Publication

Exact Computation of Area Moments for Spline and Wavelet Curves

Michaël Unser, Thierry Blu, Mathews Jacob
2000
Conference Papers

Abstract

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 multidimensional filter on the coefficients of the curve and thereafter computing a scalar product. We compare this algorithm with existing methods such as pixel-based approaches and approximation of the region by a polygon.

Official source

https://infoscience.epfl.ch/entities/publication/c796ec5a-821d-4166-bac8-255fa2b64d4f

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Michaël Unser, Thierry Blu, Mathews Jacob
2000
Conference Papers

Abstract

Official source

https://infoscience.epfl.ch/entities/publication/c796ec5a-821d-4166-bac8-255fa2b64d4f

About this result

Related concepts (32)

Plane curve

In mathematics, a plane curve is a curve in a plane that may be either a Euclidean plane, an affine plane or a projective plane. The most frequently studied cases are smooth plane curves (including piecewise smooth plane curves), and algebraic plane curves. Plane curves also include the Jordan curves (curves that enclose a region of the plane but need not be smooth) and the graphs of continuous functions. A plane curve can often be represented in Cartesian coordinates by an implicit equation of the form for some specific function f.

Algorithm

In mathematics and computer science, an algorithm (ˈælɡərɪðəm) is a finite sequence of rigorous instructions, typically used to solve a class of specific problems or to perform a computation. Algorithms are used as specifications for performing calculations and data processing. More advanced algorithms can use conditionals to divert the code execution through various routes (referred to as automated decision-making) and deduce valid inferences (referred to as automated reasoning), achieving automation eventually.

Wavelet

A wavelet is a wave-like oscillation with an amplitude that begins at zero, increases or decreases, and then returns to zero one or more times. Wavelets are termed a "brief oscillation". A taxonomy of wavelets has been established, based on the number and direction of its pulses. Wavelets are imbued with specific properties that make them useful for signal processing. For example, a wavelet could be created to have a frequency of Middle C and a short duration of roughly one tenth of a second.

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Exact Computation of Area Moments for Spline and Wavelet Curves

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