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Alexander Vasilevskiy, Kaleem Siddiqi, "Flux Maximizing Geometric Flows," IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 24, no. 12, pp. 15651578, December, 2002.  
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@article{ 10.1109/TPAMI.2002.1114849, author = {Alexander Vasilevskiy and Kaleem Siddiqi}, title = {Flux Maximizing Geometric Flows}, journal ={IEEE Transactions on Pattern Analysis and Machine Intelligence}, volume = {24}, number = {12}, issn = {01628828}, year = {2002}, pages = {15651578}, doi = {http://doi.ieeecomputersociety.org/10.1109/TPAMI.2002.1114849}, publisher = {IEEE Computer Society}, address = {Los Alamitos, CA, USA}, }  
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TY  JOUR JO  IEEE Transactions on Pattern Analysis and Machine Intelligence TI  Flux Maximizing Geometric Flows IS  12 SN  01628828 SP1565 EP1578 EPD  15651578 A1  Alexander Vasilevskiy, A1  Kaleem Siddiqi, PY  2002 KW  Geometric active contours KW  gradient flows KW  shape analysis KW  divergence and flux KW  blood vessel segmentation. VL  24 JA  IEEE Transactions on Pattern Analysis and Machine Intelligence ER   
Abstract—Several geometric active contour models have been proposed for segmentation in computer vision and image analysis. The essential idea is to evolve a curve (in 2D) or a surface (in 3D) under constraints from image forces so that it clings to features of interest in an intensity image. Recent variations on this theme take into account properties of enclosed regions and allow for multiple curves or surfaces to be simultaneously represented. However, it is still unclear how to apply these techniques to images of narrow elongated structures, such as blood vessels, where intensity contrast may be low and reliable region statistics cannot be computed. To address this problem, we derive the gradient flows which maximize the rate of increase of flux of an appropriate vector field through a curve (in 2D) or a surface (in 3D). The key idea is to exploit the direction of the vector field along with its magnitude. The calculations lead to a simple and elegant interpretation which is essentially parameter free and has the same form in both dimensions. We illustrate its advantages with several levelsetbased segmentations of 2D and 3D angiography images of blood vessels.
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