# Diff of /branches/doubleplusgood/doc/inversion/Regularization.tex

revision 4344 by jfenwick, Wed Feb 27 03:42:40 2013 UTC revision 4345 by jfenwick, Fri Mar 29 07:09:41 2013 UTC
# Line 25  $\chi$ is a given symmetric, non-negativ Line 25  $\chi$ is a given symmetric, non-negativ
25  \label{EQU:REG:4}  \label{EQU:REG:4}
26   \chi(a,b) =  ( a_{,i} a_{,i}) \cdot ( b_{,j} b_{,j}) -   ( a_{,i} b_{,i})^2   \chi(a,b) =  ( a_{,i} a_{,i}) \cdot ( b_{,j} b_{,j}) -   ( a_{,i} b_{,i})^2
27
28  where summations over $i$ and $j$  are performed. Notice that cross-gradient function  where summations over $i$ and $j$  are performed, see~\cite{GALLARDO2005a}. Notice that cross-gradient function
29  is measuring the angle between the surface normals of contours of level set functions. So  is measuring the angle between the surface normals of contours of level set functions. So
30  minimizing the cost function will align the surface normals of the contours.  minimizing the cost function will align the surface normals of the contours.
31
# Line 93  sets the number of level set functions t Line 93  sets the number of level set functions t
93  $\omega^{(0)}$,  $\omega^{(0)}$,
94  $\omega^{(1)}$ and  $\omega^{(1)}$ and
95  $\omega^{(c)}$, respectively. A value for \member{w0} or \member{w1} or both must be given.  $\omega^{(c)}$, respectively. A value for \member{w0} or \member{w1} or both must be given.
96  If more then one level set function is involved  \member{wc} must be given.  If more than one level set function is involved  \member{wc} must be given.
97  \member{location_of_set_m} sets the characteristic function $q$  \member{location_of_set_m} sets the characteristic function $q$
98  to define locations where the level set function is set to zero, see equation~(\ref{ref:EQU:REG:7}).  to define locations where the level set function is set to zero, see equation~(\ref{ref:EQU:REG:7}).
99  \member{scale} and  \member{scale} and

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