Minimum Likelihood Image Feature and Scale Detection

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# Minimum Likelihood Image Feature and Scale Detection - PowerPoint PPT Presentation

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

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)

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.

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)

Gaussian Processes in Practice

Linear scale-space derivatives
• Scale-space derivatives:

Gaussian Processes in Practice

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
• 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

Gaussian Processes in Practice

FBm in Jet space
• (Result from Pedersen (2003))

Gaussian Processes in Practice

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?
• 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

Gaussian Processes in Practice

Synthetic examples: Blurred step edge

Gaussian Processes in Practice

Real Example: Sunflowers

Gaussian Processes in Practice

Sunflowers: Multi-scale

Gaussian Processes in Practice

Sunflowers: Fixed scale

Gaussian Processes in Practice

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