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Bézier and B-Spline Techniques
This book provides a solid and uniform derivation of the various properties Bezier and B-spline representations have, and shows the beauty of the underlying rich mathematical structure. The book focuses on the core concepts of Computer Aided Geometric Design and provides a clear and illustrative presentation of the basic principles, as well as a treatment of advanced material including multivariate splines, some subdivision techniques and constructions of free form surfaces with arbitrary smoothness. The text is beautifully illustrated with many excellent figures to emphasize the geometric constructive approach of this book.
Machine Learning Methods for Reverse Engineering of Defective Structured Surfaces
Pascal Laube presents machine learning approaches for three key problems of reverse engineering of defective structured surfaces: parametrization of curves and surfaces, geometric primitive classification and inpainting of high-resolution textures. The proposed methods aim to improve the reconstruction quality while further automating the process. The contributions demonstrate that machine learning can be a viable part of the CAD reverse engineering pipeline.
Analysis, Modelling, Optimization, and Numerical Techniques
This book highlights recent compelling research results and trends in various aspects of contemporary mathematics, emphasizing applicabilitions to real-world situations. The chapters present exciting new findings and developments in situations where mathematical rigor is combined with common sense. A multi-disciplinary approach, both within each chapter and in the volume as a whole, leads to practical insights that may result in a more synthetic understanding of specific global issues as well as their possible solutions. The volume will be of interest not only to experts in mathematics, but also to graduate students, scientists, and practitioners from other fields including physics, biology, geology, management, and medicine.
Exponential Data Fitting and Its Applications
"Real and complex exponential data fitting is an important activity in many different areas of science and engineering, ranging from Nuclear Magnetic Resonance Spectroscopy and Lattice Quantum Chromodynamics to Electrical and Chemical Engineering, Vision a"
Geometric Modeling for Scientific Visualization
Geometric Modeling and Scientific Visualization are both established disciplines, each with their own series of workshops, conferences and journals. But clearly both disciplines overlap; this observation led to the idea of composing a book on Geometric Modeling for Scientific Visualization.
Optical Coherence Tomography guided Laser-Cochleostomy
Despite the high precision of laser, it remains challenging to control the laser-bone ablation without injuring the underlying critical structures. Providing an axial resolution on micrometre scale, OCT is a promising candidate for imaging microstructures beneath the bone surface and monitoring the ablation process. In this work, a bridge connecting these two technologies is established. A closed-loop control of laser-bone ablation under the monitoring with OCT has been successfully realised.
Computer Graphics and Geometric Modelling
The second book of a two-volume work in which the author presents an overview of computer graphics as seen in the context of geometric modeling and the mathematics required to understand the subject.
Probabilistic Parametric Curves for Sequence Modeling
This work proposes a probabilistic extension to Bézier curves as a basis for effectively modeling stochastic processes with a bounded index set. The proposed stochastic process model is based on Mixture Density Networks and Bézier curves with Gaussian random variables as control points. A key advantage of this model is given by the ability to generate multi-mode predictions in a single inference step, thus avoiding the need for Monte Carlo simulation.
