Robustness and modularity of 2-dimensional size functions: an experimental study

Authors:
Silvia Biasotti;Andrea Cerri;Daniela Giorgi
Affiliations:
IMATI, Consiglio Nazionale delle Ricerche, Genova, Italy;Vienna University of Technology, Faculty of Informatics, Pattern Recognition and Image Processing Group, Austria;IMATI, Consiglio Nazionale delle Ricerche, Genova, Italy
Venue:
CAIP'11 Proceedings of the 14th international conference on Computer analysis of images and patterns - Volume Part I
Year:
2011

Citing 10
Cited 0

Content-Based Image Retrieval at the End of the Early Years

IEEE Transactions on Pattern Analysis and Machine Intelligence
Topology matching for fully automatic similarity estimation of 3D shapes

Proceedings of the 28th annual conference on Computer graphics and interactive techniques
Rotation invariant spherical harmonic representation of 3D shape descriptors

Proceedings of the 2003 Eurographics/ACM SIGGRAPH symposium on Geometry processing
Retrieval of trademark images by means of size functions

Graphical Models - Special issue on the vision, video and graphics conference 2005
The theory of multidimensional persistence

SCG '07 Proceedings of the twenty-third annual symposium on Computational geometry
Size functions for comparing 3D models

Pattern Recognition
Describing shapes by geometrical-topological properties of real functions

ACM Computing Surveys (CSUR)
A survey of content based 3D shape retrieval methods

Multimedia Tools and Applications
Multidimensional Size Functions for Shape Comparison

Journal of Mathematical Imaging and Vision
A concise and provably informative multi-scale signature based on heat diffusion

SGP '09 Proceedings of the Symposium on Geometry Processing

Quantified Score

Hi-index	0.01

Visualization

Abstract

This paper deals with the concepts of 2-dimensional size function and 2-dimensional matching distance. These are two ingredients of (2-dimensional) Size Theory, a geometrical/topological approach to shape analysis and comparison. 2-dimensional size functions are shape descriptors providing a signature of the shapes under study, while the 2- dimensional distance is the tool to compare them. The aim of the present paper is to validate, through some experiments on 3D-models, a computational framework recently introduced to deal with 2-dimensional Size Theory. We will show that the cited framework is modular and robust with respect to noise, non-rigid and non-metric-preserving shape transformations. The proposed framework allows us to improve the ability of 2-dimensional size functions in discriminating between shapes.