Computation procedure

The computation procedure for the 3D Fast Marching algorithm described in table 2 can be found in (Deschamps & Cohen, 2001). We give here additional calculation details to update the distance function estimate vk of an xtop's neighbour xk with a cost Tk.

Procedure FMComputeV(Neigh(xt0p))

01} Loop : for all configurations xk in Neigh(xtop)

{02} If xk is Unvisited, then remove it from Unvisited and insert it in Current with vk = <x>

{03} If xk is Current then apply case 1 or case 2 for the computation of vk.

{04} Sort Current list according to the priority assignment._

Table 2. Pseudo code of the FM procedure for updating Neigh(xtop)

One, two or three Accepted configurations are used to solve equation (8). We note {A1, A2}, {B1, B2} and {C1, C2} the three couples of opposite neighbours of xk (in 6-connexity) with the ordering u(Ai) < u(A2), u(Bi) < u(B2), u(Ci) < u(C2) and u(Ai) < u(Bi) < u(Ci). Two different cases are to be examined sequentially:

Case 1: considering that vk > u(C1) > u(B1) > u(A1), the upwind scheme (8) is equivalent to:

(vk - u(Aj ))2 + (vk - u(B ))2 + (vk - u(C ))2 = Tk (9)

Computing the discriminant of equation (9) there are two possibilities:

• if tk > u(Ai)2 + ufo)2 + 2u(C)(u(C)-ufo)-u^)) and ufo)<

Learn Photoshop Now

Learn Photoshop Now

This first volume will guide you through the basics of Photoshop. Well start at the beginning and slowly be working our way through to the more advanced stuff but dont worry its all aimed at the total newbie.

Get My Free Ebook

Post a comment