Independent Modes of Variation in Point Distribution Models

A Point Distribution Model requires first the choice of an appropriate representation for the data and then the estimation of the density within this representation. Independent Component Analysis is a linear transform that represents the data in a space where statistical dependencies between the components are minimized. In this paper, we propose Independent Component Analysis as a representation for point distributions. We observe that within this representation, the density estimation is greatly simplified and propose solutions to the most common problems concerning shapes. Mainly, testing shape feasibility and finding the nearest feasible shape. We also observe how the description of shape deformations in terms of statistically independent modes provides a more intuitive and manageable framework. We perform experiments to illustrate the results and compare them with existing approaches.

[1]  J. Cardoso.  Infomax and maximum likelihood for blind source separation , 1997, IEEE Signal Processing Letters.

[2]  Aapo Hyvärinen,et al.  Survey on Independent Component Analysis , 1999 .

[3]  Terrence J. Sejnowski,et al.  The “independent components” of natural scenes are edge filters , 1997, Vision Research.

[4]  Timothy F. Cootes,et al.  A mixture model for representing shape variation , 1999, Image Vis. Comput..

[5]  M Sarhadi,et al.  Cluster based nonlinear principle component analysis , 1997 .

[6]  Timothy F. Cootes,et al.  Non-Linear Point Distribution Modelling using a Multi-Layer Perceptron , 1995, BMVC.

[7]  M Sarhadi,et al.  Cluster Based non-linear Principle Component Analysis , 1997 .

[8]  Terrence J. Sejnowski,et al.  An Information-Maximization Approach to Blind Separation and Blind Deconvolution , 1995, Neural Computation.

[9]  J. Gower.  Generalized procrustes analysis , 1975 .

[10]  David C. Hogg,et al.  3D Deformable Hand Models , 1996, Gesture Workshop.

[11]  D. Rubin,et al.  Maximum likelihood from incomplete data via the EM - algorithm plus discussions on the paper , 1977 .

[12]  Timothy F. Cootes,et al.  A Non-linear Generalisation of PDMs using Polynomial Regression , 1994, BMVC.

[13]  Aapo Hyvärinen,et al.  Sparse Code Shrinkage: Denoising of Nongaussian Data by Maximum Likelihood Estimation , 1999, Neural Computation.

[14]  Timothy F. Cootes,et al.  Active Shape Models-Their Training and Application , 1995, Comput. Vis. Image Underst..

[15]  Aapo Hyvärinen,et al.  A Fast Fixed-Point Algorithm for Independent Component Analysis , 1997, Neural Computation.

[16]  Christopher M. Bishop,et al.  Neural networks for pattern recognition , 1995 .

[17]  Terrence J. Sejnowski,et al.  Independent Component Analysis Using an Extended Infomax Algorithm for Mixed Subgaussian and Supergaussian Sources , 1999, Neural Computation.

[18]  David C. Hogg,et al.  Improving Specificity in PDMs using a Hierarchical Approach , 1997, BMVC.

[19]  Pierre Comon,et al.  Independent component analysis, A new concept? , 1994, Signal Process..

[20]  David C. Hogg,et al.  An efficient method for contour tracking using active shape models , 1994, Proceedings of 1994 IEEE Workshop on Motion of Non-rigid and Articulated Objects.