Surface derivatives computation using Fourier Transform

Yohann Béarzi 1 Julie Digne 1
1 GeoMod - Modélisation Géométrique, Géométrie Algorithmique, Fractales
LIRIS - Laboratoire d'InfoRmatique en Image et Systèmes d'information
Abstract : We present a method for computing high order derivatives on a smooth surface S at a point p by analyzing the vibrations of the surface along circles in the tangent plane, centered at p. By computing the Discrete Fourier Transform of the deviation of S from the tangent plane restricted to those circles, a linear relation between the Fourier coefficients and the derivatives can be expressed. Thus, given a smooth scalar field defined on the surface, all its derivatives at p can be computed simultaneously. The originality of this method is that no direct derivation process is applied to the data. Instead, integration is performed through the Discrete Fourier Transform, and the result is expressed as a one dimensional polynomial. We derive two applications of our framework namely normal correction and curvature estimation which we demonstrate on synthetic and real data.
Complete list of metadatas

Cited literature [10 references]  Display  Hide  Download
Contributor : Julie Digne <>
Submitted on : Friday, March 16, 2018 - 1:57:18 PM
Last modification on : Thursday, June 6, 2019 - 9:49:40 AM
Long-term archiving on : Monday, September 10, 2018 - 9:31:23 PM


Files produced by the author(s)


  • HAL Id : hal-01735374, version 1


Yohann Béarzi, Julie Digne. Surface derivatives computation using Fourier Transform. JFIG 2016, Nov 2016, Grenoble, France. ⟨hal-01735374⟩



Record views


Files downloads