Rachid FAHMI Ph.D. Defense April 30, 2008
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Transcript of Rachid FAHMI Ph.D. Defense April 30, 2008
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Rachid FAHMI
Ph.D. Defense
April 30, 2008
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Variational Methods For Shape And Image
Registrations
Advisor: Prof. Aly A. Farag
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Outline
Generic Image Registration Problem.
Shape Registration: Representation of shapes
Global Alignment
Statistical shape modeling and shape-based
segmentation.
Elastic shape registration
Application: 3D face recognition in presence of
expression.
Image/Volume registration & F.E.-based
validation.
Application: Autism and dyslexia research.
Conclusions and future work.
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Why Registration? Goal: find geometric transformation between two or more images that aligns corresponding features.
Applications:
•Surgical Planning and decisions.
•Diagnosis + Assess clinical outcome.
•Longitudinal studies (Brain disorder, developmental growth).
•Segmentation.
•Object recognition and retrieval.
•Tracking and animation…
The 0.5 T open magnet system of the Brigham and Women’s Hospital
http://splweb.bwh.harvard.edu:8000/
Shape Registrati
on
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Outline
Generic Image Registration Problem.
Shape Registration: Representation of shapes
Global Alignment
Statistical shape modeling and shape-based
segmentation.
Elastic shape registration
Application: 3D face recognition in presence of
expression.
Image/Volume registration & F.E.-based
validation.
Application: Autism and dyslexia research.
Conclusions and future work.
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Generic Registration Problem
Given: two images, a reference R and a template T
Wanted:
: ,TR
such that
R
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SSD:
MI:
Dissimilarity Measures:
Appropriate for mono-modal registration & for aligning shapes without variations of scales.
Appropriate for multi-modal registration & for aligning shapes with variations of scales (Huang et al PAMI’06).
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Ill Posed Problem in the sense of Hadamard
Registration as optimization problem
Regularization
Ex.: Tikhonov Model
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Euler-Lagrange equations
Solve using a Gradient Descent strategy
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Outline
Generic Image Registration Problem.
Shape Registration: Representation of shapes
Global Alignment
Statistical shape modeling and shape-based
segmentation.
Elastic shape registration
Application: 3D face recognition in presence of
expression.
Image/Volume registration & F.E.-based
validation.
Application: Autism and dyslexia research.
Conclusions and future work.
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Registration of Shapes
Shape Representation
Transformation Model
How to recover registration parameters?
?Global Alignment
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• Scale variations are not handled.Scale variations are not handled.
• Dependency on the initialization.Dependency on the initialization.
• Local deformations can not be covered Local deformations can not be covered efficiently.efficiently.
TransformationTransformation
==Global + LocalGlobal + Local
Source Target
Several approaches Several approaches (Cohen’98, Fitzgibbon’01, (Cohen’98, Fitzgibbon’01,
Paragios’02, Huang’06)Paragios’02, Huang’06) are proposed but they have the are proposed but they have the following problems:following problems:
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Shape Representation Through VDF
Given a closed subset
X-component of VDF
Y-component of VDF
For all
with
(Gomes & Faugeras’01)
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Shape Representation Using Signed Distance (SD) S is an imaged shape s.t., the image domain )\( SS
S \
S
x +-
is continuous and differentiable around the zero level.
dist(x,S) is the min Euclidean distance
from x to S.
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Examples : Signed Distance Representation
Direct computations of the distance map for “moderate”
2D shapes
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Use the FMM to solve the following Eickonal
equation to approximate the distance map for
3D shapes
3D Cases
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Global Matching of Shapes
Given: Two shapes, S and T (one is a deformed version of the other) with representations
Goal: recover the transformation that aligns S and T
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Transformation model: Affine
2D case:
3D case:
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where:
Paragios et al. (J. Comp. Vis. & Im. Unders.’03)
Existing SDF-based alignment model
This model fails to handle the scale variation cases.
Assumption: sss yx
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Euler Lagrange Equations
where:
Alignment Using the VDF
Dissimilarity Measure