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Geometric Transformation of Images using Spline-Interpolation (m11154)
Maintainers: Alena Scott, Sujesh Sreedharan, Rebecca Willett, Adan Galvan, Charlet Reedstrom
Keywords: B-splines, Image transforms, interpolation, splines
Summary: To perform geometric transforms on discrete images such as a rotation or zooming we need to first fit the discrete data to a continuous function. This can be done using splines. B-splines can be used to interpolate and form the continuos image from the discrete samples.
Subject: Science and Technology
Language: English
Popularity: 83.33%
Revised: 2005-06-09
Revisions: 3
Multiresolution Properties of Splines (m11128)
Maintainers: Alena Scott, Sujesh Sreedharan, Rebecca Willett, Adan Galvan, Charlet Reedstrom
Keywords: basis, biorthogonal filters, B-Splines, dilation, multiresolution, Splines
Summary: B-splines form a simple set of scaling functions satisfying the dilation equation with binomial filter coefficients. However B-Splines other than the zeroth order B-spline (the Haar function) are not orthogonal to its own shifts. Hence to form a perfect reconstruction(PR) filter bank system, biorthogonal scaling functions ... bank system.
Subject: Science and Technology
Language: English
Popularity: 66.72%
Revised: 2005-06-09
Revisions: 3
Sampling Theory and Spline Interpolation (m11126)
Maintainers: Alena Scott, Sujesh Sreedharan, Rebecca Willett, Adan Galvan, Charlet Reedstrom
Keywords: analog, B-splines, cardinal splines, samples, Shannon, sinc
Summary: In this module, Shannon's classical sampling theory is compared to digital to analog signal reconstruction using spline interpolation. In the spline method, the signal is reconstructed using sample-weighted cardinal splines as opposed to sample-weighted sinc functions.
Subject: Science and Technology
Language: English
Popularity: 95.53%
Revised: 2003-09-24
Revisions: 4
Scaling Function Order of Approximation (m11122)
Maintainers: Alena Scott, Sujesh Sreedharan, Rebecca Willett, Adan Galvan, Charlet Reedstrom
Keywords: Sobolev, smoothness, rates of convergence
Summary: Wavelets can be characterized in terms of how well scaling functions can approximate functions in certain smoothness classes. In this module, this relationship is defined.
Subject: Science and Technology
Language: English
Popularity: 50.52%
Revised: 2005-06-07
Revisions: 3
Sobolev Spaces (m11125)
Maintainers: Alena Scott, Sujesh Sreedharan, Rebecca Willett, Adan Galvan, Charlet Reedstrom
Keywords: Holder, Besov, Fourier, smoothness
Summary: Sobolev smoothness spaces are discussed and defined in this module.
Subject: Mathematics and Statistics, Science and Technology
Language: English
Popularity: 77.89%
Revised: 2004-09-14
Revisions: 2
Unser-Blu Scaling Function / Spline Factorization Theorem (m11121)
Maintainers: Alena Scott, Sujesh Sreedharan, Rebecca Willett, Adan Galvan, Charlet Reedstrom
Keywords: B-spline, wavelet, scaling function
Summary: In this module, the reader will be introduced to the scaling function spline factorization theorm by M. Unser and T. Blu. This factorization allows many key wavelet properties to be derived in a relatively straightforward manner.
Subject: Science and Technology
Language: English
Popularity: 52.54%
Revised: 2005-06-07
Revisions: 4
Wavelets, Splines, and the Reproduction of Polynomials (m11123)
Maintainers: Alena Scott, Sujesh Sreedharan, Rebecca Willett, Adan Galvan, Charlet Reedstrom
Keywords: wavelets, B-spline, vanishing moments, polynomials, basis
Summary: On well-known property of valid scaling functions in wavelet analysis is that the scaling functions can perfectly reproduce a polynomial of degree no more than the wavelet smoothness. This property can be easily derived using the Unser-Blu Scaling Function / Spline Factorization Theorem.
Subject: Mathematics and Statistics, Science and Technology
Language: English
Popularity: 46.71%
Revised: 2005-06-07
Revisions: 4
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