & Ponce)
Hysteresis
• Check that maximum value of gradient
value is sufficiently large
– drop-outs? use hysteresis
• use a high threshold to start edge curves and a low
threshold to continue them.
CS440 / ECE 448 – Fall 2006
Lecture #2
Effect of  (Gaussian kernel size)
original
Canny with
• The choice of
– large
– small
Canny with
depends on desired behavior
detects large scale edges
detects fine features
CS440 / ECE 448 – Fall 2006
Lecture #2