31/07/2006

Des maths...

La programmation, c’est principalement une façon déguisée de faire des maths. Alors voici une petite série qui va vous rafraîchir la mémoire sur des domaines aussi divers que le Lambda Calcul ou la logique sur l'excellent blog "Good Math" :

 

Information Theory (index)


Group Theory (index)


Automata Theory (index)

Logic (index)


Lamda Calculus (Index)

 

13:55 Publié dans Maths | Lien permanent | Commentaires (0)

28/07/2006

Introduction aux Wavelets

Et hop, une petite introduction aux Wavelet, en alternative à l’analyse de Fourier.

 

Multiresolution techniques and the use of hierarchy have a long history in computer graphics. Most recently these approaches have received a significant boost and increased interest through the introduction of the mathematical framework of wavelets.

 

With their roots in signal processing and harmonic analysis, wavelets have lead to a number of efficient and easy to implement algorithms. Wavelets have already had a major impact in several areas of computer graphics:

 

  • Image Compression and Processing: some of the most powerful compression techniques for still and moving images are based on wavelet transforms;

  • Global Illumination: wavelet radiosity and radiance algorithms are asymptotically faster than other finite element techniques;

  • Hierarchical Modeling: using multiresolution representations for curves and surfaces accelerates and simplifies many common editing tasks;

  • Animation: the large constrained optimization tasks which arise in physically based modeling and animation subject to goal constraints can be solved faster and more robustly with wavelets;

  • Volume Rendering and Processing: wavelets can greatly facilitate dealing with huge data sets since they can be used for compression as well as feature detection and enhancement;

  • Multiresolution Painting: using multiresolution analysis one can build efficient ``infinite'' resolution paint systems;

  • Image Query: using a small number of the largest wavelet coefficients of an image results in a perceptually useful signature for fast search and retrieval.
 
Some of the very recent and most exciting generalizations and extensions of classical wavelet constructions have been developed by researchers in the context of graphics applications. Following the success of the wavelets courses at SIGGRAPH 94 and 95 and based on the experiences of the organizers and lecturers, there will be another wavelets course at SIGGRAPH 96.
 
 
Since new wavelet constructions now exist, which are easy to implement and do not require any heavy mathematical machinery to describe, the course will be accessible to those who do not have any prior knowledge of wavelets or a strong background in mathematical Fourier theory.
 

 


09:10 Publié dans Maths | Lien permanent | Commentaires (0)