Minimum Likelihood Image Feature and Scale Detection

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Minimum Likelihood Image Feature and Scale
Detection

• Kim Steenstrup Pedersen
• Collaborators
• Pieter van Dorst, TUe, The Netherlands
• Marco Loog, ITU, Denmark

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What is an image feature?

• Marrs (1982) primal sketch (edges, bars,
  corners, blobs)
• Geometrical features, Marrs features defined by
  differential geometry Canny (1986),
  Lindeberg (1998)
• Iconic features Koenderink (1993), Griffin
  Lillholm (2005)

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?
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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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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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Linear scale-space derivatives

• Scale-space derivatives

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Scale Space k-Jet Representation

• We use the k-jet as representationof the local
  geometry
• (The coefficients of the truncatedTaylor
  expansion of the blurredimage.)
• Biologically plausiblerepresentation
  (Koenderink et al., 1987)

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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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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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Synthetic examples Blurred step edge
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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)?