Registration with Uncertainties and Statistical Modeling of Shapes with Variable Metric Kernels

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.