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A common way to encourage a deformable model to move toward the edge map is to take the spatial gradient of the edge map, yielding a vector field. Since the edge map has its highest intensities directly on the edge and drops to zero away from the edge, these gradient vectors provide directions for the active contour to move. When the gradient vectors are zero, the active contour will not move, and this is the correct behavior when the contour rests on the peak of the edge map itself. However, because the edge itself is defined by local operators, these gradient vectors will also be zero far away from the edge and therefore the active contour will not move toward the edge when initialized far away from the edge.
Gradient vector flow (GVF) is the process that spatially extends the edge map gradient vectors, yielding a new vector field that contains
information about the ___location of object edges throughout the entire image ___domain. GVF is defined as a diffusion process operating on the
components of the input vector field. It is designed to balance the fidelity of the original vector field, so it is not changed too much,
with a regularization that is intended to produce a smooth field on its output.
Although GVF was designed originally for the purpose of segmenting objects using active contours attracted to edges, it has been since
adapted and used for many alternative purposes. Some newer purposes including defining a continuous medial axis representation~\cite{HasxPAMI09}, regularizing image anisotropic diffusion algorithms~\cite{YuxTIP06}, finding the centers of ribbon-like objects~\cite{HanxNI04}, constructing graphs for optimal surface segmentations~\cite{MirxCMIG17}, creating a shape prior~\cite{BaixCMIG18}, and much more.
==Related Concepts==
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