In this paper, we formulate the shape localization problem in the Bayesian framework. In the learning stage, we propose the Constrained RankBoost approach to model the likelihood of local features associated with the key points of an object, like face, while preserve the prior ranking order between the ground truth position of a key point and its neighbors; in the inferring stage, a simple efficient iterative algorithm is proposed to uncover the MAP shape by locally modeling the likelihood distribution around each key point via our proposed variational Locally Weighted Learning (VLWL) method. Our proposed framework has the following benefits: 1) compared to the classical PCA models, the likelihood presented by the ranking prior likelihood model has more discriminating power as to the optimal position and its neighbors, especially in the problem with ambiguity between the optimal positions and their neighbors; 2) the VLWL method guarantees that the posterior probability of the derived shape increases monotonously; and 3) the above two methods are both based on accurate probability formulation, which spontaneously leads to a robust confidence measure for the discovered shape. Moreover, we present a theoretical analysis for the convergence of the Constrained Rank-Boost. Extensive experiments compared with the Active Shape Models demonstrate the accuracy, robustness, and stability of our proposed framework. 1.

Typical aims of shape analysis are to match or register configurations, to estimate mean shapes and to investigate shape variability. Procrustes analysis is a popular method for the shape analysis of labeled point configurations, based on a least squares criterion. We consider alternative procedures which are highly resistant to outlier points. In particular we consider procedures based on S-estimators, Least Median of Squares and Least Quartile Difference estimators. Practical implementation issues and relative performances are discussed in a simulation study. A procedure for mean shape estimation is also considered. We demonstrate the methodology by comparing resistant mean estimation and principal component analysis with the Procrustes procedure on a dataset of mouse vertebral landmarks and a simulated dataset. In our examples the estimated mean configurations from the resistant and Procrustes procedures were very similar, and the principal components did not differ substantially. I...

In this paper we model shape objects variability and spatial relationships between characteristics of this object. What is an object? We consider that an object is a set of shapes and points. We establish here a formalism unifying shapes and points by approximating shape contours by composite B ezier curves. These are equivalent to their control points. We then propose a non linear invariant statistical model and we learn the average object, it's variability and relationships. We finally evaluate our methodology in cephalometry, by modeling anatomical structures and points. 1.

We develop a statistical shape model for the analysis of local shape variation. In particular, we consider models of shapes that exhibit self-similarity along their contours such as fractal and space filling curves.

Two key aspects of coupled multi-object shape analysis and atlas generation are the choice of representation