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Spline Kernels for Continuous-Space Image Processing

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Splines and Wavelets: New Perspectives for Pattern Recognition

Michaël Unser

We provide an overview of spline and wavelet techniques with an emphasis on applications in pattern recognition. The presentation is divided in three parts. In the first one, we argue that the spline representation is ideally suited for all processing task ...

DAGM e. V2003

Discretization of the radon transform and of its inverse by spline convolutions

Michaël Unser, Michael Stefan Daniel Liebling, Stefan Horbelt

We present an explicit formula for B-spline convolution kernels; these are defined as the convolution of several B-splines of variable widths hi and degrees ni. We apply our results to derive spline-convolution-based algorithms for two closely related prob ...

IEEE2002

Splines: A Perfect Fit for Medical Imaging

Michaël Unser

Splines, which were invented by Schoenberg more than fifty years ago, constitute an elegant framework for dealing with interpolation and discretization problems. They are widely used in computer-aided design and computer graphics, but have been neglected i ...

SPIE2002

Filter Design for Filtered Back-Projection Guided by the Interpolation Model

Michaël Unser

We consider using spline interpolation to improve the standard filtered back-projection (FBP) tomographic reconstruction algorithm. In particular, we propose to link the design of the filtering operator with the interpolation model that is applied to the s ...

SPIE2002

Nondyadic and nonlinear multiresolution image approximations

Maria Arrate Munoz Barrutia

This thesis focuses on the development of novel multiresolution image approximations. Specifically, we present two kinds of generalization of multiresolution techniques: image reduction for arbitrary scales, and nonlinear approximations using other metrics ...

EPFL2002

Sampling signals with finite rate of innovation

Martin Vetterli, Pina Marziliano, Thierry Blu

Consider classes of signals that have a finite number of degrees of freedom per unit of time and call this number the rate of innovation. Examples of signals with a finite rate of innovation include streams of Diracs (e.g., the Poisson process), nonuniform ...

Institute of Electrical and Electronics Engineers2002

A sampling theorem for periodic piecewise polynomial signals

Martin Vetterli, Pina Marziliano, Thierry Blu

We consider the problem of sampling signals which are not bandlimited, but still have a finite number of degrees of freedom per unit of time, such as, for example, piecewise polynomials. We demonstrate that by using an adequate sampling kernel and a sampli ...

2001

Least-Squares Image Resizing Using Finite Differences

Michaël Unser, Thierry Blu

We present an optimal spline-based algorithm for the enlargement or reduction of digital images with arbitrary (noninteger) scaling factors. This projection-based approach can be realized thanks to a new finite difference method that allows the computation ...

IEEE2001

Fractional Derivatives, Splines and Tomography

Michaël Unser, Thierry Blu

We develop a spline calculus for dealing with fractional derivatives. After a brief review of fractional splines, we present the main formulas for computing the fractional derivatives of the underlying basis functions. In particular, we show that the $ γ ...

EURASIP2000

Fractional derivatives, splines and tomography

Michaël Unser, Thierry Blu, Stefan Horbelt

2000