Texture Synthesis and Nonparametric Resampling of Random Fields by Elizaveta Levina
نویسندگان
چکیده
This paper introduces a nonparametric algorithm for bootstrapping a stationary random field and proves certain consistency properties of the algorithm for the case of mixing random fields. The motivation for this paper comes from relating a heuristic texture synthesis algorithm popular in computer vision to general nonparametric bootstrapping of stationary random fields. We give a formal resampling scheme for the heuristic texture algorithm and prove that it produces a consistent estimate of the joint distribution of pixels in a window of certain size under mixing and regularity conditions on the random field. The joint distribution of pixels is the quantity of interest here because theories of human perception of texture suggest that two textures with the same joint distribution of pixel values in a suitably chosen window will appear similar to a human. Thus we provide theoretical justification for an algorithm that has already been very successful in practice, and suggest an explanation for its perceptually good results.
منابع مشابه
Local resampling for patch-based texture synthesis in vector fields
We develop a direct and accurate approach for local resampling in vector fields, and then use the approach to synthesise textures on 2D manifold surfaces directly from a texture exemplar. Regular-grid patches produced by the local resampling are used as building blocks for texture synthesis. Then, texture optimisation and patch-based sampling are generalised to synthesise texture directly in ve...
متن کاملEstimation of Large Covariance Matrices
This paper considers estimating a covariance matrix of p variables from n observations by either banding or tapering the sample covariance matrix, or estimating a banded version of the inverse of the covariance. We show that these estimates are consistent in the operator norm as long as (logp)/n→ 0, and obtain explicit rates. The results are uniform over some fairly natural well-conditioned fam...
متن کاملTexture synthesis via a noncausal nonparametric multiscale Markov random field
Our noncausal, nonparametric, multiscale, Markov random field (MRF) model is capable of synthesizing and capturing the characteristics of a wide variety of textures, from the highly structured to the stochastic. We use a multiscale synthesis algorithm incorporating local annealing to obtain larger realizations of texture visually indistinguishable from the training texture.
متن کاملThe Earth Mover's Distance is the Mallows Distance: Some Insights from Statistics
The Earth Mover’s distance was first introduced as a purely empirical way to measure texture and color similarities. We show that it has a rigorous probabilistic interpretation and is conceptually equivalent to the Mallows distance on probability distributions. The two distances are exactly the same when applied to probability distributions, but behave differently when applied to unnormalized d...
متن کاملTexture synthesis and unsupervised recognition with a nonparametric multiscale Markov random field model
In this paper we present noncausal, nonparametric, multiscale, Markov Random Field (MRF) model for synthesising and recognising texture. The model has the ability to capture the characteristics of a wide variety of textures, varying from the structured to the stochastic. For texture synthesis, we use our own novel multiscale approach, incorporating local annealing, allowing us to use large neig...
متن کامل