Active Contour Model (Snake)

1. Active Contour Model (Snake) rew

2. Outline • Introduce Active Contour Model

3. Active Contour Model • First introduced by Kass, Witkin, and Terzopoulos[1987]

4. 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.

5. What’s 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

6. What’s snake? • Customizable • Initialization • Weights • User constraints

7. 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.

8. Internal Energy • The internal energy provides a smoothness constraint. • α(i) is a measure of the elasticity of the snake. • β(i) is a measure of the stiffness of the snake. • The first order term makes the snake act like a membrane • The constant α controls the tension along the spine. • The second order term makes the snake act like a thin plate • The constant β controls the rigidity of the spine • If β=0 then the function is discontinuous in its tangent, i.e. it may develop a corner at that point. • If α=β=0 then this also allows a break in the contour, a positional discontinuity.

9. Image Energy • The image energy is derived from the image data. • where ω 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.

10. 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.