Transcript Minimum Likelihood Image Feature and Scale Detection Based

Minimum Likelihood Image Feature
and Scale Detection
Kim Steenstrup Pedersen
Collaborators:
Pieter van Dorst, TUe, The Netherlands
Marco Loog, ITU, Denmark
What is an image feature?
• Marr’s (1982) primal sketch (edges, bars,
corners, blobs)
• Geometrical features, Marr’s features
defined by differential geometry:
Canny (1986), Lindeberg (1998)
• Iconic features: Koenderink (1993),
Griffin & Lillholm (2005)
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Observation: Features are usually points
and curves, i.e. sparsely distributed in
space (unlikely events).
Features have an intrinsic scale / size.
How blurred is the edge?
What is the size if a bar?
Gaussian Processes in Practice
A probabilistic primal sketch
Our definition: Features are points that are unlikely to occure under an
image model.
Similarly the scale of the feature is defined as the most unlikely scale.
• We use fractional Brownian images as a generic model of the
intensity correlation found in natural images. Captures second order
statistics of generic image points (non-feature points).
• The model includes feature scale naturally.
• This leads to a probabilistic feature and scale detection.
Possible applications:
Feature detection, interest points for object recognition,
correspondance in stereo, tracking, etc.
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Gaussian Processes in Practice
Probabilistic feature detection
Feature detection:
• Konishi et al. (1999, 2002, 2003)
• Lillholm & Pedersen (2004)
Scale selection:
• Pedersen & Nielsen (1999)
• Loog et al. (2005)
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Gaussian Processes in Practice
Linear scale-space derivatives
Scale-space derivatives:
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Scale Space k-Jet Representation
We use the k-jet as representation
of the local geometry:
(The coefficients of the truncated
Taylor expansion of the blurred
image.)
Biologically plausible
representation
(Koenderink et al., 1987)
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Gaussian Processes in Practice
Probabilistic image models
Key results on natural image statistics:
• Scale invariance / Self-similarity:
Power spectrum,
: Field (1987),
Ruderman & Bialek (1994)
• In general non-Gaussian filter responses!
Fractional Brownian images as model of natural images:
• Mumford & Gidas (2001), Pedersen (2003),
Markussen et al. (2005)
• Jet covariance of natural images resembles that of
fractional Brownian images: Pedersen (2003)
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Gaussian Processes in Practice
Fractional Brownian images
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FBm in Jet space
(Result from Pedersen (2003))
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Detecting Features and Scales
Detecting points in scale-space that are locally
unlikely (minima):
(We could also have maximised
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.)
Why minimum likeli scales?
Lindeberg (1998) maximises polynomials of
derivatives in order to detect features and scales.
Similarly, we maximise
in order to detect features and scales.
The difference lies in the choice of polynomial!
We use an image model and Lindeberg uses a
feature model.
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Synthetic examples: Double blobs
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Gaussian Processes in Practice
Synthetic examples: Blurred step edge
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0.9
0.8
Probability
0.7





0.6
0.5
0.4
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1.5
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2.5
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0.1
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Measurement scale (in  )
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50
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Real Example: Sunflowers
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Sunflowers: Multi-scale
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Sunflowers: Fixed scale
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Summary
• Minimising the likelihood of an image point under
the fractional Brownian image model detects
feature points and their intrinsic scale.
• There is a relationship between feature types
and the  parameter.
• Why over estimation of the scale?
• Preliminary results look promising, a
performance evaluation is needed (task based?).
• The method is pointwise. How to handle curve
features (edges, bars, ridges)?
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