Many applications in science and engineering require a digital model of a real physical object. Advanced scanning technology has made it possible to scan such objects and generate point samples on their boundaries. This book, first published in 2007, shows how to compute a digital model from this point sample. After developing the basics of sampling theory and its connections to various geometric and topological properties, the author describes a suite of algorithms that have been designed for the reconstruction problem, including algorithms for surface reconstruction from dense samples, from samples that are not adequately dense and from noisy samples. Voronoi- and Delaunay-based techniques, implicit surface-based methods and Morse theory-based methods are covered. Scientists and engineers working in drug design, medical imaging, CAD, GIS, and many other areas will benefit from this first book on the subject.
• Provides fundamentals of point cloud data processing • Algorithms with correctness proofs are presented • Many figures, a set of exercises, and a brief history for each chapter
1. Basics; 2. Curve reconstruction; 3. Surface samples; 4. Surface reconstruction; 5. Undersampling; 6. Watertight reconstructions; 7. Noisy samples; 8. Noise and reconstruction; 9. Implicit surface based reconstructions; 10. Morse theoretic reconstructions.
'The text is well written, and present the algorithms in a way that makes them quite understandable. Instead of presenting the algorithms as single, monolithic and complex methods, they are broken into parts that can be explained and mathematically analyzed in an order that makes clear how they are later composed into the larger task.' SIGACT News