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Gaussian models for fast synthesis and inpainting of microtextures

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If you have a question about this talk, please contact Carola-Bibiane Schoenlieb.

Among the various existing models of textures, Gaussian textures form an interesting class, in particular because they rely on a mathematical model that is very well adapted to theoretical investigations. They allow for by-example texture synthesis and also texture mixing. However, the classical spectral simulation of Gaussian textures is not very flexible (not parallel) and becomes computationally heavy for very large domains.

A Gaussian texture can be approximated by a high-intensity discrete spot noise (DSN), obtained by summing randomly-shifted copies of a kernel along the points of a Poisson process. The direct simulation of the DSN is simple and allows parallel local evaluation using standard computer graphics techniques for the Poisson process simulation. Still, the DSN approximation of a Gaussian texture is satisfying only for sufficiently high intensity, so that the DSN simulation is generally not faster than the spectral simulation.

In our paper [1], we proposed an algorithm that summarizes a texture sample into a “synthesis-oriented texton”, that is, a kernel with prescribed small support for which the DSN simulation is more efficient than the classical convolution algorithm. Using this synthesis-oriented texton, Gaussian textures can be generated on-demand in a faster, simpler, and more flexible way.

In the first part of this talk, after describing the discrete spot noise, we will explain how to compute a synthesis-oriented texton, and show that it allows to synthesize Gaussian textures with a very low computational cost. In the second part, we will show how Gaussian texture models can be used to address microtexture inpainting. We will see that in the Gaussian case, we can rely on a perfect conditional simulation algorithm based on kriging estimation.

[1] “A Texton for Fast and Flexible Gaussian Texture Synthesis” (Bruno Galerne, Arthur Leclaire, Lionel Moisan), proceedings of the European Signal Processing Conference (Eusipco), 2014

This talk is part of the Applied and Computational Analysis series.

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