Concept

B-spline

Publications associées (42)

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Non-linear subdivision of univariate signals and discrete surfaces

Nicolas Aspert

During the last 20 years, the joint expansion of computing power, computer graphics, networking capabilities and multiresolution analysis have stimulated several research domains, and developed the need for new types of data such as 3D models, i.e. discret ...

EPFL2003

Harmonic Spline Series Representation of Scaling Functions

Michaël Unser, Thierry Blu

We present here an explicit time-domain representation of any compactly supported dyadic scaling function as a sum of harmonic splines. The leading term in the decomposition corresponds to the fractional splines, a recent, continuous-order generalization o ...

SPIE2003

Precision Isosurface Rendering of 3-D Image Data

Michaël Unser, Philippe Thévenaz

We address the task of rendering by ray tracing the isosurface of a high-quality continuous model of volumetric discrete and regular data. Based on first principles, we identify the quadratic B-spline as the best model for our purpose. The nonnegativity of ...

IEEE2003

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

Spline Kernels for Continuous-Space Image Processing

Michaël Unser, Thierry Blu

We present an explicit formula for spline kernels; these are defined as the convolution of several B-splines of variable widths h and degrees n. The spline kernels are useful for continuous signal processing algorithms that involve B-spline inner-products ...

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

B-Spline Snakes: A Flexible Tool for Parametric Contour Detection

Michaël Unser

We present a novel formulation for B-spline snakes that can be used as a tool for fast and intuitive contour outlining. We start with a theoretical argument in favor of splines in the traditional formulation by showing that the optimal, curvature-constrain ...

IEEE2000

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

Aperture apodization using cubic spline interpolation: application in digital holographic microscopy

Christian Depeursinge, Etienne Cuche, Pierre Marquet

A method is proposed for designing apodized apertures with a transmission profile which follows a curve defined using a cubic spline interpolation. The method is applied in digital holographic microscopy to perform digitally the apodization of the aperture ...

2000