Outline
• Announcement
• Perceptual organization, grouping, and segmentation
– Hough transform
– Read Chapter 17 of the textbook
File: week14-m.ppt

Announcement
• Class evaluation this coming Friday
– Please come to class on time so that we can start the class evaluation first
• Class presentation
– Your presentation should be about 20 minutes following a brief question-and-answer section which is about 5 minutes
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Introduction – cont.
• Computational models/implementations
– There are generally two kinds of computational models/implementations for segmentation
• Based on homogeneity measure to group pixels with similar attributes together
– Region growing/split-and-merge
• Based on discontinuity of attributes to detect boundaries/contours of regions
– Active contours
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Introduction – cont.
• Hough transform
– An algorithm to group edge points from edge detectors or from any other process
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Hough Transform
• Straight line case
– Consider a single isolated edge point ( x i
, y i
)
• There are an infinite number of lines that could pass through the points
– Each of these lines can be characterized by some particular equation y i
 mx i
 c
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Hough Transform – cont.
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Hough Transform – cont.
• Hough transform algorithm
1. Find all of the desired feature points in the image
2. For each feature point
For each possibility i in the accumulator that passes through the feature point
Increment that position in the accumulator
3. Find local maxima in the accumulator
4. If desired, map each maximum in the accumulator back to image space
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Hough Transform – cont.
• A better way of expressing lines for hough transform x i cos
  y i sin
  
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Hough Transform – cont.
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Hough Transform – cont.
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Hough Transform – cont.
• Circles
– Hough transform can also be used for circles
( x
 a )
2 
( y
 b )
2  r
2
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Hough Transform – cont.
Here the radius is fixed
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Hough Transform – cont.
A 3-dimensional parameter space for circles in general
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Hough Transform – cont.
• More complicated shapes
– As you can see, the hough transform can be used to find shapes with arbitrary complexity as long as we can describe the shape with some fixed number of parameters
– The number of parameters required indicates the dimensionality of the accumulator
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Generalized Hough Transform
• Some shapes may not be easily expressed using a small set of parameters
– In this case, we explicitly list all the points on the shape
– This variation of Hough transform is known as generalized Hough transform
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Hough Transform – cont.
• Implementation issues
– Quantization of the accumulator space
– Utilization of additional information
• For line-matching Hough transform, the orientation of an edge point from the Canny edge detector can be used to limit the votes in the accumulator space
– Smoothing the accumulator
• To reduce the effects of noise
– Gray-level voting
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Hough Transform – cont.
• Implementation issues - continued
– Refining the accumulator
• Find a maximum and vote only near the maximum with a higher resolution of the parameter space
– Randomized Hough transform
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