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413
Flux Maximizing Geometric Flows
 IEEE Transactions on Pattern Analysis and Machine Intelligence
, 2001
"... 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 variatio ..."
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Cited by 126 (8 self)
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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
Flux Maximizing Geometric Flows
, 2002
"... Several geometric active contour models have been proposed for segmentation in computer vision. 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 ta ..."
Abstract
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the gradient flow which maximizes the rate of increase of flux of an auxiliary vector field through a curve or surface. The calculation leads to a simple and elegant interpretation which is essentially parameter free. We illustrate its advantages with levelset based segmentations of 2D and 3D MRA images
Surface Recovery from 3D Point Data Using a Combined Parametric and Geometric Flow Approach
 In EMMCVPR’03
, 2003
"... This paper presents a novel method for surface recovery from discrete 3D point data sets. In order to produce improved reconstruction results, the algorithm presented in this paper combines the advantages of a parametric approach to model local surface structure, with the generality and the topol ..."
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Cited by 5 (1 self)
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in 3D and to then incorporate a flux maximizing geometric flow for surface reconstruction. The approach is illustrated with experimental results on a variety of data sets.
3D Flux Maximizing Flows
 LECTURE NOTES IN COPMUTER SCIENCE
, 2001
"... A number of geometric active contour and surface models have been proposed for shape segmentation in the literature. The essential idea is to evolve a curve (in 2D) or a surface (in 3D) so that it clings to the features of interest in an intensity image. Several of these models have been derived, ..."
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Cited by 3 (0 self)
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, using a variational formulation, as gradient flows which minimize or maximize a particular energy functional. However, in practice these models often fail on images of low contrast or narrow structures. To address this problem we have recently proposed the idea of maximizing the rate of increase
A MultiScale Geometric Flow for Segmenting Vasculature
 School of Computer Science, McGill University
, 2004
"... Abstract. Often in neurosurgical planning a dual echo acquisition is performed that yields proton density (PD) and T2weighted images to evaluate edema near a tumour or lesion. The development of vessel segmentation algorithms for PD images is of general interest since this type of acquisition is wi ..."
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Cited by 22 (3 self)
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scale measure is then distributed to create a vector field which is orthogonal to vessel boundaries so that the flux maximizing flow algorithm of [17] can be applied to recover them. We validate the approach qualitatively with PD, angiography and Gadolinium enhanced MRI volumes. 1
Reconstructing Volume Tracking
 J. Comput. Phys
, 1997
"... A new algorithm for the volume tracking of interfaces in two dimensions is presented. The algorithm is based upon a welldefined, secondorder geometric solution of a volume evolution equation. The method utilitizes local discrete material volume and velocity data to track interfaces of arbitrari ..."
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Cited by 131 (3 self)
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geometricallybased solution method, in which material volume fluxes are computed systematically with a set of simple geometric tasks. We then interrogate the method by testing its ability to track interfaces through large (yet controlled) topology changes, whereby an initially simple interface configuration
Classification and Uniqueness of Invariant Geometric Flows
, 1994
"... In this note we classify geometric flows invariant to subgroups of the projective group. We proof that the geometric heat flow is the simplest of all possible flows. These results are based on the theory of differential invariants and symmetry groups. Classification et Unicit'e des Flux G' ..."
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Cited by 12 (5 self)
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In this note we classify geometric flows invariant to subgroups of the projective group. We proof that the geometric heat flow is the simplest of all possible flows. These results are based on the theory of differential invariants and symmetry groups. Classification et Unicit'e des Flux G
A Geometric Flow for Segmenting Vasculature in ProtonDensity Weighted MRI
"... Modern neurosurgery takes advantage of magnetic resonance images (MRI) of a patient’s cerebral anatomy and vasculature for planning before surgery and guidance during the procedure. Dual echo acquisitions are often performed that yield proton density (PD) and T2weighted images to evaluate edema nea ..."
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Cited by 6 (0 self)
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centerlines of tubular structures along with their estimated radii. This measure is then distributed to create a vector field which allows the flux maximizing flow algorithm of [2] to be applied to recover vessel boundaries. We carry out a qualitative validation of the approach on PD, MR angiography
Renormalization group equations and geometric flows
"... The quantum field theory of twodimensional sigma models with bulk and boundary couplings provides a natural framework to realize and unite different species of geometric flows that are of current interest in mathematics. In particular, the bulk renormalization group equation gives rise to the Ricci ..."
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Cited by 3 (0 self)
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The quantum field theory of twodimensional sigma models with bulk and boundary couplings provides a natural framework to realize and unite different species of geometric flows that are of current interest in mathematics. In particular, the bulk renormalization group equation gives rise
Effect of Geometrical and Chemical Constraints on Water Flux across Artificial Membranes
"... ABSTRACT Studies have been made on the temperature dependence of both the hydraulic conductivity, L, and the THO diffusion coefficient, co, for a series of cellulose acetate membranes (CA) of varying porosity. A similar study was also made of a much less polar cellulose triacetate membrane (CTA). Th ..."
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Cited by 3 (1 self)
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viscous flow, in which the hydraulic conductivity is inversely related to bulk water viscosity, has been demonstrated across membranes with very small equivalent pores. Watermembrane interactions, which depend upon both chemical and geometrical factors are of particular importance in diffusion
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