Outline
• Perceptual organization, grouping, and
segmentation
– Active contours and deformable templates
File: week14-m.ppt
Introduction
• Segmentation
– Roughly speaking, segmentation is to partition
the images into meaningful parts that are
relatively homogenous in certain sense
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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.
• Problems with edge detection
– Edge detectors do not give rise to meaningful
contours of objects due to their intrinsically local
nature
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Active Contours
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SNAKE
• A snake is an active contour defined by
( s )  ( x( s ), y ( s ))
– Was introduced first by Kass, Witkin, and
Terzopoulos
– An energy is associate with each contour
1
Esnake   Eint ((s))  Eimage((s))  Econ ((s))ds
0
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SNAKE – cont.
• The internal energy term provides a
smoothness constraint on contours
 d ( s ) 
 d( s ) 

Eint   ( s )
   ( s )
2
 ds 
 ds 
2
2
2
– What kind of contours is preferred
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SNAKE – cont.
• The image energy term provides an image
related measure
Eimage   | I  I |
– Should have a large gradient along the contour,
i.e., the contour should consist of edge points
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SNAKE – cont.
• The constraint term can be used to impose
additional constraints
– For example, some control points are available
and they should be very close to the contour
• Called spring
– Some information may indicate the contours
should be as far as possible from some points
• Called volcano
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SNAKE – cont.
• Minimization of the energy
– This is a standard variational problem
• In order to apply calculus of variations, one needs to
use a smooth representation of contours
– Minimization by steepest descent
• Requires the functional derivatives of the energy
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SNAKE – cont.
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SNAKE – cont.
• Problems with the original SNAKE model
– A good initial result must be available
• If the initial conditional is too far from the correct
solution, the snake might be trapped to a meaningless
local minimum
• Balloon model
– Introduce an additional term which pushes the
contour out or in along its normal
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Deformable Templates
• Active contours are closely related to
deformable templates
– Objects are often represented by their contours
– Object recognition is then to deform the standard
contour such that the energy is minimum
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Deformable Templates – cont.
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Deformable Templates – cont.
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Deformable Templates – cont.
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Deformable Templates – cont.
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Tracking
• Active contours can be used very effectively
for tracking
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Tracking – cont.
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Lip-Reading
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Actor-Driven Facial Animation
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Human-computer Interaction
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Traffic Monitoring
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Medical Image Analysis
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Medical Image Analysis
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