Gradient vector flow: Difference between revisions

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central ___location, thereby defining a type of geometric feature that is related to the boundary configuration, but not directly evident from

the edge map. For example, ''perceptual edges'' are gaps in the edge map which tend to be connected visually by human

perception~\cite{&nbsp;<ref name =":KasxIJCV88}.> {{Cite GVFjournal helps| totitle connect= themSnakes: byactive diffusingcontour opposingmodels edge| gradientjournal vectors= acrossInternational theJournal gap;of andComputer evenVision though| there

year = 1988 | volume = 1 | pages = 321-331 | last1 = Kass | first1 = M. | last2 = Witkin | first2 = A. | last3 = Terzopoulos | first3 = D.}}</ref>.

is no actual edge map, active contour will converse to the perceptual edge because the GVF vectors drive them there (see \cite{GVF_Web}).

GVF helps to connect them by diffusing opposing edge gradient vectors across the gap; and even though there

is no actual edge map, active contour will converse to the perceptual edge because the GVF vectors drive them there (see \cite&nbsp;{GVF_Web}){cite web |url=http://www.iacl.ece.jhu.edu/static/gvf |title=Active contours, deformable models, and gradient vector flow |last1 = Xu |

first1 = C. | last2 = Prince | first2 = J.L. |publisher = Online resource including code download | date = 2012}}).

This property carries over when there are so-called ''weak edges'' identified by regions of edge maps having lower values.

GVF vectors also meet in opposition at central locations of objects thereby defining a type of medialness. This property has been

exploited as an alternative definition of the skeleton of objects~\cite{&nbsp;<ref name =":HasxPAMI09">{{Cite journal | title = Variational curve skeletons using gradient vector flow | journal = IEEE Transactions on Pattern Analysis and Machine Intelligence | year = 2009 | volume = 31 | pages = 2257-2274 | issue = 12 | last1 = Hassouna | first1 = M.S. | last2 = Farag | first2 = A.Y.}}</ref> and also as a way to initialize deformable models within objects such that convergence to the boundary is more likely.

models within objects such that convergence to the boundary is more likely.

==Applications==

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generally kept fairly small so that true edge positions are not overly

distorted. Given this edge map, the GVF vector field

<math>\textstyle\mathbf{v}(\mathbf{x})</math> can be computed by solving (\ref{eq:gvf-euler}2).

The deformable model itself can be implemented in a variety of ways

including parametric models such as the original

snake~\cite{KasxIJCV88} or active surfaces and implicit models

including geometric deformable models&nbsp;<ref name=":XuxCSSC00">{{Cite conference | first1 = C. | last1 = Xu | first2 = A. | last2 = Yezzi | first3 = J.L. | last3 = Prince | title = On the relationship between parametric and geometric active contours and its applications | book-title = 34th Asilomar Conference on Signals, Systems and Computers | volume = 1 | pages = 483-489 | date = October 2000}}</ref>. In the case

including geometric deformable models~\cite{XuxCSSC00}. In the case

of parametric deformable models, the GVF vector field <math>\mathbf{v}</math>

can be used directly as the external forces in the model. If the deformable model is defined by the evolution of the