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SNAKES

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that can wiggle in the image. represented as a chain of points ... One more.. The Energy Functional ... Magnitude of the gradient should be LARGE. Dual-Snakes ... – PowerPoint PPT presentation

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Title: SNAKES


1
SNAKES
Adapted from Octavia Camps, Penn. State UCF.
2
Deformable Contours
  • They are also called
  • Snakes
  • Active contours
  • Think of a snake as an elastic band
  • of arbitrary shape
  • sensitive to image gradient
  • that can wiggle in the image
  • represented as a chain of points

3
Main Idea
Drop (initialize) a snake
Let the snake wiggle, attracted by image
gradient, until it glues itself against a
boundary to result in a contour Video Example One
more..
4
The Energy Functional
  • Associate to each possible shape and location of
    the snake a value E.
  • Values should be s.t. the image contour to be
    detected has the minimum value.
  • E is called the energy of the snake.
  • Keep wiggling the snake towards smaller values of
    E.

5
Energy Functional Design
  • We need a function that given a snake state,
    associates to it an Energy value E.
  • The function should be designed so that the snake
    moves towards the contour that we are seeking!

6
What moves the snake?
  • Forces applied to its points

7
Forces moving the snake(External)
  • It needs to be attracted to contours
  • Edge pixels must pull the snake points.
  • The stronger the edge, the stronger the pull.
  • The force is proportional to ? I

8
Forces preserving the snake(Internal)
  • The snake should not break apart!
  • Points on the snake must stay close to each other
  • Each point on the snake pulls its neighbors
  • The farther the neighbors, the stronger the force
  • The force is proportional to the distance Pi
    Pi-1

9
Forces preserving the snake(Internal)
  • The snake should be smooth
  • Penalize high curvature
  • Force proportional to snake curvature

10
Snake Forces
Edge attraction
Continuity
Smoothness
11
Snake stateContour Parametrization
Consider a contour parametrization cc(s) where s
is the arc length
s
Each point Pi on the contour has coordinates
(xi(s),yi(s))
Pi
12
Snake Energy Functional
Given a snake with N points p1,p2,,pN
Define the following Energy Functional
Where
Continuity
Smoothness
Edgeness
ai,bi,ci are weights to control influence
13
Continuity Term
Given a snake with N points p1,p2,,pN
Let d be the average distance between points
Define the continuity term of the Energy
Functional
Distance between points should be kept close to
average
14
Smoothness Term
Given a snake with N points p1,p2,,pN
Curvature should be kept small
Define the smoothness term of the Energy
Functional
Second derivative
15
Edgeness Term
Given a snake with N points p1,p2,,pN
Define the edgeness term of the Energy Functional
Magnitude of the gradient should be LARGE
16
Dual-Snakes
  • movie
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