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Smoothing spline ➤ The solution (among all functions) of the smoothing spline problem is a cardinal spline of degree 2m-1. Its coefficients can be obtained by suitable digital filtering of the input samples: ➤ ➤ Related to: MMSE (Wiener filtering); splines form optimal space!!! Special case: the draftman’s spline Minimum curvature interpolant is obtained for = cubic spline! [Unser & Blu 2005; Ramani et al. 2005] 18
Spline fitting: (3) least-square spline ➤ ➤ ➤ Spline interpolation Smoothing spline Least-square spline (approximation between spline spaces) spline model resampling & filtering error such that 19
Page 1 and 2: Point Lattices in Computer Graphics
Page 3 and 4: Notations ➤ one-sided ➤ Fourier
Page 5 and 6: Polynomial B-splines ➤ B-spline o
Page 7 and 8: Fundamental B-spline properties ➤
Page 9 and 10: B-spline differential property “p
Page 11 and 12: Spline fitting ➤ How to find the
Page 13 and 14: Spline interpolation ➤ Discrete B
Page 15 and 16: Spline interpolation ➤ Interpolat
Page 17: Spline fitting: (2) smoothing splin
Page 21 and 22: Least-square spline ➤ Special cas
Page 23 and 24: Quantitative approximation quality
Page 25 and 26: High-quality image interpolation pe
Page 27 and 28: High-quality isosurface rendering
Page 29 and 30: Wavelets ➤ Admissible scaling fun
Page 31 and 32: Haar wavelet transform revisited +
Page 33 and 34: Wavelets ➤ Wavelets act as differ
Page 35 and 36: Hexagonal lattices r 2 Voronoi cell
Page 37 and 38: Hex-splines ➤ Basis functions for
Page 39 and 40: Hex-splines ➤ Basis functions for
Page 41 and 42: Hex-splines versus B-splines ➤ Ke
Page 43 and 44: Hex-splines versus B-splines ➤ Cl
Page 45: And finally ➤ Many thanks go to M

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