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Medical Image AnalysisSegmentationDeformable Modelsfor Medical Image Segmentation"!!!Mauricio Reyes, PhD!
!University of BernInstitute for Surgical Technologies and Biomechanics!Medical Image Analysis Group!
Segmentation Overview – Big Picture"
Deformable Models for Segmentation!
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Simple Methods!
># Thresholding!># Region-
Growing!># …!
Classification!+ Clustering!
># kNN!># SVM!># …
Deformable Models!!>#Snakes!>#Level-Sets!>#…!
Active Models!
># ASM!># AAM!!!
Atlas-based!Segmentation!
># Brain!># Heart!># …!!!
Random Fields & Graph-Cuts!
># MRF!># CRF!!!
Contents"
> Explicit deformable models – SNAKES!
> Implicit deformable models – LEVEL SETS!
Deformable Models for Segmentation!
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Many of the following slides courtesy of Dr. Irving Dindoyal!
Contouring"
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Edge Detection"
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The problem with contours"
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Use of deformable models"
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Deformable Models for Segmentation!
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A snake is ..."
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Lagrangian frame of reference"
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Snake examples"
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Damped harmonic oscillator"
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Damped harmonic oscillator"
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Euler method"
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Spatial discretisation"
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Snake energy equation"
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Snake equation"
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Internal forces"
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Image interaction"
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Ballon term"
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Damping term"
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Snake update equation"
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Snake algorithm"
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Advantages of explicit correspondence (one-to-one mapping between snaxels)"
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Disadvantages of snakes"
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Disadvantages of snakes"
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Extensions to 3D"
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The Level Set Method"
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Level SetsImplicit deformable models"
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Level set concept"
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Origins of level sets"
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Lipschitz function"
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Level set evolution"
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Level set PDE"
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Level set edge-based"
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Edge term"
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Curvature"
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Topological adaptability"
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Level-set illustration video"
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Multiseed initialisation"
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Advantages of level sets"
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Disadvantages of level sets"
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Tricks for speeding-up"
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Narrow banding"
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Multi-resolution"
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Deformable model initialisation"
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Function minimization"
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Deformable Model Summary"
Explicit – Snakes ""> Tracking of vertices!> Compact shape representation!> O(N) computational complexity!> Extension to 3D is non-trivial!> Self-intersection is a problem!> Topological changes not easy to handle!> Difficult to parallelize!> Low memory requirements!> Corresponding points defined during
evolution!> User interaction to drag contour
possible during evolution!> Governed by physical connected mass
equations!
Implicit – Level-sets"> No tracking of vertices!> Discretised at integer multiple of image
resolution!> O(N^3) computational complexity!> Extension to n-D is natural!> No self intersection!> Topological changes are naturally
handled!> Parallelisation same as for low level
image processing!> Much higher memory requirements!> Correspondence has to be recomputed
in order to track zero levels!> User interaction difficult to implement
during evolution!> Governed by curve evolution theory!
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Literature"
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• T. McInerney and D. Terzopoulos, “Deformable models in medical image analysis: a survey,” Med. Image Anal., vol. 1, no. 2, pp. 91–108, 1996.
• R. Tsai and S. Osher, “Level Set Methods and their Applications in Image Science,” Commun. Math. Sci., vol. 1, no. 4, pp. 623–656, 2003.
• V. Caselles, F. Catt�, T. Coll, and F. Dibos, “A geometric model for active contours in image processing,” Numer. Math., vol. 66, no. 1, 1993.
• T. F. Chan and L. a Vese, “Active contours without edges.,” IEEE Trans. Image Process., vol. 10, no. 2, pp. 266–77, Jan. 2001.
Application: Skull-Stripping"
> Aim: Separate brain region from the rest in a pre-processing step!— Register atlas, propagate brain mask!— Take this as initialization for a deformable model, refine brain
segmentation by evolving a level-set towards brain-skull boundary!
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Bauer et al., Insight Journal, 2012 http://hdl.handle.net/10380/3353
Take Home Message"
> Deformable models: segmentation of object with weak shape constraints!— Explicit: snakes!— Implicit: level sets!
> Evolve contour after initialization towards region boundary based on energy minimization, energy usually consists of!— Image term (usually edge or region intensity properties)!— Shape term (usually length, curvature)!— External constraint (usually balloon force)!
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Medical Image AnalysisSegmentationDeformable Modelsfor Medical Image Segmentation"!!!Mauricio Reyes, PhD!
!University of BernInstitute for Surgical Technologies and Biomechanics!Medical Image Analysis Group!