Papers:Texture:Bonet-NonPara-Stat-Model

A Non-parametric Multi-Scale Statistical Model for Natural Images

J. S. De Bonet and P. Viola.

NIPS (1997)

The paper presents a non-parametric generative model of images based on Laplacian pyramid. It extends Heeger and Bergen's work by explicitly modeling the relation cross different resolutions.
The paper's contributions mainly lie in the following three aspect:
- Subband decomposition using Laplacian Pyramid. (This idea is derived from fromo Heeger and Bergen's work)
- Filter bands are applied to acquire localized features.
- Parent vector - unify the representation in different scales together.
- Markov tree - Model the cross-level(scale) relation with localized conditional distribution.
The paper discusses several applications of the proposed model
- Compare textures - use generative likelihood as the measure of similarity
- Denoising - use Monte Carlo averaging

This work is an important improvement over Heeger and Bergen's work. The authors convincingly showed that the cross-resolution relations play crucial roles in texture modeling with spatial structures.
Using localized dependency instead of global histograms makes it more effective in modeling inhomoegeneous images.
The sampling strategy used in the paper is heuristic rather than rigorous. It simply looks for the locations with similar parent structures and randomly draw one from them. Is MCMC a better choice?
Really nice work. What if combine it with texton models?
The model is examplar-based - the sampling is directly done in input image. Is it possible to derive some example-independent representation so that we need not to store all examples in the model, while retain the advantages of nonparametric sampling?