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Thierry Blu

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Publications associées (160)

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Exact Computation of Area Moments for Spline and Wavelet Curves

Michaël Unser, Thierry Blu, Mathews Jacob

We present an exact algorithm for the computation of the moments of a region bounded by a curve represented in 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 ...

IEEE2000

Non-Uniform to Uniform Grid Conversion Using Least-Squares Splines

Michaël Unser, Thierry Blu

We propose a new technique to perform nonuniform to uniform grid conversion: first, interpolate using nonuniform splines, then project the resulting function onto a uniform spline space and finally, resample. We derive a closed form solution to the least-s ...

EURASIP2000

Non-Euclidean Pyramids

Michaël Unser, Thierry Blu

We propose to design the reduction operator of an image pyramid so as to minimize the approximation error in the

l _{ p }

sense (not restricted to the usual p = 2), where p can take non-integer values. The underlying image model is specified using arbi ...

SPIE2000

Complete Parametrization of Piecewise-Polynomial Interpolators According to Degree, Support, Regularity, and Order

Michaël Unser, Philippe Thévenaz, Thierry Blu

The most essential ingredient of interpolation is its basis function. We have shown in previous papers that this basis need not be necessarily interpolating to achieve good results. On the contrary, several recent studies have confirmed that non-interpolat ...

IEEE2000

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

Interpolation Revisited

Michaël Unser, Philippe Thévenaz, Thierry Blu

Based on the theory of approximation, this paper presents a unified analysis of interpolation and resampling techniques. An important issue is the choice of adequate basis functions. We show that, contrary to the common belief, those that perform best are ...

IEEE2000

Image Interpolation and Resampling

Michaël Unser, Philippe Thévenaz, Thierry Blu

This chapter presents a survey of interpolation and resampling techniques in the context of exact, separable interpolation of regularly sampled data. In this context, the traditional view of interpolation is to represent an arbitrary continuous function as ...

Academic Press2000

Construction of Fractional Spline Wavelet Bases

Michaël Unser, Thierry Blu

We extend Schoenberg's B-splines to all fractional degrees α > -1/2. These splines are constructed using linear combinations of the integer shifts of the power functions

x _{ + } ^{ \alpha }

(one-sided) or

|x| _{ * } ^{ \alpha }

(symmetric); in eac ...

SPIE1999

Approximation Error for Quasi-Interpolators and (Multi-) Wavelet Expansions

Michaël Unser, Thierry Blu

We investigate the approximation properties of general polynomial preserving operators that approximate a function into some scaled subspace of

L _{ 2 }

via an appropriate sequence of inner products. In particular, we consider integer shift-invariant a ...

Academic Press1999

Non-Euclidean Pyramids

Michaël Unser, Thierry Blu

We propose to design the reduction operator of an image pyramid so as to minimize the approximation error in the

l _{ p }

sense (not restricted to the usual p = 2), where p can take non-integer values. The underlying image model is specified using arbi ...

SPIE2000

Construction of Fractional Spline Wavelet Bases

Michaël Unser, Thierry Blu

We extend Schoenberg's B-splines to all fractional degrees α > -1/2. These splines are constructed using linear combinations of the integer shifts of the power functions

x _{ + } ^{ \alpha }

(one-sided) or

|x| _{ * } ^{ \alpha }

(symmetric); in eac ...

SPIE1999

Approximation Error for Quasi-Interpolators and (Multi-) Wavelet Expansions

Michaël Unser, Thierry Blu

We investigate the approximation properties of general polynomial preserving operators that approximate a function into some scaled subspace of

L _{ 2 }

via an appropriate sequence of inner products. In particular, we consider integer shift-invariant a ...

Academic Press1999