Constant Guillot1 [email protected] Maxime Taron1 [email protected] Patrick Sayd1 [email protected] Quoc-Cuong Pham1 [email protected] Christophe Tilmant2 [email protected] Jean-Marc Lavest2 [email protected] 1 CEA LIST Laboratoire Vision et Ingenierie des Contenus, BP 94, Gif-sur-Yvette, F-91191 France 2 LASMEA UMR 6602, PRES Clermont Universite/CNRS, 63177 Aubiere cedex, France

Registration and modeling of shapes are two important problems in computer vision and pattern recognition. Despite enormous progress made over the past decade, these problems are still open. In this paper, we advance the state of the art in both directions. First we consider an efficient registration method that aims to recover a one-to-one correspondence between shapes and introduce measures of uncertainties driven from the data which explain the local support of the recovered transformations. To this end, a free form deformation is used to describe the deformation model. The transformation is combined with an objective function defined in the space of implicit functions used to represent shapes. Once the registration parameters have been recovered, we introduce a novel technique for model building and statistical interpretation of the training examples based on a variable bandwidth kernel approach. The support on the kernels varies spatially and is determined according to the uncertainties of the registration process. Such a technique introduces the ability to account for potential registration errors in the model. Hand-written character recognition and knowledge-based object extraction in medical images are examples of applications that demonstrate the potentials of the proposed framework.

Reliable segmentation of the left ventricle is a long sought objective in medical imaging for automatic retrieval of anatomical and pathological measurements and detection of malfunctions. In this paper, we propose a novel model-constrained approach to address this task. The method is based on an implicit representation of the shape model used in a shape registration framework with a Thin Plate Spline transform to retrieve possible deformations. The main innovation of our approach resides in the use of uncertainties defined on the registered shape to augment the training set and improve the robustness of the statistical deformable model. We use ICA to reduce the dimensionality of the space of deformations and provide a good separation of the different deformable parts of the heart. Furthermore the estimation of uncertainties is also introduced in the segmentation process which is addressed in a variational framework where prior knowledge and visual support are considered. The method lead to very promising qualitative and quantitative experimental results in CT.

In this paper, we introduce a new technique for shape modelling in the space of implicit polynomials. Registration consists of recovering an optimal one-to-one transformation of a higher order polynomial along with uncertainties measures that are determined according to the covariance matrix of the correspondences at the zero isosurface. In the modelling phase, these measures are used to weight the importance of the training samples phase according to a variable bandwidth non-parametric density estimation process. The selection of the most appropriate kernels to represent the training set is done through the maximum likelihood criterion. Excellent results for patterns of digits, related with the registration and the modelling aspects of our approach demonstrate the potentials of our method