Gradient vector flow: Difference between revisions

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The variational formulation of GVF has also been modified in ''motion GVF'' (MGVF) to incorporate object motion in

an image sequence&nbsp;.<ref name =":RayxTMI04"> {{Cite journal | title = Motion gradient vector flow: An external force for tracking rolling leukocytes with shape and size constrained active contours | journal = IEEE Transactions on Medical Imaging | year = 2004 | volume = 23 |

pages = 1466-1478 | issue = 12 | last1 = Ray | first1 = N. | last2 = Acton | first2 = S.T.}}</ref>.

Whereas the diffusion of GVF vectors from a conventional edge map acts in an isotropic manner, the formulation of

MGVF incorporates the expected object motion between image frames.

An alternative to GVF called vector field convolution (VFC) provides many of the advantages of GVF, has superior noise robustness, and

can be computed very fast&nbsp;.<ref name =":LixTIP07"> {{Cite journal | title = Active contour external force using vector field convolution for image segmentation | journal = IEEE Transactions on Image Processing | year = 2007 | volume = 16 | pages = 2096-2106 | issue = 8 | last1 = Li | first1 = B. | last2 = Acton | first2 = S.T.}}</ref>. The VFC field <math>\textstyle\mathbf{v}_{\mathrm{VFC}}</math> is defined as the convolution of the edge map <math>f</math> with a vector field kernel <math>\mathbf{k}</math>

{{numBlk||

:<math display = "block">

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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&nbsp;.<ref name =":KasxIJCV88> {{Cite journal | title = Snakes: active contour models | journal = International Journal of Computer Vision |

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

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 converge to the perceptual edge because the GVF vectors drive them there (see&nbsp;{{cite web |url=http://www.iacl.ece.jhu.edu/static/gvf |title=Active contours, deformable models, and gradient vector flow |last1 = Xu |

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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&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.

==Applications==

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The deformable model itself can be implemented in a variety of ways including parametric models such as the original

snake&nbsp;<ref name=":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

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 (two-dimensional) active contour <math>\mathbf{X}(s,t)</math>, then a simple

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the geodesic active contour flow with GVF forces was proposed

in&nbsp;<ref name=":ParxTPAMI04">{{Cite journal | first1 = N. | last1 = Paragios | first2 = O. | last2 = Mellina-Gottardo | first3 = V. | last3 = Ramesh | title = Gradient vector flow fast geometric active contours | journal = IEEE Transactions on Pattern Analysis and Machine Intelligence | year = 2004 | volume = 26 | pages = 402-407 | issue = 3}}</ref>. This paper also shows how to apply the Additive

Operator Splitting schema&nbsp;<ref name=":GolxTIP01">{{Cite journal |first1 = R. | last1 = Goldenberg | first2 = R. | last2 = Kimmel | first3 = E. | last3 = Rivlin

| first4 = M. | last4 = Rudzsky | title = Fast geodesic active contours | journal = IEEE Transactions on Image Processing | year = 2001

| volume = {10 | pages = 1467-1475 | issue = 10}}</ref> for rapid computation of this segmentation method. The uniqueness and existence of this

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to achieve even better segmentation for images with complex geometric objects.

GVF has been used to find both inner, central, and central cortical surfaces in the analysis of brain images&nbsp;,<ref name=":HanxNI04"/>, as shown in Figure&nbsp;4. The

process first finds the inner surface using a three-dimensional geometric deformable model with conventional forces. Then the central

surface is found by exploiting the central tendency property of GVF. In particular, the cortical membership function of the human brain

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Several notable recent applications of GVF include constructing graphs for optimal surface segmentation in spectral-___domain optical coherence

tomography volumes&nbsp;,<ref name=":MirxCMIG17"/>, a learning based probabilistic GVF active contour formulation to give more weights to objects

of interest in ultrasound image segmentation&nbsp;,<ref name =":HafxCBM14"/>, and an adaptive multi-feature GVF active contour

for improved ultrasound image segmentation without hand tuned paramaters&nbsp;.<ref name=":RodxJVCIR13>{{Cite journal | title=Multi-feature gradient vector flow snakes for adaptive segmentation of the ultrasound images of breast cancer | last1 = Rodtook | first1 = A. | last2 = Makhanov | first2 = S.S. | journal=Journal of Visual Communication and Image Representation | volume=24 | issue = 8 | pages=1414-1430 | year=2013 | publisher=Elsevier}}</ref>

==Related concepts==