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Third International Congress on Mathematical Software, Kobe : Japon (2010)

A Library of OpenGL-Based Mathematical Image Filters

Martin Von Gagern 1, Christian Mercat 2, 3

(2010)

There are a lot of transformations that can turn one raster image into a derived one in a mathematically interesting way. This article describes a collection of such filters, implemented in OpenGL in order to use the high degree of parallelism modern GPUs provide, thereby providing performance required to process e.g. live camera images in real-time. The filters contained in this library include wallpaper groups, conformal maps described by meromorphic functions, as well as hyperbolic symmetry groups. Using examples of increasing complexity, several key implementation techniques are explained, including texture wrap configurations, user-configurable control points, and custom fragment shader programs. This work might exhibit aesthetic aspects of mathematics to the masses and provide useful building blocks for scientists as well as artists.

1:	Zentrum Mathematik (M10)
	Technische Universität München (TUM)
2:	Institut Camille Jordan (ICJ)
	CNRS : UMR5208 – Université Claude Bernard - Lyon I – Ecole Centrale de Lyon – Institut National des Sciences Appliquées (INSA) - Lyon
3:	Sciences et Société ; Historicité, Éducation et Pratiques (EA S2HEP)
	Université Claude Bernard - Lyon I : EA4148 – École Normale Supérieure - Lyon

Research team: Zentrum Mathematik

Subject

:

Computer Science/Mathematical Software

Keyword(s): Transformation – tiling – wallpaper group – conformal map – meromorphic function – hyperbolic geometry – GPU – parallelism – webcam

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From: Christian Mercat <>

Submitted on: Thursday, 12 January 2012 08:50:48

Updated on: Thursday, 12 January 2012 09:01:23