Short course, International Conference on Computer Vision, 28 September 2009, Kyoto, Japan

Introduction to non-rigid world - Rock, Paper, Scissors - Invariant similarity - Invariant correspondence - Analysis and synthesis - Landscape - Two perspectives - Metric model - Isometry - Examples of metrics - Rigid isometry - Hausdorff distance - ICP - Fairy tale shape similarity problem - Non-rigid similarity - Canonical forms - Isometric embedding - Mapmaker's problem - Minimum distortion embedding - Multidimensional scaling - Discrete embedding problem - Minimization of quadratic stress - Shapes as graphs - Discrete geodesic problem - Dijkstra's algorithm - Troubles with the metric - Metrication error - Eikonal equation - Fast marching - Raster scan fast marching - Parallelization

Examples of canonical forms - Expression-invariant face recognition - Canonical forms, revisited - Metric coupling - Gromov-Hausdorff distance - Correspondence - Generalized multidimensional scaling - A problem with geodesics - Heat equation - Heat kernel - Diffusion distance - GMDS with diffusion geometry - Joint intrinsic/extrinsic similarity - Self-similarity and symmetry - Extrinsic vs intrinsic symmetry - Partial similarity - Recognition by parts - Significance - Statistical significance - Not only size matters - Regularity - Numerical optimization

"Natural" correspondence - Minimum distortion correspondence - Partial correspondence - Texture transfer - Calculus of shapes - Metamorphing - Face caricaturization - Shape space - Choice of trajectory - Choice of metric - Minimum distortion trajectory

Computer vision perspective - Bags of words - Images vs shapes - Diffusion scalespace - Heat kernel descriptors - Geometric vocabulary - Bags of features - Expressions - Spatially-sensitive bags of features - Shape Google - Similarity-preserving hashing