Geometric Morphometrics

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Geometric Morphometrics
Lecturer Dr. Keqin Wu
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To do

• work on programming assignment 2
• Continue to think about final project
• Form final group

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Geometric MorphologyWhat is it?

• Deals with the study of shape

Morphing the Armadillo model
(Funck 2006)
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Set Operations
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Set Operations
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Set Operations
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Set Operations
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Set Operations
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Set Operations
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Set Operations
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Set Operations
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Set Operations
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Set Operations
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Set Operations
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Set Operations
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Set Operations
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Set Operations
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As-Rigid-As-Possible Shape Manipulation

• T. Igarashi, T. Mascovich, J. F. Hughes
• Presented in SIGGRAPH 2005

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Demo

• http//www.youtube.com/watch?v1M_oyUEOHK8

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Deformable Models in Image Analysis
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Mathematical Foundations

• Geometry
• Physics
• Approximation theory

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Mathematical Foundations

• Geometry

• Broad shape coverage by employing geometric
  representations that involve many degrees of
  freedom, such as splines.
• The model remains manageable because the degrees
  of freedom are generally not permitted to evolve
  independently

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Mathematical Foundations

• Physics

• The physical interpretation views deformable
  models as elastic bodies which respond naturally
  to applied forces and constraints.
• The energy grows monotonically as the model
  deforms away from a specified natural or rest
  shape
• Often includes terms that constrain the
  smoothness or symmetry of the model
• The deformation energy gives rise to elastic
  forces internal to the model.

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Deformable model geometry

• Approximation theory

• In physics-based view of classical optimal
  approximation, external potential energy
  functions are defined in terms of the data of
  interest to which the model is to be fitted.
• These potential energies give rise to external
  forces which deform the model such that it fits
  the data

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Image Analysis with Deformable Models

• Medical image interpretation tasks include
  segmentation, matching, and motion analysis.

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Snakes Active Contour Models (MICHAEL KASS,
1988)

• A snake is an energy-minimizing spline
  guided by external constraint forces and
  influenced by image forces that pull it
  toward features such as lines and edges.
• The interface allows a user to select starting
  points and exert forces on snakes interactively
  as they minimize their energy.

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Image Segmentation with Deformable Curve

• Algorithm

• Initial Points defined around Feature to be
  extracted
• Explicitly defined
• Approximation of an Ellipse
• Pre-defined number of Points generated
• Points are moved through an Iterative Process
• Energy Function for each point in the Local
  Neighbourhood is calculated
• Move to point with lowest Energy Function
• Repeat for every point
• Iterate until Termination Condition met
• Defined number of iterations
• Stability of the position of the points

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Volume Image Segmentation with Deformable
Surfaces

• Medical image interpretation tasks including
  segmentation, matching, and motion analysis.
• On matching deformable models to images. (D.
  Terzopoulos, 1986)

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Matching

• Matching of regions in images can be performed
  between
• the representation of a region and a model
  (labeling) or be- tween the representation of two
  distinct regions (registration).
• Incorporating Priori Knowledge
• Deformable atlas technique

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Deformable atlas technique
A General Scheme for Automatically Building 3D
Morphometric Anatomical Atlases application to a
Skull Atlas (Ge rard Subsol, 1995)
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Deformable atlas technique
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Deformable atlas technique
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Motion Tracking and Analysis

• Vector Field Based Shape Deformations (Wolfram
  von Funck 2006) Demo

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