Synonyms
Related Concepts
Definition
What is shape? Although the use of words shape or shape analysis is very common in computer vision, its definition is seldom made precise in a mathematical sense. According to the Oxford English Dictionary, it means “the external form or appearance of someone or something as produced by their outline.” Kendall [1] described shape as a mathematical property that remains unchanged under certain transformations such as rotation, translation, and global scaling. Shape analysis seeks to represent shapes as mathematical quantities, such as vectors or functions, that can be manipulated using appropriate rules and metrics. Statistical shape analysis is concerned with quantifying shape as a random quantity and developing tools for generating shape comparisons, averages, probability models, hypothesis tests, Bayesian estimates, and other statistical procedures on shape spaces.
Background
Shape...
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Kendall DG (1984) Shape manifolds, procrustean metrics and complex projective spaces. Bull Lond Math Soc 16: 81–121
Cootes TF, Taylor CJ, Cooper DH, Graham J (1995) Active shape models: their training and application. Comput Vis Image Underst 61:38–59
Dryden IL, Mardia K (1998) Statistical shape analysis. Wiley, Chichester/New York
Younes L (1998) Computable elastic distance between shapes. SIAM J Appl Math 58(2):565–586
Younes L, Michor PW, Shah J, Mumford D, Lincei R (2008) A metric on shape space with explicit geodesics. Mat E Appl 19(1):25–57
Mio W, Srivastava A, Joshi SH (2007) On shape of plane elastic curves. Intl J Comput Vis 73(3):307–324
. Joshi SH, Klassen E, Srivastava A, Jermyn IH (2007) A novel representation for riemannian analysis of elastic curves in \({\mathbb R}^n\). In: Proceedings of IEEE conference on computer vision pattern recognition (CVPR), Minneapolis, pp 1–7
. Srivastava A, Klassen E, Joshi SH, Jermyn IH (2010) Shape analysis of elastic curves in euclidean spaces. IEEE Trans Pattern Anal Mach Intell (Accepted for publication). doi:10.1109/TPAMI.2010.184
. Klassen E, Srivastava A (2006) Geodesics between 3D closed curves using path-straightening. In: Proceedings of European conference on computer vision (ECCV) Graz. Lecture notes in computer science I, pp 95–106
Karcher H (1977) Riemannian center of mass and mollifier smoothing. Commun Pure Appl Math 30(5):509–541
Le HL, Kendall DG (1993) The riemannian structure of euclidean shape spaces: a novel environment for statistics. Ann Stat 21(3):1225–1271
Srivastava A, Joshi SH, Mio W, Liu X (2005) Statistical shape anlaysis: clustering, learning and testing. IEEE Trans Pattern Anal Mach Intell 27(4):590–602
Kurtek S, Klassen E, Ding Z, Jacobson S, Jacobson J, Avison M, and Srivastava A (2011) Parameterization-invariant shape comparisons of anatomical surfaces. IEEE Trans Med Imaging 30(3):849–858
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2014 Springer Science+Business Media New York
About this entry
Cite this entry
Srivastava, A., Kurtek, S., Klassen, E. (2014). Statistical Shape Analysis. In: Ikeuchi, K. (eds) Computer Vision. Springer, Boston, MA. https://doi.org/10.1007/978-0-387-31439-6_778
Download citation
DOI: https://doi.org/10.1007/978-0-387-31439-6_778
Published:
Publisher Name: Springer, Boston, MA
Print ISBN: 978-0-387-30771-8
Online ISBN: 978-0-387-31439-6
eBook Packages: Computer ScienceReference Module Computer Science and Engineering