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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. What is an image feature?. Marr’s (1982) primal sketch (edges, bars, corners, blobs)

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Minimum likelihood image feature and scale detection

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
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)

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
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.

Gaussian Processes in Practice


Probabilistic feature detection
Probabilistic feature detection

  • Feature detection:

  • Konishi et al. (1999, 2002, 2003)

  • Lillholm & Pedersen (2004)

  • Scale selection:

  • Pedersen & Nielsen (1999)

  • Loog et al. (2005)

Gaussian Processes in Practice


Linear scale space derivatives
Linear scale-space derivatives

  • Scale-space derivatives:

Gaussian Processes in Practice


Scale space k jet representation
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)

Gaussian Processes in Practice


Probabilistic image models
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)

Gaussian Processes in Practice


Fractional brownian images
Fractional Brownian images

Gaussian Processes in Practice


Fbm in jet space
FBm in Jet space

  • (Result from Pedersen (2003))

Gaussian Processes in Practice


Detecting features and scales
Detecting Features and Scales

  • Detecting points in scale-space that are locally unlikely (minima):

  • (We could also have maximised .)

Gaussian Processes in Practice


Why minimum likeli scales
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.

Gaussian Processes in Practice


Synthetic examples double blobs
Synthetic examples: Double blobs

Gaussian Processes in Practice


Synthetic examples blurred step edge
Synthetic examples: Blurred step edge

Gaussian Processes in Practice


Real example sunflowers
Real Example: Sunflowers

Gaussian Processes in Practice


Sunflowers multi scale
Sunflowers: Multi-scale

Gaussian Processes in Practice


Sunflowers fixed scale
Sunflowers: Fixed scale

Gaussian Processes in Practice


Summary
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)?

Gaussian Processes in Practice


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