Whatisactuallytheinformationdirectlyrepresentedinthescale-space?Istarted to wonder about this shortly after Peter Johansen, 15 years ago, showed me his intriguing paper on how uniquely to reconstruct a band-limited 1D signal from its scale-space toppoints. Still, I have not fully understood its implications. Merely recording where structure vanishes under blurring is su?cient to fully reconstruct the details. Of course, technicalities exist, for example, you must also know negative scale toppoints. Nevertheless, I ?nd it surprising that we may trade the metric properties of a signal with the positions of its inherent structure. The result has been generalizedto analytic signals, shown also for the zero crossings of the Laplacean, but has not yet been generalized to 2D. This remains an open problem. In 2003, Peter Giblin, Liverpool University, Luc Florack, Eindhoven Univ- sity of Technology, Jon Sporring, University of Copenhagen, my colleague Ole Fogh Olsen, and several others started the project collaborationDeep Structure and Singularities in Computer Vision under the European Union, IST, Future and Emerging Technologies program, trying to obtain further knowledge about what informationis actuallycarriedby the singularitiesof shapesand gray-scale images. In this project, we probed from several directions the question of how much of the metric information is actually encoded in the structure of shapes and images. We, and many others, have given hints in this direction.

Inhalt
Oral Presentations.- Blurred Correlation Versus Correlation Blur.- A Scale Invariant Covariance Structure on Jet Space.- Essential Loops and Their Relevance for Skeletons and Symmetry Sets.- Pre-symmetry Sets of 3D Shapes.- Deep Structure of Images in Populations Via Geometric Models in Populations.- Estimating the Statistics of Multi-object Anatomic Geometry Using Inter-object Relationships.- Histogram Statistics of Local Model-Relative Image Regions.- The Bessel Scale-Space.- Linear Image Reconstruction from a Sparse Set of ?-Scale Space Features by Means of Inner Products of Sobolev Type.- A Riemannian Framework for the Processing of Tensor-Valued Images.- From Stochastic Completion Fields to Tensor Voting.- Deep Structure from a Geometric Point of View.- Maximum Likely Scale Estimation.- Adaptive Trees and Pose Identification from External Contours of Polyhedra.- Poster Presentations.- Exploiting Deep Structure.- Scale-Space Hierarchy of Singularities.- Computing 3D Symmetry Sets; A Case Study.- Irradiation Orientation from Obliquely Viewed Texture.- Using Top-Points as Interest Points for Image Matching.- Transitions of Multi-scale Singularity Trees.- A Comparison of the Deep Structure of ?-Scale Spaces.- A Note on Local Morse Theory in Scale Space and Gaussian Deformations.