Bézier and Splines in Image Processing and Machine Vision

Digital image processing and machine vision have grown considerably during the last few decades. Of the various techniques, developed so far, splines play a significant role in many of them. This book deals with various image processing and machine vision problems efficiently with splines and includes: the significance of Bernstein Polynomial in splines, detailed coverage of Beta-splines applications which are relatively new, Splines in motion tracking, various deformative models and their uses.Finally the book covers wavelet splines which are efficient and effective in different image applications.

Digital image processing and machine vision have both grown considerably during the last few decades. Of the various techniques that have been so far developed, splines play a significant role in a number. This book, which will be essential reading for graduate researchers, deals with various image processing and machine vision problems efficiently with splines and includes: the significance of Bernstein Polynomial in splines, detailed coverage of beta-splines applications which are relatively new, splines in motion tracking, various deformative models and their uses. Finally the book covers wavelet splines which are efficient and effective in different image applications.

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).