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Minimum Likelihood Image Feature and Scale Detection

This study presents a probabilistic framework for detecting image features and their intrinsic scales utilizing fractional Brownian images as a model. Image features, defined as unlikely events, are identified through their points and curves. The approach captures second-order statistical properties of natural images, ensuring scale selection occurs naturally. Applications include object recognition, stereo correspondence, and tracking. The results suggest that minimizing the likelihood of observation points effectively identifies features and scales, though further performance evaluation is needed.

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Minimum Likelihood Image Feature and Scale Detection

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  1. Minimum Likelihood Image Feature and Scale Detection Kim Steenstrup Pedersen Collaborators: Pieter van Dorst, TUe, The Netherlands Marco Loog, ITU, Denmark

  2. 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

  3. 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

  4. 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

  5. Linear scale-space derivatives • Scale-space derivatives: Gaussian Processes in Practice

  6. 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

  7. 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

  8. Fractional Brownian images Gaussian Processes in Practice

  9. FBm in Jet space • (Result from Pedersen (2003)) Gaussian Processes in Practice

  10. Detecting Features and Scales • Detecting points in scale-space that are locally unlikely (minima): • (We could also have maximised .) Gaussian Processes in Practice

  11. 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

  12. Synthetic examples: Double blobs Gaussian Processes in Practice

  13. Synthetic examples: Blurred step edge Gaussian Processes in Practice

  14. Real Example: Sunflowers Gaussian Processes in Practice

  15. Sunflowers: Multi-scale Gaussian Processes in Practice

  16. Sunflowers: Fixed scale Gaussian Processes in Practice

  17. 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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