Curvature Scale Space for Shape Similarity Retrieval under Affine Transforms

  • Farzin Mokhtarian
  • Sadegh Abbasi
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1689)


The maxima of Curvature Scale Space (CSS) image have already been used to represent 2-D shapes in different applications. The representation has showed robustness under the similarity transformations. In this paper, we examine the performance of the representation under affine transformations. Since the CSS image employs the arc length parametrisation which is not affine invariant, we expect some deviation in the maxima of the CSS image under shear. However, we show that the locations of the maxima of the CSS image do not change dramatically even under large affine transformations.

Applying transformations to every object boundary of our database of 1100 images, we construct a large database of 5500 boundary contours. The contours in the database demonstrate a great range of shape variation. The CSS representation is then used to find similar shapes from this prototype database. We observe that for this database, 95% of transformed versions of the original shapes are among the first 20 outputs of the system. This provides substantial evidence of stability of the the CSS image and its contour maxima under affine transformation.


Affine transformation Image databases Shape Similarity 


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Copyright information

© Springer-Verlag Berlin Heidelberg 1999

Authors and Affiliations

  • Farzin Mokhtarian
    • 1
  • Sadegh Abbasi
    • 1
  1. 1.Centre for Vision, Speech, and Signal Processing Department of Electronic and Electrical EngineeringUniversity of SurreyGuildfordUK

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