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Figure 1: A snake with traditional potential forces cannot move into the concave boundary region.

\fbox{\resizebox{4cm}{4cm}{\includegraphics{images/concave_bound.eps}}}
(a)

\fbox{\resizebox{4cm}{4cm}{\includegraphics{images/concave_oldsnake.eps}}}
(c)






\fbox{\resizebox{9cm}{9cm}{\includegraphics{images/concave_oldforce.eps}}}
(b)





  
Figure 2: A snake with GVF external forces moves into the concave boundary region.

\fbox{\resizebox{4cm}{4cm}{\includegraphics{images/concave_bound.eps}}}
(a)

\fbox{\resizebox{4cm}{4cm}{\includegraphics{images/concave1.eps}}}
(c)






\fbox{\resizebox{9cm}{9cm}{\includegraphics{images/U_scale.eps}}}
(b)





  
Figure 3: A GVF snake converges to the same result from either the inside or the outside.

\fbox{\resizebox{9cm}{9cm}{\includegraphics{images/square_bound_scale.eps}}}
(a)





\fbox{\resizebox{4cm}{4cm}{\includegraphics{images/square1.eps}}}
(b)

\fbox{\resizebox{4cm}{4cm}{\includegraphics{images/square2.eps}}}
(c)






  
Figure 4: A GVF snake can also be initialized across the object boundary.

\fbox{\resizebox{7cm}{7cm}{\includegraphics{images/square4.eps}}}
(a)





\fbox{\resizebox{7cm}{7cm}{\includegraphics{images/concave2.eps}}}
(b)





  
Figure 5: A GVF snake correctly reconstructs the subjective contour.

\fbox{\resizebox{4cm}{4cm}{\includegraphics{images/broken0.eps}}}
(a)

\fbox{\resizebox{4cm}{4cm}{\includegraphics{images/broken2.eps}}}
(c)






\fbox{\resizebox{9cm}{9cm}{\includegraphics{images/broken1.eps}}}
(b)





  
Figure 6: A GVF snake can find the boundary represented by scattered points.

\fbox{\resizebox{4cm}{4cm}{\includegraphics{images/dots.eps}}}
(a)

\fbox{\resizebox{4cm}{4cm}{\includegraphics{images/dots_bound.eps}}}
(c)






\fbox{\resizebox{9cm}{9cm}{\includegraphics{images/dots_scale.eps}}}
(b)





 \begin{landscape}% latex2html id marker 1991
\begin{figure}
\begin{center}
\begi...
..., and (h) 600 iterations.}
\end{minipage}\end{center}\end{figure}\end{landscape}


  
Figure 8: Stream lines of the particles shown in Fig. 7.

\fbox{\resizebox{4in}{4in}{\includegraphics{images/stream_grid.epsf}}}





  
Figure 9: Stream lines of particles in (a) a potential force field and (b) a GVF field.

\fbox{\rotatebox{-90}{\resizebox{7cm}{7cm}{\includegraphics{images/stream_grad.epsf}}}}
(a)





\fbox{\rotatebox{-90}{\resizebox{7cm}{7cm}{\includegraphics{images/stream_gvf.epsf}}}}
(b)





  
Figure: (a) A $64\times 64$ image of the U-shape object corrupted by additive white Gaussian noise (6 dB) (b) The edge map $\vert\nabla (G_\sigma *I)\vert$ with $\sigma = 1.5$ (normalized to the range [0,1]). (c) The computed GVF. (d) Initial and intermediate contours (gray curves) and the final contour (white curve) of a GVF snake.

\fbox{\resizebox{7cm}{7cm}{\includegraphics{images/gray_U_noise.eps}}}
(a)





\fbox{\resizebox{7cm}{7cm}{\includegraphics{images/gray_U_edge.eps}}}
(b)




\fbox{\resizebox{7cm}{7cm}{\includegraphics{images/gray_U_gvf.eps}}}
(c)





\fbox{\resizebox{7cm}{7cm}{\includegraphics{images/gray_U_snake.eps}}}
(d)





  
Figure: (a) A ( $160\times 160$) magnetic resonance image of the left ventrical of a human heart (short-axis section). (b) The edge map $\vert\nabla (G_\sigma *I)\vert$ with $\sigma = 2.5$ (normalized to the range [0,1]). (c) The computed GVF (shown subsampled by a factor of two). (d) Initial and intermediate contours (gray curves) and the final contour (white curve) of the GVF snake.

\fbox{\resizebox{7cm}{7cm}{\includegraphics{images/gray_heart.eps}}}
(a)





\fbox{\resizebox{7cm}{7cm}{\includegraphics{images/gray_heart_edge.eps}}}
(b)




\fbox{\resizebox{7cm}{7cm}{\includegraphics{images/gray_heart_gvf.eps}}}
(a)





\fbox{\resizebox{7cm}{7cm}{\includegraphics{images/gray_heart_snake.eps}}}
(b)





 \begin{landscape}% latex2html id marker 2183
\begin{figure}
\begin{center}
\begi...
..., and (h) 100 iterations.}
\end{minipage}\end{center}\end{figure}\end{landscape}


  
Figure 13: The magnitude of the GVF field gives information about the medial axis of a shape.

\fbox{\resizebox{3.6cm}{3.6cm}{\includegraphics{images/core_disk.eps}}} \fbox{\resizebox{3.6cm}{3.6cm}{\includegraphics{images/core_disk1.eps}}}
(a)





\fbox{\resizebox{3.6cm}{3.6cm}{\includegraphics{images/core_square.eps}}} \fbox{\resizebox{3.6cm}{3.6cm}{\includegraphics{images/core_square1.eps}}}
(b)




\fbox{\resizebox{3.6cm}{3.6cm}{\includegraphics{images/core_rectangle.eps}}} \fbox{\resizebox{3.6cm}{3.6cm}{\includegraphics{images/core_rectangle1.eps}}}
(c)





\fbox{\resizebox{3.6cm}{3.6cm}{\includegraphics{images/core_core.eps}}} \fbox{\resizebox{3.6cm}{3.6cm}{\includegraphics{images/core_core1.eps}}}
(d)




\fbox{\resizebox{3.6cm}{3.6cm}{\includegraphics{images/core_saw.eps}}} \fbox{\resizebox{3.6cm}{3.6cm}{\includegraphics{images/core_saw1.eps}}}
(e)





\fbox{\resizebox{3.6cm}{3.6cm}{\includegraphics{images/core_screw.eps}}} \fbox{\resizebox{3.6cm}{3.6cm}{\includegraphics{images/core_screw1.eps}}}
(f)




\fbox{\resizebox{3.6cm}{3.6cm}{\includegraphics{images/core_blob.eps}}} \fbox{\resizebox{3.6cm}{3.6cm}{\includegraphics{images/core_blob1.eps}}}
(g)





\fbox{\resizebox{3.6cm}{3.6cm}{\includegraphics{images/core_dumbbell.eps}}} \fbox{\resizebox{3.6cm}{3.6cm}{\includegraphics{images/core_dumbbell1.eps}}}
(h)





  
Figure: The medialness map ${\cal M}^1(x,y)$(q=0.05) of a teardrop shape, shown as (a) a gray-level image and (b) a surface plot.

\fbox{\resizebox{7cm}{7cm}{\includegraphics{images/coreGvf2d.eps}}}
(a)





\fbox{\resizebox{7cm}{7cm}{\includegraphics{images/coreGvf3d.epsf}}}
(b)





next up previous
Next: About this document ... Up: No Title Previous: Acknowledgements
Chenyang Xu
1999-11-06