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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

- 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

- 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

- Feature detection:
- Konishi et al. (1999, 2002, 2003)
- Lillholm & Pedersen (2004)
- Scale selection:
- Pedersen & Nielsen (1999)
- Loog et al. (2005)

Gaussian Processes in Practice

- Scale-space derivatives:

Gaussian Processes in Practice

- 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

- 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

Gaussian Processes in Practice

- (Result from Pedersen (2003))

Gaussian Processes in Practice

- Detecting points in scale-space that are locally unlikely (minima):
- (We could also have maximised .)

Gaussian Processes in Practice

- 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

Gaussian Processes in Practice

Gaussian Processes in Practice

Gaussian Processes in Practice

Gaussian Processes in Practice

Gaussian Processes in Practice

- 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