Abstract
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.
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References
K. Arbter et al. Applications of affine-invariant fourier descriptors to recognition of 3-d objects. IEEE Trans. Pattern Analysis and Machine Intelligence, 12(7):640–646, July 1990.
J. Flusser and T. Suk. Pattern recognition by affine moment invariants. Pattern Recognition, 26(1):167–174, January 1993.
H. W. Guggenheimer. Differential Geometry. McGraw-Hill, New York, 1963.
B. B. Kimia and K. Siddiqi. Geometric heat equation and nonlinear diffusion of shapes and images. Computer Vision and Image Understanding, 64(3):305–332, 1996.
F. Mokhtarian, S. Abbasi, and J. Kittler. Robust and efficient shape indexing through curvature scale space. In Proceedings of the seventh British Machine Vision Conference, BMVC'96, volume 1, pages 53–62, Edinburgh, September 1996.
G. Sapiro and A. Tannenbaum. Affine invariant scale space. International Journal of Computer Vision, 11(1):25–44, 1993.
D. Tsai and M. Chen. Curve fitting approach for tangent angle and curvature measurement. Pattern Recognition, 27(5):699–711, 1994.
A. Zhao and J. Chen. Affine curve moment invariants for shape recognition. Pattern Recognition, 30(6):895–901, 1997.
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© 1999 Springer-Verlag Berlin Heidelberg
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Mokhtarian, F., Abbasi, S. (1999). Curvature Scale Space for Shape Similarity Retrieval under Affine Transforms. In: Solina, F., Leonardis, A. (eds) Computer Analysis of Images and Patterns. CAIP 1999. Lecture Notes in Computer Science, vol 1689. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-48375-6_9
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DOI: https://doi.org/10.1007/3-540-48375-6_9
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