Then, to this point, we have described a ridge with three segments specified in 

 terms of S and F: the sigmoidal effect to the left of the left orientation line; the 

 sigmoidal effect to the right of the right orientation line; and the flat ridge area 

 between these lines at a value of t = 10. 



Finally, a sigmoidal truncation of the front end of this ridge is achieved 

 through multiplication of all components of the descriptor by an appropriate sigmoid, 

 changing in value from zero to one within the range <_ S <_ 2000, and being applicable 

 for < S < 5000. 



In general terms, we have: 



Lsig and Rsig = left- and right-segment sigmoids, respectively 

 LO, RO = left- and right-orientation lines, respectively 

 CC = center segment, constant 



Tsig = truncator sigmoid 



Then 



t = Tsig (Lsig + CC + Rsig) 



and 



Tsig = f(S) 



Lsig = f(L0,F) 



Rsig = f(R0,F) 



LO = f(S) 

 R0 = f(S) 

 Limits 



For Lsig, 

 For Rsig, 

 For CC, 



LO < F <_ 28 

 < F < RO 

 LO < F < RO 



and, <_ S <_ 5000 



The final descriptor form is shown in figure 5 along with the original planar form for 

 comparison. It can be seen that the descriptor does a creditable job of emulating the 

 planar form while smoothing the corners, all with 3 segments in place of the original 

 11 segments. 



6 



