Towards a Mathematical Theory of Primal Sketch and Sketchability

  • Authors:
  • Cheng-en Guo;Song-Chun Zhu;Ying Nian Wu

  • Affiliations:
  • -;-;-

  • Venue:
  • ICCV '03 Proceedings of the Ninth IEEE International Conference on Computer Vision - Volume 2
  • Year:
  • 2003

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Abstract

In this paper, we present a mathematical theory for Marr'sprimal sketch. We first conduct a theoretical study ofthe descriptive Markov random field model and the generativewavelet/sparse coding model from the perspectiveof entropy and complexity. The competition between thetwo types of models defines the concept of "sketchability",which divides image into texture and geometry. We then proposea primal sketch model that integrates the two modelsand, in addition, a Gestalt field model for spatial organization.We also propose a sketching pursuit process that coordinatesthe competition between two pursuit algorithms:the matching pursuit [8] and the filter pursuit [12], that seekto explain the image by bases and filters respectively. Themodel can be used to learn a dictionary of image primitives,or textons in Julesz's language, for natural images.The primal sketch model is not only parsimonious for imagerepresentation, but produces meaningful sketches overa large number of generic images.