Active Contours

Active Contours deals with the analysis of moving images - a topic of growing importance within the computer graphics industry. In particular it is concerned with understanding, specifying and learning prior models of varying strength and applying them to dynamic contours. Its aim is to develop and analyse these modelling tools in depth and within a consistent framework.

Inhalt
1 Introduction.- 1.1 Organisation of the book.- 1.2 Applications.- 2 Active shape models.- 2.1 Snakes.- 2.2 Deformable templates.- 2.3 Dynamic contours.- I Geometrical Fundamentals.- 3 Spline curves.- 3.1 B-spline functions.- 3.2 Finite bases.- 3.3 Multiple knots.- 3.4 Norm and inner product for spline functions.- 3.5 B-spline parametric curves.- 3.6 Curves with vertices.- 3.7 Control vector.- 3.8 Norm for curves.- 3.9 Areas and moments.- 4 Shape-space models.- 4.1 Representing transformations in shape-space.- 4.2 The space of Euclidean similarities.- 4.3 Planar affine shape-space.- 4.4 Norms and moments in a shape-space.- 4.5 Perspective and weak perspective.- 4.6 Three-dimensional affine shape-space.- 4.7 Key-frames.- 4.8 Articulated motion.- 5 Image processing techniques for feature location.- 5.1 Linear scanning.- 5.2 Image filtering.- 5.3 Using colour.- 5.4 Correlation matching.- 5.5 Background subtraction.- 6 Fitting spline templates.- 6.1 Regularised matching.- 6.2 Normal displacement in curve fitting.- 6.3 Recursive solution of curve-fitting problems.- 6.4 Examples.- 7 Pose recovery.- 7.1 Calculating the pose of a planar object.- 7.2 Pose recovery for three-dimensional objects.- 7.3 Separation of rigid and non-rigid motion.- II Probabilistic Modelling.- 8 Probabilistic models of shape.- 8.1 Probability distributions over curves.- 8.2 Posterior distribution.- 8.3 Probabilistic modelling of image features.- 8.4 Validation gate.- 8.5 Learning the prior.- 8.6 Principal Components Analysis (PCA).- 9 Dynamical models.- 9.1 Some simple dynamical prior distributions.- 9.2 First-order Auto-regressive processes.- 9.3 Limitations of first-order dynamical models.- 9.4 Second-order dynamical models.- 9.5 Second-order AR processes in shape-space.- 9.6 Setting dynamical parameters.- 10 Dynamic contour tracking.- 10.1 Temporal fusion by Kaiman filter.- 10.2 Tracking performance.- 10.3 Choosing dynamical parameters.- 10.4 Case study.- 11 Learning motion.- 11.1 Learning one-dimensional dynamics.- 11.2 Learning AR process dynamics in shape-space.- 11.3 Dynamical modes.- 11.4 Performance of trained trackers.- 12 Non-Gaussian models and random sampling algorithms.- 12.1 Factored sampling.- 12.2 The CONDENSATION algorithm.- 12.3 An observation model.- 12.4 Applications of the CONDENSATION algorithm.- A Mathematical background.- A.1 Vectors and matrices.- A.2 B-spline basis functions.- A.3 Probability.- B Stochastic dynamical systems.- B.1 Continuous-time first-order dynamics.- B.2 Second-order dynamics in continuous time.- B.3 Accuracy of learning.- C Farther shape-space models.- C.1 Recursive synthesis of shape-spaces.- Glossary of notation.- Author Index.

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