Concept

Multidimensional discrete convolution

Related publications (55)

Variational B-Spline Level-Set: A Linear Filtering Approach for Fast Deformable Model Evolution

Michaël Unser, Philippe Thévenaz, Olivier Bernard

In the field of image segmentation, most level-set-based active-contour approaches take advantage of a discrete representation of the associated implicit function. We present in this paper a different formulation where the implicit function is modeled as a ...

IEEE2009

Variational B-Spline Level-Set Method for Fast Image Segmentation

Michaël Unser, Philippe Thévenaz

In the field of image segmentation, most of level-set-based active contour approaches are based on a discrete representation of the associated implicit function. We present in this paper a different formulation where the level-set is modelled as a continuo ...

IEEE2008

On Interpolation and Resampling of Discrete Data

Pouya Dehghani Tafti

This letter introduces a new representation of discrete signals based on the mathematical notions of functionals and continuous dual spaces. A new and more general sampling theorem is also suggested. Next, the problems of interpolating and resampling discr ...

IEEE2006

Polyharmonic Smoothing Splines and the Multidimensional Wiener Filtering of Fractal-Like Signals

Michaël Unser, Dimitri Nestor Alice Van De Ville

Motivated by the fractal-like behavior of natural images, we develop a smoothing technique that uses a regularization functional which is a fractional iterate of the Laplacian. This type of functional was initially introduced by Duchon for the approximatio ...

IEEE2006

Cardinal Exponential Splines: Part II—Think Analog, Act Digital

Michaël Unser

By interpreting the Green-function reproduction property of exponential splines in signal processing terms, we uncover a fundamental relation that connects the impulse responses of allpole analog filters to their discrete counterparts. The link is that the ...

IEEE2005

Sampling in Practice: Is the Best Reconstruction Space Bandlimited?

Michaël Unser, Dimitri Nestor Alice Van De Ville, Sathish Ramani

Shannon's sampling theory and its variants provide effective solutions to the problem of reconstructing a signal from its samples in some “shift-invariant” space, which may or may not be bandlimited. In this paper, we present some further justification for ...

IEEE2005

An Exact Method for Computing the Area Moments of Wavelet and Spline Curves

Michaël Unser, Thierry Blu, Mathews Jacob

We present a method for the exact computation of the moments of a region bounded by a curve represented by a scaling function or wavelet basis. Using Green's Theorem, we show that the computation of the area moments is equivalent to applying a suitable mul ...

IEEE2001

Spectral processing of point-sampled geometry

Mark Pauly

We present a new framework for processing point-sampled objects using spectral methods. By establishing a concept of local frequencies on geometry, we introduce a versatile spectral representation that provides a rich repository of signal processing algori ...

2001

Quantitative Fourier Analysis of Approximation Techniques: Part I—Interpolators and Projectors

Michaël Unser, Thierry Blu

We present a general Fourier-based method that provides an accurate prediction of the approximation error as a function of the sampling step T. Our formalism applies to an extended class of convolution-based signal approximation techniques, which includes ...

IEEE1999

Determination of homonuclear scalar coupling constants by combining selective two-dimensional NMR spectroscopy with convolution and deconvolution: applications to paclitaxel (taxol)

Geoffrey Bodenhausen

Homonuclear proton-proton coupling consts. can be detd. accurately by recording selective two-dimensional correlation spectra and by analyzing the resulting multiplets by two-dimensional convolution and deconvolution methods. These methods were evaluated b ...

1997

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