Pattern Analysis & Applications

, Volume 4, Issue 1, pp 1–8

Affine Curvature Scale Space with Affine Length Parametrisation

  • F. Mokhtarian
  • S. Abbasi

DOI: 10.1007/PL00010984

Cite this article as:
Mokhtarian, F. & Abbasi, S. Pattern Analysis & Applications (2001) 4: 1. doi:10.1007/PL00010984


The maxima of Curvature Scale Space (CSS) image have been used to represent 2D shapes under affine transforms. The CSS image is expected to be in the MPEG-7 package of standards. Since the CSS image employs the arc length parametrisation which is not affine invariant, we expect some deviations in the maxima of the CSS image under general affine transforms. Affine length and affine curvature have already been introduced and used as alternatives to arc length and conventional curvature in affine transformed environments. The utility of using these parameters to enrich the CSS representation is addressed in this paper. We use arc length to parametrise the curve prior to computing its CSS image. The parametrisation has been proven to be invariant under affine transformation and has been used in many affine invariant shape recognition methods. Since the organisation of the CSS image is based on curvature zero crossings of the curve, in this paper, we also investigate the advantages and shortcomings of using affine curvature in computation of the CSS image. The enriched CSS representations are then used to find similar shapes from a very large prototype database, and also a small classified database, both consisting of original as well as affine transformed shapes. An improvement is observed over the conventional CSS image.

Keywords:Affine curvature; Affine length; Affine transformation; Curvature scale space; Image databases; Shape similarity retrieval

Copyright information

© Springer-Verlag London 2001

Authors and Affiliations

  • F. Mokhtarian
    • 1
  • S. Abbasi
    • 1
  1. 1.Centre for Vision Speech and Signal Processing, Department of Electronic & Electrical Engineering, University of Surrey, Guildford, UKGB