CSci 8810 Image Processing. Active Contours - SNAKES. Meghana Viswanath March 19, 2009. Object Recognition… How?. Edge detectors. Works well for some images. Not so much for others. Too many spurious edges Linking edges belonging to the same object is difficult. Active Contours or Snakes.
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March 19, 2009
Works well for some images
vi = (xi, yi), i = 0, .... n-1
Find the local minimum and move towards it.
The snake - v(s) = [x(s), y(s)], is defined as a function of a real variable s ϵ [0,1]
The energy of the snake is given by -
Esnake = 0∫1 (Eint + Eext)ds
Eint = (α (v’)2 + β (v”)2)
Eint = Σα (distance b/w control pt. and left neighbour)2
Eext = -|∇I(x,y)|2
Eext = -|∇ I(x,y)|2
Eext = -|∇ (Gσ(x,y) * I(x,y))|2
For a binary image
Eext = I(x,y)
Eext = Gσ(x,y) * I(x,y)External Energy
α v”(s)- β v””(s) -∇Eext = 0
Minimizing energy equation can be interpreted as a force balance equation
Fint + Fext = 0
Fint = α v” - β v””
Fext = −∇ Eext
The internal force Fint discourages stretching and bending while the external potential force Fext pulls the snake toward the desired image edges
Both problems with traditional snakes are related to external force field.
Xu and Prince formulate a new type of static external force called Gradient Vector Flow.
Fext = v
Eg.Eext =-|∇ I(x,y)|2
=> a snake initialized close to the edge will converge to a stable configuration near the edge
=> small capture range
=> homogeneous regions will have no external forces
Ɛ = ∫ ∫ Ч(ux2+uy2+vx2+vy2)+|∇ f |2|v-∇ f |2dxdy
Therefore, GVF snakes can move into boundary concavities
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Technical papers -