Bézier and Splines in Image Processing and Machine Vision

Part I Early Background.- 1 Bernstein Polynomial and Bézier-Bernstein Spline.- Significance of Bernstein Polynomial in Splines.- 2 Image Segmentation.- Two Different Concepts of Segmentation.- Contour Based Segmentation.- Region Based Segmentation.- 3 1-d B-B Spline Polynomial and Hilbert Scan for Graylevel Image Coding.- Hilbert Scanned Image.- Shortcomings of Bernstein Polynomial and Error of Approximation.- 4 Image Compression.- SLIC: Sub-image Based Lossy Image Compression.- Part II Intermediate Steps.- 5 B-Splines and its Applications.- B-Spline Function.- 6 Beta-Splines: A Flexible Model.- Beta-Spline Curve.- 7 Discrete Spline and Vision.- Smoothing Discrete Spline and Vision.- Cardinal B-spline Basis and Riesz Basis.- 8 Spline Wavelets: Construction, Implication and Uses.- Cardinal B-spline Basis and Riesz Basis.- 9 Snakes and Active Contours.- Splines and Energy Minimisation Techniques.- Part III Advanced Methodologies.- 10 Globally Optimal Energy Minimisation Techinques.- Globally Minimal Surfaces (GMS).