On using functions to describe the shape

Research output: Contribution to journalReview articlepeer-review


In this paper, a systematic review of various contour functions and methods of their analysis, as applied in the field of shape description and characterization, is presented. Contour functions are derived from planar object outlines and are used as an intermediate representation from which various shape properties can be obtained. All the functions are introduced and analyzed following the same scheme, thus making it possible to compare various representations. Although only a small subset of contour functions is included in the survey (cross-section, radius-vector, support, width, parametric, complex, tangent-angle, curvature, polynomial, and parametric cubic), the paper demonstrates a multitude of techniques for shape description that are based on this approach. Several analysis tools, such as statistics, line moments and invariants, Fourier and other series expansions, curvature scale space image, wavelet, and Radon transform are described.

Original languageEnglish (US)
Pages (from-to)225-245
Number of pages21
JournalJournal of Mathematical Imaging and Vision
Issue number3
StatePublished - May 2003


  • 2D object recognition
  • Contour functions
  • Shape
  • Shape analysis

ASJC Scopus subject areas

  • Statistics and Probability
  • Modeling and Simulation
  • Condensed Matter Physics
  • Computer Vision and Pattern Recognition
  • Geometry and Topology
  • Applied Mathematics


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