Bézier and Splines in Image Processing and Machine Vision

Abstract

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).