Character posing is of interest in computer animation. It is difficult due to its dependence on inverse kinematics (IK) techniques and articulate property of human characters . To solve the IK problem, classical methods that rely on numerical solutions often suffer from the under-determination problem and can not guarantee naturalness. Existing data-driven methods address this problem by learning from motion capture data. When facing a large variety of poses however, these methods may not be able to capture the pose styles or be applicable in real-time environment. Inspired from the low-rank motion de-noising and completion model in lai2011motion , we propose a novel model for character posing based on sparse coding. Unlike conventional approaches, our model directly captures the pose styles in Euclidean space to provide intuitive training error measurements and facilitate pose synthesis. A pose dictionary is learned in training stage and based on it natural poses are synthesized to satisfy users' constraints . We compare our model with existing models for tasks of pose de-noising and completion. Experiments show our model obtains lower de-noising and completion error. We also provide User Interface(UI) examples illustrating that our model is effective for interactive character posing.
A straightforward model for modelling the prior is to use the Gaussian distribution. Due to the connection in the covariance matrix, this approach is related to Principal Component analysis (PCA) which restricts the solution to lie in the subspace span by the principal components. By imposing the Gaussian prior, we force the solution to approach the mean from the direction of one principal component or a linear combination of them. Instead of using the Gaussian model directly, we can also first partition the motion data by clustering algorithm and then build a Gaussian prior for each cluster. This is similar to the mixture of local linear models which have been used as baseline models in @cite_7 .
@cite_7
2169779569 2158339409 2124449497 2147426468
In this paper we introduce a new underlying probabilistic model for principal component analysis (PCA). Our formulation interprets PCA as a particular Gaussian process prior on a mapping from a latent space to the observed data-space. We show that if the prior's covariance function constrains the mappings to be linear the model is equivalent to PCA, we then extend the model by considering less restrictive covariance functions which allow non-linear mappings. This more general Gaussian process latent variable model (GPLVM) is then evaluated as an approach to the visualisation of high dimensional data for three different data-sets. Additionally our non-linear algorithm can be further kernelised leading to 'twin kernel PCA' in which a mapping between feature spaces occurs. In this paper, we consider principal component analysis (PCA) in decomposable Gaussian graphical models. We exploit the prior information in these models in order to distribute PCA computation. For this purpose, we reformulate the PCA problem in the sparse inverse covariance (concentration) domain and address the global eigenvalue problem by solving a sequence of local eigenvalue problems in each of the cliques of the decomposable graph. We illustrate our methodology in the context of decentralized anomaly detection in the Abilene backbone network. Based on the topology of the network, we propose an approximate statistical graphical model and distribute the computation of PCA. When faced with high-dimensional data, one often uses principal component analysis (PCA) for dimension reduction. Classical PCA constructs a set of uncorrelated variables, which correspond to eigenvectors of the sample covariance matrix. However, it is well-known that this covariance matrix is strongly affected by anomalous observations. It is therefore necessary to apply robust methods that are resistant to possible outliers. Li and Chen [J. Am. Stat. Assoc. 80 (1985) 759] proposed a solution based on projection pursuit (PP). The idea is to search for the direction in which the projected observations have the largest robust scale. In subsequent steps, each new direction is constrained to be orthogonal to all previous directions. This method is very well suited for high-dimensional data, even when the number of variables p is higher than the number of observations n. However, the algorithm of Li and Chen has a high computational cost. In the references [C. Croux, A. Ruiz-Gazen, in COMPSTAT: Proceedings in Computational Statistics 1996, Physica-Verlag, Heidelberg, 1996, pp. 211–217; C. Croux and A. Ruiz-Gazen, High Breakdown Estimators for Principal Components: the Projection-Pursuit Approach Revisited, 2000, submitted for publication.], a computationally much more attractive method is presented, but in high dimensions (large p) it has a numerical accuracy problem and still consumes much computation time. In this paper, we construct a faster two-step algorithm that is more stable numerically. The new algorithm is illustrated on a data set with four dimensions and on two chemometrical data sets with 1200 and 600 dimensions. We consider full Bayesian inference in the multivariate normal mean model in the situation that the mean vector is sparse. The prior distribution on the vector of means is constructed hierarchically by first choosing a collection of nonzero means and next a prior on the nonzero values.We consider the posterior distribution in the frequentist set-up that the observations are generated according to a fixed mean vector, and are interested in the posterior distribution of the number of nonzero components and the contraction of the posterior distribution to the true mean vector. We find various combinations of priors on the number of nonzero coefficients and on these coefficients that give desirable performance. We also find priors that give suboptimal convergence, for instance, Gaussian priors on the nonzero coefficients.We illustrate the results by simulations. © 2012 Institute of Mathematical Statistics.