Frank R. Schmidt

In this work, we introduce a novel implicit representation of shape which is based on assigning to each pixel a probability that this pixel is inside the shape. This probabilistic representation of shape resolves two important drawbacks of alternative implicit shape representations such as the level set method: Firstly, the space of shapes is convex in the sense that arbitrary convex combinations of a set of shapes again correspond to a valid shape. Secondly, we prove that the introduction of shape priors into variational image segmentation leads to functionals which are convex with respect to shape deformations.
For a large class of commonly considered (spatially continuous) functionals, we prove that - under mild regularity assumptions – segmentation and tracking with statistical shape priors can be performed in a globally optimal manner. In experiments on tracking a walking person through a cluttered scene we demonstrate the advantage of global versus local optimality.

@InProceedings\{CSB08,
  author       = "Cremers, Daniel and Schmidt, Frank R. and Barthel, Frank",
  title        = "Shape Priors in Variational Image Segmentation: Convexity, Lipschitz Continuity and Globally Optimal Solutions",
  booktitle    = "IEEE Conference on Computer Vision and Pattern Recognition (CVPR)",
  month        = "Jun",
  year         = "2008",
  address      = "Anchorage, Alaska",
  url          = "http://frank-r-schmidt.de/Publications/2008/CSB08"
}