Maximum entropy methods for texture synthesis: theory and practice


Recent years have seen the rise of convolutional neural network techniques in exemplar-based image synthesis. These methods often rely on the minimization of some variational formulation on the image space for which the minimizers are assumed to be the solutions of the synthesis problem. In this paper we investigate, both theoretically and experimentally, another framework to deal with this problem using an alternate sampling/minimization scheme. First, we use results from information geometry to assess that our method yields a probability measure which has maximum entropy under some constraints in expectation. Then, we turn to the analysis of our method and we show, using recent results from the Markov chain literature, that its error can be explicitly bounded with constants which depends polynomially in the dimension even in the non-convex setting. Finally, we present an extensive experimental study of the model, including a comparison with state-of-the-art methods and an extension to style transfer.

Additional content

Here is a video of the algorithm for the estimation of the covariance matrix of a periodic texture

Code and slides

The code is available here.
Below are the slides I presented at the Centre Borelli (previously CMLA) imaging seminar.

in SIAM Mathematics of Data Science