Bézier and Splines in Image Processing and Machine Vision

By Sambhunath Biswas and Brian C. Lovell

Part I Early Background.- 1 Bernstein Polynomial and B zier-Bernstein Spline.- 1.1 Introduction.- 1.2 Significance of Bernstein Polynomial in Splines.- 1.3 Bernstein Polynomial.- 1.3.1 Determination of the Order of the Polynomial.- 1.4 Use in Computer Graphics and Image Data Approximation.- 1.4.1 B zier-Bernstein Curves.- 1.4.2 B zier-Bernstein Surfaces.- 1.4.3 Curve and Surface Design.- 1.4.4 Approximation of Binary Images.- 1.5 Key Pixels and Contour Approximation.- 1.5.1 Key Pixels.- 1.5.2 Detection of Inflexion Points.- 1.6 Regeneration Technique.- 1.6.1 Method 1.- 1.6.2 Method 2.- 1.6. 3 Recursive Computation Algorithm.- 1.6.4 Implementation Strategies.- 1.7 Approximation Capability and Effectiveness.- 1.8 Concluding Remarks.- 2 Image Segmentation.- 2.1 Introduction.- 2.2 Two Different Concepts of Segmentation.- 2.2.1 Contour Based Segmentation.- 2.2.2 Region Based Segmentation.- 2.3 Segmentation for Compression.- 2.4 Extraction of Compact Homogeneous Regions.- 2.4.1 Partition/ Decomposition Principle for Gray Images.- 2.4.2 Approximation Problem.- 2.4.3 Polynomial Order Determination.- 2.4.4 Algorithms.- 2.4.5 Merging of Small Regions.- 2. 5 Evaluation of Segmentation.- 2.6 Comparison with Multilevel Thresholding Algorithms.- 2.6.1 Results and Discussion.- 2.7 Some Justifications for Image Data Compression.- 2.8 Concluding Remarks.- 3 1-d B-B Spline Polynomial and Hilbert Scan for Graylevel Image Coding.- 3.1 Introduction.- 3.2 Hilbert Scanned Image.- 3.2.1 Construction of Hilbert Curve.- 3.3 Shortcomings of Bernstein Polynomial and Error of Approximation.- 3.4 Approximation Technique.- 3.4.1 B zier-Bernstein (B-B) Polynomial.- 3.4.2 Algorithm 1: Approximation Criteria of f(t).- 3.4.3 Implementation Strategy.- 3.4. 4 Algorithm 2.- 3.5 Image Data Compression.- 3.5.1 Discrimination Features of the Algorithms.- 3.6 Regeneration.- 3. 7 Results and Discussion.- 3. 8 Concluding Remarks.- 4 Image Compression.- 4.1 Introduction.- 4.2 SLIC: Sub-image Based Lossy Image Compression.- 4.2.1 Approximation and Choice of Weights.-4.2.2 Texture Coding.- 4.2.3 Contour Coding.- 4.3 Quantitative Assessment for Reconstructed Images.- 4.4 Results and Discussion.- 4.4.1 Result of SLIC Algorithm for 64 x 64 Images.- 4.4.2 Results of SLIC Algorithm for 256 x 256 Images.- 4.4.3 Effects of the Increase of Spatial Resolution on Compression and Quality.- 4.5 Concluding Remarks.- Part II Intermediate Steps.- 5 B-Splines and its Applications.- 5.1 Introduction.- 5.2 B-Spline Function.-5.2.1 B-spline Knot for Uniform, Open Uniform and Nonuniform basis.- 5.3 Computation of B-Spline Basis Functions.- 5.3.1 Computaion of Uniform Periodic B-spline Basis.- 5.4 B-Spline Curves on Unit Interval.- 5.4.1 Properties of B-spline Curves.- 5.4.2 Effect of Multiplicity.- 5.4.3 End Condition.-5.5 Rational B-Spline Curve.- 5.5.1 Homogeneous Co-ordinates.-5.5.2 Essentials of Rational B-spline Curves.- 5.6 B-Spline Surface.- 5.7 Application.- 5.7.1 Differential invariants of Image Velocity Fields.-5.7.2 3D Shape and Viewer Ego-motion.- 5.7.3 Geometric Significance.- 5.7.4 Constraints.-5.7.5 Extraction of Differential Invariants.-5.8 Recovery of Time to Contact and Surface Orientation.- 5.8.1 Braking and Object Manipulation.- 5.9 Concluding Remarks.- 6 Beta-Splines: A Flexible Model.- 6.1 Introduction.- 6.2 Beta-Spline Curve.- 6.3 Design Criteria for a Curve.-6.3.1 Shape Parameters.-6.3.2 End Conditions of Beta spline Curves.- 6.4 Beta-Spline Surface.-6.5 Possible Applications in Vision.- 6.6 Concluding Remarks.-Part III Advanced Methodologies.- 7 Discrete Spline and Vision.- 7.1 Introduction.- 7.2 Discrete Splines.- 7.2.1 Relation between ai, k and Bi, k>2.- 7.2.2 Some Properties of ai, k (j).- 7.2.3 Algorithms.- 7.3 Subdivision of Control Polygon.- 7.4 Smoothing Discrete Spline and Vision.- 7.5. Occluding Boundaries and Shape from Shading.- 7.5.1 Image Irradiance Equation.- 7.5.2 Method Based on Regularization.- 7.5.3 Discrete Smoothing Splines.- 7.5.4 Necess

• Format: Paperback
• Language: English
• ISBN: 1849966877
• ISBN13: 9781849966870
• Release Date: October 2010
• Publisher: Springer
• Length: 246 Pages
• Weight: 0.83 lbs.
• Dimensions: 0.6" x 6.1" x 9.2"