Restricted delaunay triangulations and normal cycle
Proceedings of the nineteenth annual symposium on Computational geometry
Computing Elevation Maxima by Searching the Gauss Sphere
SEA '09 Proceedings of the 8th International Symposium on Experimental Algorithms
Stability of curvature measures
SGP '09 Proceedings of the Symposium on Geometry Processing
Measuring bloat, overfitting and functional complexity in genetic programming
Proceedings of the 12th annual conference on Genetic and evolutionary computation
Computing elevation maxima by searching the gauss sphere
Journal of Experimental Algorithmics (JEA)
Generalized shape operators on polyhedral surfaces
Computer Aided Geometric Design
An empirical study of functional complexity as an indicator of overfitting in genetic programming
EuroGP'11 Proceedings of the 14th European conference on Genetic programming
3D Facial expression recognition based on histograms of surface differential quantities
ACIVS'11 Proceedings of the 13th international conference on Advanced concepts for intelligent vision systems
On a linear programming approach to the discrete willmore boundary value problem and generalizations
Proceedings of the 7th international conference on Curves and Surfaces
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The intent of this book is to set the modern foundations of the theory of generalized curvature measures. This subject has a long history, beginning with J. Steiner (1850), H. Weyl (1939), H. Federer (1959), P. Wintgen (1982), and continues today with young and brilliant mathematicians. In the last decades, a renewal of interest in mathematics as well as computer science has arisen (finding new applications in computer graphics, medical imaging, computational geometry, visualization ). Following a historical and didactic approach, the book introduces the mathematical background of the subject, beginning with curves and surfaces, going on with convex subsets, smooth submanifolds, subsets of positive reach, polyhedra and triangulations, and ending with surface reconstruction. We focus on the theory of normal cycle, which allows to compute and approximate curvature measures of a large class of smooth or discrete objects of the Euclidean space. We give explicit computations when the object is a 2 or 3 dimensional polyhedron. This book can serve as a textbook to any mathematician or computer scientist, engineer or researcher who is interested in the theory of curvature measures.