Minimum likelihood image feature and scale detection
This presentation is the property of its rightful owner.
Sponsored Links
1 / 17

Minimum Likelihood Image Feature and Scale Detection PowerPoint PPT Presentation


  • 42 Views
  • Uploaded on
  • Presentation posted in: General

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)

Download Presentation

Minimum Likelihood Image Feature and Scale Detection

An Image/Link below is provided (as is) to download presentation

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.


- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -

Presentation Transcript


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


  • Login