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The second order local-image-structure solid.

Lewis D Griffin1

  • 1Computer Science Department, University College London, Malet Place Engineering Building, London, WC1E 6BT, UK. L.Griffin@cs.ucl.ac.uk

IEEE Transactions on Pattern Analysis and Machine Intelligence
|June 15, 2007
PubMed
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This study characterizes local image structure using Gaussian derivatives. It defines a novel geometric space, the "second order local-image-structure solid," revealing an excess of 1D structures in natural images.

Area of Science:

  • Computer Vision
  • Differential Geometry
  • Image Analysis

Background:

  • Local image structure is crucial for understanding image content.
  • Existing methods for characterizing structure are sensitive to transformations like scaling and rotation.
  • A robust representation invariant to certain transformations is needed.

Purpose of the Study:

  • To develop a new geometric framework for characterizing second-order local image structure.
  • To define a representation invariant to affine intensity scaling, rotation, and reflection.
  • To analyze the distribution of local image structures in noise and natural images.

Main Methods:

  • Utilized 6D vectors (jets) of Gaussian derivative measurements.
  • Investigated the effect of structure-preserving transformations on jets, defining orbits in jet space.

Related Experiment Videos

  • Constructed a 3D orbifold from these orbits and induced a metric tensor.
  • Developed a volume-preserving embedding of the orbifold into Euclidean 3-space, termed the 'second order local-image-structure solid'.

    • Main Results:

    • The group of transformations stratifies jet space into orbits, forming a 3D orbifold.
    • The induced metric reveals intrinsic curvature of the orbifold.
    • The 'second order local-image-structure solid' provides a visualizable and computable representation.
    • Analysis of natural images shows an excess of locally 1D structures compared to noise images.

    Conclusions:

    • The proposed geometric framework offers a robust method for analyzing local image structure.
    • The 'second order local-image-structure solid' is a valuable tool for image analysis and visualization.
    • Natural images exhibit a distinct distribution of local structures, with a prevalence of 1D features.