1. Challenges in Computer Vision Understanding the ”seeing machine” The input (images) The output (shapes, actions?, diagnosis?) The mapping (statistics, learning) The computation (algorithms) Images Shapes Statistics Computation

2. Fundamental problems Input space is high (infinite) dimensional Modeling of shape Mapping is nonlinear Generalization from few examples Finite memory and computational time

3. Fundamental challenge Computational efficient, statistical optimal mapping from images to models/actions: The optimal mapping is unreachable (Kolmogorov) Infinite computation time using optimal mapping (Ryabko) So only hacking is left, so let’s hack Only theories that proove themselves in practice are good theories

4. Desired properties Generalisation -> metric in input and model space Universality -> Flexible/scalable models Fast convergence -> ”least committed priors” and ”good learning”

5. Concrete challeges Statistical well-founded metric on images Geometrical metrics on shapes Universal shape models Information reduction or ”visual attention” Marginalisation over hidden model parameters Computational efficient approximative methods Statistics on trees/graphs

6. Metrics on images Scale-space Independent component analysis Geometry of images

7. Metrics on shapes Shape-space theory Grenander’s ”Theory of shape” Invariant parametrisations Brownian motions Warps of embedding spaces Lie-group methods

8. Universal shape models Fourier descriptors Landmark representations Medial models Level sets

9. Information reduction Dimensionality reduction Feature selection ”AdaBoost”

10. Marginalisation over hidden parameters Common sense Mean field analysis?

11. Computational efficient methods PDEs Particle filters Hierachical representations Sequential testing