this article, we present a variational approach to MAP estimation with a more qualitative and tutorial emphasis. The key idea behind this approach is to use geometric insight in helping construct regularizing functionals and avoiding a subjective choice of a prior in MAP estimation. Using tools from robust statistics and information theory, weshow that we can extend this strategy and develop two gradient descent flows for image denoising with a demonstrated performance

this report we describe our framework of constructing and using a shape prior in estimation problems. The key novelty of our technique is a new way to use high level, global shape knowledge to derive a local driving force in a curve evolution context. We capture information about shape in the form of a family of shape distributions (cumulative distribution functions) of features related to the shape. We design a prior objective function that penalizes the di#erences between model shape distributions and those of an estimate. We incorporate this prior in a curve evolution formulation for function minimization. Shape distribution-based representations are shown to satisfy several desired properties, such as robustness and invariance. They also have good discriminative and generalizing properties. To our knowledge, shape distribution-based representations have only been used for shape classification. Our work represents the development of a tractable framework for their incorporation in estimation problems. We apply our framework to three applications: shape morphing, average shape calculation, and image segmentation

Abstract. We present a new software package for interactive segmentation of 3D images by geodesic snakes, with manual editing. Several variants of level set snakes are incorporated, including both gradientmagnitude based snakes as well as region-competition snakes. A complete segmentation pipeline, including image preprocessing, bubble initialization and parameter control, is provided in an intuitive user interface. Slice-based overpainting is also provided in the same framework, for manual editing of the automatic snake segmentation. This tool is already in daily use by clinicians and offers a vast improvement in speed over traditional manual segmentation. We present examples from several clinical studies, as well as validation results comparing the automatic geodesic snakes segmentation with manual expert rater segmentation. 1