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Interpreting Complex Images Using Appearance Models
Chris Taylor
Imaging Science and Biomedical Engineering University of Manchester
Interpreting Complex Images Using Appearance Models Chris Taylor - - PowerPoint PPT Presentation
Interpreting Complex Images Using Appearance Models Chris Taylor - - PowerPoint PPT Presentation
Interpreting Complex Images Using Appearance Models Chris Taylor Imaging Science and Biomedical Engineering University of Manchester Acknowlegments Tim Cootes Gareth Edwards Christine Beeston Rhodri Davies (IPMI 2003 and PhD
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Overview
Problem definition / motivation Modelling shape Modelling appearance Interpreting images using appearance models Practical applications
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Problem Definition / Motivation
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Complex and Variable Objects
Faces Medical images Manufactured assemblies
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Understanding Images
Relating image to a conceptual model
– high-level interpretation
‘Explaining’ the image
– class of valid interpretations
Labelling structures
– basis for analysis
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What Makes a Good Approach?
Principled
– makes assumptions explicit – uses domain knowledge systematically
Generic
– can be applied directly to new problems
Computationally tractable
– practical using standard PC/workstation
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Interpretation by Synthesis
Interpret images using generative models of appearance – ‘explain’ the image
Fit Model
Labels Model Parameters
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Generative Models
High-level description
– shape – spatial relationships – grey-level appearance (texture map)
Compact Parameterised
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Modelling Issues
General
– deformable to represent any example of class
Specific
– only represent ‘legal’ examples of class
Learn from examples
– knowledge of how things vary – generic
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Modelling Shape
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Modelling
From: PhD thesis Rhodri Davies
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Modelling
From: PhD thesis Rhodri Davies
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Modelling Shape
Define each example using points Each (aligned) example is a vector
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xi = {xi1 , yi1 , xi2 , yi2 …xin , yin}
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Statistical Shape Models
Shape vector
– statistical analysis – correspondence problem
1 2 3 4 n
x1 = (x1, y1, …, xn, yn)T xns-1 = (x1, y1, …, xn, yn)T xns = (x1, y1, …, xn, yn)T
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Modelling Shape
Points tend to move in correlated ways
x1 x2 b1 xi x
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Statistics of Shape Variability
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Statistics of Shape Variability
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Statistics of Shape Variability
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Statistics of Shape Variability
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Statistics of Shape Variability
Eigenvalues (example with 22 shapes) Cumulative function of eigenvalues, normalized
90% variability explained by 7 eigenmodes
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Statistics of Shape Variability
Each shape x with dimensionality 2n can be expressed with
a b-vector with dimensionality t, t << 2n)
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Modelling Shape
Principal component analysis (PCA) Reduced dimensionality
– typically 10 - 50 shape parameters
modes of variation shape vector = + = = x x Pb P b
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Statistical Shape Models
Principal components analysis (PCA) Generative shape model: Reduced dimensionality
– typically 10 - 50 shape parameters x : mean shape P : modes of variation bi : shape parameters
i i
= + x x Pb
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Hand Model
Modes of shape variation
b
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b
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b
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Hand Model: Eigenmodes of Variation
From: PhD thesis Rhodri Davies
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Importance of Correspondence
From: PhD thesis Rhodri Davies Left: Arc-length parametrization Right: Manual placement of corresponding landmarks
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Correspondence and quality of shape model
From: PhD thesis Rhodri Davies Left: Manual placement, Right: Arc-length parametrization
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Face Model
Shape and spatial relationships
b
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b
2