Problem statement

In this section the influence of the cost function t on the smoothness of a trajectory C is analyzed. Here C is the solution of the functional minimization problem:

where Q is the set of all the possible curves in Q, {c } is the set of all the possible curves in Q between xi and x2 and p is the continuous metric:

The Fast Marching method computes a derivable solution C associated with the continuous metric p. Therefore, tools from differential geometry can be used to examine the curvature properties of C.

Let us define the curvature parameters considered here.

d 2C d2s 1

• Lower bound on the curvature radius along a curve C: Rmin(C) = infse[01]R(C(s))

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