High-Order Models in Semantic Image Segmentation

I. Introduction
II. Introductory Background
II.1 Discrete representations
II.1.a Graphs
II.2 Continuous representations
II.2.a Curves
II.2.b Level Sets
II.3 First-order regional terms
II.4 Second-order boundary terms
II.5 High-order terms
II.6 Convexity
II.7 Sub-modularity and super-modularity
III Basic segmentation models
III.1 Bayesian statement
III.2 The Boykov-Jolly model
III.3 The Chan-Vese model
III.4 The GrabCut model
III.5 Other parametric models
III.6 An information-theoretic view
IV Standard optimization techniques
IV.1 Gradient descent
IV.1.a Euler-Lagrange equations
IV.1.b Basic functional derivatives
IV.2 Block-coordinate descent
IV.3 Curve evolution and level sets
IV.4 Convex relaxation
IV.5 Graph Cuts
V High-order segmentation models
V.1 Entropy-based clustering
V.2 Balanced clustering
V.2.a Average association
V.2.b Normalized Cuts
V.2.c Kernel clustering
V.3 Distribution matching
V.4 Shape priors
V.4.a Generic priors
V.4.a.i Shape compactness
V.4.a.ii Shape convexity
V.4.b Specific priors
V.4.b.i Shape representations
V.4.b.ii Statistical shape models
V.5 Soft constraints
VI. Advanced optimization techniques
VI.1 Duality and linear programming relaxation
VI.2 Interior-point methods
VI.3 Trust region
VI.4 Bound and Pseudo-bound optimization
VII. Advanced medical imaging applications
VIII. Appendix