Snakes and Active Contours - Bezier and Splines in Image Processing and Machine Vision - page 183

Fig. 9.3. Application of a Kass et al. closed snake for screening for cervical cancer
using Pap smear images. Here we wish to segment the cell nucleus from the cytoplasm
(from [11]).

behavior of snakes is easier to understand if we examine the discrete form of
the internal energy as follows [3]:

2
membrane term

2

E int ( ν i )= α i | ν i − ν i− 1 | + β i | ν i +1 − 2 ν i + ν i − 1 | . (9.5)

thin-plate term

Now the membrane term

2 = ( x i −

| ν i − ν i− 1 | x i− 1 ) 2 +( y i − y i− 1 ) 2

just represents the square of the distance between successive control points.
Since E int is the sum of the squared distances between the control points, this
energy is minimized when the distances are all equal and the control points
are collinear. In the case of an open snake, this low energy configuration will