Form representions and means for landmarks: A survey and comparative study

Computer Vision and Image Understanding

Volumn 102, Issue 2, 2006, Pages 188-203

  Heo, Giseon ^a   Small, Christopher G ^b  

^a UNIVERSITY OF ALBERTA   (Canada)

^b UNIVERSITY OF WATERLOO   (Canada)

Author keywords

Form; Image analysis; Invariance; Landmark; Shape; Tomography

Indexed keywords

INFORMATION ANALYSIS; MATHEMATICAL TECHNIQUES; STATISTICAL METHODS; SURVEYING; TOMOGRAPHY;

FORM; INVARIANCE; LANDMARK; SHAPE;

IMAGE ANALYSIS;

EID: 33645800369     PISSN: 10773142     EISSN: 1090235X     Source Type: Journal    
DOI: 10.1016/j.cviu.2006.01.003     Document Type: Article

References (15)

1. Goodall C. Procrustes methods in the statistical analysis of shape. J. R. Stat. Soc. B 53 (1991) 285-339 Statistical inferences based on procrustes shape statistics are presented
2. 3 with more than three landmarks
3. Goodall C.R., and Mardia K.V. Multivariate aspects of shape theory. Ann. Stat. 21 (1993) 848-866 Obtains (reflection) size-and-shape and shape distributions under Gaussian error model by using the QR decomposition
4. Gower J.C. Some distance properties of latent root and vector methods used in multivariate analysis. Biometrika 53 (1966) 325-338 Constructs the principal components analysis (PCA) of the association matrix and discusses the duality between PCA of the association matrix and PCA of the correlation matrix. The applications of PCA to factor analysis and to proximity analysis are presented
5. Huxley J.S. Problems of Relative Growth. second ed. (1972), Dover, New York Quantitative theory is formulated to explain the different rates of growth of whole organs relative to the rest of the body and the distribution of growth potential
6. Karcher H. Riemannian center of mass and mollifier smoothing. Comm. Pure Appl. Math. 30 (1977) 509-541 Generalizes the mollifier smoothing to maps between Riemannian manifolds
7. Kendall D.G., Barden D., Carne T.K., and Le H. Shape and Shape Theory (1999), John Wiley & Sons Ltd, Chichester Mathematical theory of D.G. Kendell's shape spaces is emphasized. Geometrical aspects of shape analysis to statistical aspects of shape and size-and-shape means are covered
8. Kendall W.S. Probability, convexity, and harmonic maps with small image I: uniqueness and fine existence. Proc. London Math. Soc. 61 (1990) 371-406 Introduces the probabilistic approach to the Dirichlet problem for harmonic maps
9. Kent J.T. The complex Bingham distribution and shape analysis. J. R. Stat. Soc. B 56 (1994) 285-299 The Bingham distribution is utilized in shape analysis. Compares several methods of computing average shape for concentrated shape data
10. 2
11. Le H. Mean size-and-shapes and mean shapes: a geometric point of view. Adv. Appl. Prob. 27 (1995) 44-55 Provides sufficient conditions for algorithms to converge to unique Procrustean mean size-and-shape and Procrustean mean shape
12. Lele S. Some comments on coordinate-free and scale-invariant methods in morphometrics. Am. J. Phys. Anthropol. 85 (1991) 407-417 Nontechnical discussion of the ideas developed further in Lele [60]. Superposition methods and ED matrix methods are compared
13. Lele S. Euclidean distance matrix analysis (EDMA): estimation of mean form and mean form difference. Math. Geol. 25 (1993) 573-602 The estimation of mean form, variation and mean form difference is studied under the Gaussian model. Method of moment estimators are shown to be consistent
14. Yezzi A.J., and Soatto S. Deformation: deforming motion, shape average and the joint registration and approximation of structures in images. Int. J. Comput. Vision 53 (2003) 153-167 The notion of mean shape is proposed to separate the motion from the deformation. The mean shape is extended to a moving mean for the purpose of tracking moving and deforming objects over time
15. H. Ziezold, On expected figures and a strong law of large numbers for random elements in quasi-metric spaces. Trans. 7th Prague Conf. Inf. Theory, Stat. Dec. Func, Random Process. Vol A. Reidel, Dordrecht, 1977, 591-602, Defines the mean figures (forms) using Fréchet's definition of expected elements in metric spaces. With an example, shows that averaging figures is not transitive.