Local or Global Minima:Local or Global Minima:Flexible Dual-Front Active Flexible Dual-Front Active

ContoursContours

Hua LiHua LiAnthony YezziAnthony Yezzi

OutlineOutline

• IntroductionIntroduction• Dual-Front Active ContoursDual-Front Active Contours• Properties of Dual-Front Active Properties of Dual-Front Active

ContoursContours• Comparison With Other Boundary Comparison With Other Boundary

Extraction Methods and Experimental Extraction Methods and Experimental ResultsResults

IntroductionIntroduction• Original snake modelOriginal snake model

1.1. P(C) is a potential which depends upon P(C) is a potential which depends upon somesome

desirable image feature.desirable image feature.

2.2. internal forces which control the internal forces which control the regularity on regularity on

curve C while the potential P attracts the curve C while the potential P attracts the

curve C toward the desired boundary.curve C toward the desired boundary.

defectdefect ：：1.1. snakes approach the nearest local minimum of snakes approach the nearest local minimum of

the initial contourthe initial contour2.2. difficult to extend the approach to segment 3D difficult to extend the approach to segment 3D

objectsobjects

• Flexible Dual-Front Active ContoursFlexible Dual-Front Active Contours we propose a novel, fast and flexible dual we propose a novel, fast and flexible dual

front front

implementation of active contours implementation of active contours motivated bymotivated by

1.1. minimal path techniques minimal path techniques

2.2. utilizing fast sweeping algorithmsutilizing fast sweeping algorithms

Dual-Front Active ContoursDual-Front Active Contours• background-Minimal Path Techniquebackground-Minimal Path Technique

background-Minimal Path Techniquebackground-Minimal Path Technique

a boundary extraction approach which detectsa boundary extraction approach which detects the global minimum of a contour energy betweethe global minimum of a contour energy betwee

n two pointsn two points Thereby avoiding local minima arising from the Thereby avoiding local minima arising from the

sensitivity to initializations in snakessensitivity to initializations in snakes

Energy minimization modelEnergy minimization model

1.1. s represents the arc-length parameter,s represents the arc-length parameter, i.ei.e2.2. . . 3.3. E(C) includes the internal regularization energy E(C) includes the internal regularization energy in potential P, and controls the smoothness of in potential P, and controls the smoothness of curve C using P and w > 0.curve C using P and w > 0.

Minimal action map modelMinimal action map model

1.1. corresponds to the minimal energy corresponds to the minimal energy integrated along a path starting from point p0integrated along a path starting from point p0 to point p.to point p.2.2. sliding back from point p to point p0 on thissliding back from point p to point p0 on this action map according to the gradient action map according to the gradient descent.descent.3.3. ..

Minimal Action Level Sets EvolutionMinimal Action Level Sets Evolution

1.1. is the normal to the closed curveis the normal to the closed curve

2.2. ‘ ‘low cost’ area the velocity is high while low cost’ area the velocity is high while atat

a ‘high cost’ area the velocity is lowa ‘high cost’ area the velocity is low

3.3. ..

• Principle of Dual-Front Active ContoursPrinciple of Dual-Front Active Contours

We choose a set of points Xi from R0 and anothWe choose a set of points Xi from R0 and anoth

er set of points Xj from R1er set of points Xj from R1 define two minimal action mapsdefine two minimal action maps All points satisfying ,form a partition bAll points satisfying ,form a partition b

oundaryoundary

Summarized in following stepsSummarized in following steps

• CommentsComments Two ways to decide the labels of the Two ways to decide the labels of the

separated boundaries in Step 2separated boundaries in Step 2

1.1. the labels may be reset in each iteration the labels may be reset in each iteration loop.loop.

2.2. In each iteration loop, the labels of the In each iteration loop, the labels of the separated boundaries of the new active separated boundaries of the new active region are decided by the result from the region are decided by the result from the previousprevious

iterationiteration

Properties of Dual-Front Active ContoursProperties of Dual-Front Active Contours

• Flexible Local or Global MinimaFlexible Local or Global Minima• Numerical ImplementationNumerical Implementation• Evolution PotentialsEvolution Potentials• Simple Regularization TermsSimple Regularization Terms• Automatic Evolution ConvergenceAutomatic Evolution Convergence

• Flexible Local or Global MinimaFlexible Local or Global Minima size and shape of active regions affects finalsize and shape of active regions affects final segmentation resultssegmentation results Use morphological dilation and erosion to generUse morphological dilation and erosion to gener

ate an active region around the current curve.ate an active region around the current curve. when an initial curve is far from the desired objewhen an initial curve is far from the desired obje

ct, we may first use wider active regionsct, we may first use wider active regions when curve nears the desired boundary, we may when curve nears the desired boundary, we may

use narrower active regionsuse narrower active regions

• Numerical ImplementationNumerical Implementation

• Evolution PotentialsEvolution Potentials

• Simple Regularization TermsSimple Regularization Terms1.1. ..

2.2. Smoothing the original imagesSmoothing the original images using isotropic nonlinear diffusion operator using isotropic nonlinear diffusion operator

to smoothing the original imagesto smoothing the original images

• Automatic Evolution ConvergenceAutomatic Evolution Convergence1.1. an automatic stopping criterion in each iteration.an automatic stopping criterion in each iteration. initial contours are classified into multiple groupinitial contours are classified into multiple group

s, all contours evolute simultaneously but based s, all contours evolute simultaneously but based on different potentials.on different potentials.

two contours from the same group meet, they mtwo contours from the same group meet, they merge into a single contourerge into a single contour

two contours from different groups meet, both ctwo contours from different groups meet, both contours stop evolving and a common boundary iontours stop evolving and a common boundary is formed by the meeting points automaticallys formed by the meeting points automatically

2.2. when current global minimum partition curve iwhen current global minimum partition curve i

s the same as that of last iteration or the differs the same as that of last iteration or the difference between them is less than a predefined tence between them is less than a predefined tolerance, the procedure may be stopped.olerance, the procedure may be stopped.

Comparison With Other Boundary ExtractioComparison With Other Boundary Extraction Methods and Experimental Resultsn Methods and Experimental Results

• comparisoncomparison

• resultsresults

The EndThe EndThanks to everyoneThanks to everyone