Active Contour Model (Snake)

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Active Contour Model (Snake)

• rew

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Outline

• Introduce Active Contour Model

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Active Contour Model

• First introduced by Kass, Witkin, and
  Terzopoulos1987

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Why snake?

• The shape of many objects is not easily
  represented by rigid primitives.
• Natural objects, such as bananas, have similar
  recognizable shapes. But no two bananas are
  exactly the same.
• In medical imaging, objects are similar but not
  exact. An exact representation of a vein's shape,
  for example, cannot be given.
• Some objects, such as lips, change over time.

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Whats snake?

• Optimization technique
• Based on a spline
• Minimization the energies of the spline
• Deforms to fit local minima
• Local, not global, so initial location must be
  provided

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Whats snake?

• Customizable
• Initialization
• Weights
• User constraints

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Energy of Snake

• A snake is defined as an energy function. To find
  the best fit between a snake and an object's
  shape, we minimize the energy.
• Where the snake is parametrically defined as
  v(i) (x(i),y(i))
• Einternal Internal spline energy caused by
  stretching and bending.
• Eimage Measure of the attraction of image
  features such as contours.
• Econstraint Measure of external constrains
  either from higher level shape information or
  user applied energy.

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Internal Energy

• The internal energy provides a smoothness
  constraint.
• a(i) is a measure of the elasticity of the snake.
• ß(i) is a measure of the stiffness of the
  snake.
• The first order term makes the snake act like a
  membrane
• The constant a controls the tension along the
  spine.
• The second order term makes the snake act like a
  thin plate
• The constant ß controls the rigidity of the
  spine
• If ß0 then the function is discontinuous in its
  tangent, i.e. it may develop a corner at that
  point.
• If aß0 then this also allows a break in the
  contour, a positional discontinuity.

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Image Energy

• The image energy is derived from the image data.
• where ? is an appropriate weighting function.
• line functional is defined simply by the image
  function,
• The edge functional is defined by
• the termination functional allows terminations
  (i.e. free ends of lines) or corners to attract
  the snake.

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Constraint Energy

• The constraint energy is determined by external
  constraints.
• This energy may come in the form of a spring
  attached by the user. Or, the constraint energy
  may come from higher knowledge about the images
  in question.