k-dimensional Size Functions for Shape Description and Comparison

This paper advises the use of k-dimensional size functions for comparison and retrieval in the context of multidimensional shapes, where by shape we mean something in two or higher dimensions having a visual appearance. The attractive feature of k-dimensional size functions is that they allow to readily establish a similarity measure between shapes of arbitrary dimension, taking into account different properties expressed by a multivalued real function defined on the shape. In particular, we outline the potential of this approach in a series of experiments.

[1]  Daniela Giorgi,et al.  Reeb graphs for shape analysis and applications , 2008, Theor. Comput. Sci..

[2]  Taku Komura,et al.  Topology matching for fully automatic similarity estimation of 3D shapes , 2001, SIGGRAPH.

[3]  Leonidas J. Guibas,et al.  Persistence Barcodes for Shapes , 2005, Int. J. Shape Model..

[4]  P. Frosini,et al.  Size Functions and Morphological Transformations , 1997 .

[5]  BENJAMIN BUSTOS,et al.  Feature-based similarity search in 3D object databases , 2005, CSUR.

[6]  Karthik Ramani,et al.  Three-dimensional shape searching: state-of-the-art review and future trends , 2005, Comput. Aided Des..

[7]  Andrea Cerri,et al.  Stability in multidimensional Size Theory , 2006, ArXiv.

[8]  Remco C. Veltkamp,et al.  A Survey of Content Based 3D Shape Retrieval Methods , 2004, SMI.

[9]  Patrizio Frosini,et al.  Size theory as a topological tool for computer vision , 1999 .

[10]  Daniela Giorgi,et al.  A Comparison Framework for 3D Object Classification Methods , 2006, MRCS.

[11]  Szymon Rusinkiewicz,et al.  Rotation Invariant Spherical Harmonic Representation of 3D Shape Descriptors , 2003, Symposium on Geometry Processing.

[12]  K. Ramani,et al.  Three-dimensional shape searching : state-ofthe-art review and future trends , 2005 .

[13]  Patrizio Frosini,et al.  Deformation Energy for Size Functions , 1999, EMMCVPR.

[14]  Daniela Giorgi,et al.  Size functions for 3D shape retrieval , 2006, SGP '06.

[15]  Daniela Giorgi,et al.  Retrieval of trademark images by means of size functions , 2006, Graph. Model..

[16]  Patrizio Frosini,et al.  On the use of size functions for shape analysis , 1993, [1993] Proceedings IEEE Workshop on Qualitative Vision.

[17]  Frédéric Chazal,et al.  Molecular shape analysis based upon the morse-smale complex and the connolly function , 2002, SCG '03.

[18]  坂上 貴之 書評 Computational Homology , 2005 .

[19]  Daniela Giorgi,et al.  Multidimensional Size Functions for Shape Comparison , 2008, Journal of Mathematical Imaging and Vision.

[20]  Alessandro Verri,et al.  Computing Size Functions from Edge Maps , 2004, International Journal of Computer Vision.

[21]  M. Ferri,et al.  Computer-aided diagnosis of melanocytic lesions. , 2005, Anticancer research.

[22]  Patrizio Frosini,et al.  Natural Pseudo-Distance and Optimal Matching between Reduced Size Functions , 2008, ArXiv.

[23]  Patrizio Frosini,et al.  Size Functions and Formal Series , 2001, Applicable Algebra in Engineering, Communication and Computing.