Geometric Hamilton–Jacobi theory for higher-order autonomous systems

Geometric and Higher Order Logicin

Higher-Order Game Theory

In applied game theory the motivation of players is a key element. It is encoded in the payoffs of the game form and often based on utility functions. But there are cases were formal descriptions in the form of a utility function do not exist. In this paper we introduce a representation of games where players’ goals are modeled based on so-called higher-order functions. Our representation provi...

Higher-Order Decision Theory

Classical decision theory models behaviour in terms of utility maximisation where utilities represent rational preference relations over outcomes. However, empirical evidence and theoretical considerations suggest that we need to go beyond this framework. We propose to represent goals by higherorder functions or operators that take other functions as arguments where the max and argmax operators...

Higher-Order Feature-Preserving Geometric Regularization

We introduce two fourth-order regularization methods that remove geometric noise without destroying significant geometric features. These methods leverage ideas from image denoising and simplification of high contrast images in which piecewise affine functions are preserved up to infinitesimally small transition zones. We combine the regularization techniques with active contour models and appl...

Image matching with higher-order geometric features.

We propose a geometric matching technique in which line segments and elliptical arcs are used as edge features. The use of these higher-order features renders feature representation efficient. We derive distance measures to evaluate the similarity between the features of the model and those of the image. The model transformation parameters are found by searching a 3-D transformation space using...