The Structure of Locally Orderless Images

  • Authors:
  • Jan J. Koenderink;Andrea J. Van Doorn

  • Affiliations:
  • Helmholtz Instituut, Universiteit Utrecht, Buys Ballot Laboratory, Princetonplein 5, 3584CC Utrecht, The Netherlands. j.j.koenderink@phys.uu.nl;Helmholtz Instituut, Universiteit Utrecht, Buys Ballot Laboratory, Princetonplein 5, 3584CC Utrecht, The Netherlands

  • Venue:
  • International Journal of Computer Vision
  • Year:
  • 1999

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Abstract

We propose a representation of images in which a global, but not a local topology is defined. Thetopology is restricted to resolutions up to the extent of the local region of interest (ROI).Although the ROI‘s may contain many pixels, there is no spatial order on the pixels within the ROI,the only information preserved is the histogram of pixel values within the ROI‘s. This can beconsidered as an extreme case of a textel (texture element) image: The histogram is the limit oftexture where the spatial order has been completely disregarded. We argue that locally orderlessimages are ubiquitous in perception and the visual arts. Formally, the orderless images are mostaptly described by three mutually intertwined scale spaces. The scale parameters correspond to thepixellation (“inner scale”), the extent of the ROI‘s (“outer scale”) and the resolution in thehistogram (“tonal scale”). We describe how to construct locally orderless images, how to renderthem, and how to use them in a variety of local and global image processing operations.