Determining local natural scales of curves

Abstract An alternative to representing curves at a single scale or a fixed number of multiple scales is to represent them only at their natural (i.e. most significant) scales. This allows all the important information concerning the different sized structures contained in the curve to be explicitly represented without the overhead of redundant representations of the curve. This paper describes several approaches to determining the local natural scales of curves. That is, various possibly overlapping sections of the curve should be represented at certain scales depending on their shape. The merits and drawbacks of the techniques are described, and the results of implementing one of them are shown.

[1]  Svetha Venkatesh,et al.  Extracting natural scales using fourier descriptors , 1993, Pattern Recognit..

[2]  Paul L. Rosin.  Representing curves at their natural scales , 1992, Pattern Recognit..

[3]  W Richards,et al.  Encoding contour shape by curvature extrema. , 1986, Journal of the Optical Society of America. A, Optics and image science.

[4]  Jan-Olof Eklundh,et al.  Shape Representation by Multiscale Contour Approximation , 1991, IEEE Trans. Pattern Anal. Mach. Intell..

[5]  Stéphane Mallat,et al.  A Theory for Multiresolution Signal Decomposition: The Wavelet Representation , 1989, IEEE Trans. Pattern Anal. Mach. Intell..

[6]  Roberto Marcondes Cesar Junior,et al.  Shape characterization in natural scales by using the multiscale bending energy , 1996, ICPR.

[7]  Walter G. Kropatsch.  Curve representations in multiple resolutions , 1987, Pattern Recognit. Lett..

[8]  M. Jagersand.  Saliency maps and attention selection in scale and spatial coordinates: an information theoretic approach , 1995, Proceedings of IEEE International Conference on Computer Vision.

[9]  Martin Jägersand,et al.  Saliency Maps and Attention Selection in Scale and Spatial Coordinates: An Information Theoretic Approach , 1995, ICCV.

[10]  Pnvid H Ivl,et al.  A Representation for Image Curves , 1984, AAAI.

[11]  Donald D. Hoffman.  Representing shapes for visual recongnition , 1983 .

[12]  Azriel Rosenfeld,et al.  Angle Detection on Digital Curves , 1973, IEEE Transactions on Computers.

[13]  Farzin Mokhtarian,et al.  A Theory of Multiscale, Curvature-Based Shape Representation for Planar Curves , 1992, IEEE Trans. Pattern Anal. Mach. Intell..

[14]  Roland T. Chin,et al.  On the Detection of Dominant Points on Digital Curves , 1989, IEEE Trans. Pattern Anal. Mach. Intell..

[15]  R. Marcondes Cesar,et al.  Shape characterization in natural scales by using the multiscale bending energy , 1996, Proceedings of 13th International Conference on Pattern Recognition.

[16]  D.J. Anderson,et al.  Optimal Estimation of Contour Properties by Cross-Validated Regularization , 1989, IEEE Trans. Pattern Anal. Mach. Intell..

[17]  Ullrich Köthe,et al.  Local Appropriate Scale in Morphological Scale-Space , 1996, ECCV.

[18]  Paul L. Rosin.  Non-Parametric Multiscale Curve Smoothing , 1994, Int. J. Pattern Recognit. Artif. Intell..

[19]  Tony Lindeberg,et al.  Scale selection for differential operators , 1994 .

[20]  Paul L. Rosin.  Multiscale Representation and Matching of Curves Using Codons , 1993, CVGIP Graph. Model. Image Process..

[21]  John K. Tsotsos,et al.  Recognizing planar curves using curvature-tuned smoothing , 1990, [1990] Proceedings. 10th International Conference on Pattern Recognition.

[22]  Joaquín Fernández-Valdivia,et al.  Representing planar curves by using a scale vector , 1994, Pattern Recognit. Lett..

[23]  Andrew P. Witkin,et al.  Scale-space filtering: A new approach to multi-scale description , 1984, ICASSP.

[24]  Steven W. Zucker,et al.  Indexing visual representations through the complexity map , 1995, Proceedings of IEEE International Conference on Computer Vision.

[25]  Keinosuke Fukunaga,et al.  Introduction to Statistical Pattern Recognition , 1972 .