Cheng-en Guo

Modeling Visual Patterns by Integrating Descriptive and Generative Methods

This paper presents a class of statistical models that integrate two statistical modeling paradigms in the literature: (I) Descriptive methods, such as Markov random fields and minimax entropy learning (Zhu, S.C., Wu, Y.N., and Mumford, D. 1997. Neural Computation, 9(8)), and (II) Generative methods, such as principal component analysis, independent component analysis (Bell, A.J. and Sejnowski, T.J. 1997. Vision Research, 37:3327–3338), transformed component analysis (Frey, B. and Jojic, N. 1999. ICCV), wavelet coding (Mallat, S. and Zhang, Z. 1993. IEEE Trans. on Signal Processing, 41:3397–3415; Chen, S., Donoho, D., and Saunders, M.A. 1999. Journal on Scientific Computing, 20(1):33–61), and sparse coding (Olshausen, B.A. and Field, D.J. 1996. Nature, 381:607–609; Lewicki, M.S. and Olshausen, B.A. 1999. JOSA, A. 16(7):1587–1601). In this paper, we demonstrate the integrated framework by constructing a class of hierarchical models for texton patterns (the term “texton” was coined by psychologist Julesz in the early 80s). At the bottom level of the model, we assume that an observed texture image is generated by multiple hidden “texton maps”, and textons on each map are translated, scaled, stretched, and oriented versions of a window function, like mini-templates or wavelet bases. The texton maps generate the observed image by occlusion or linear superposition. This bottom level of the model is generative in nature. At the top level of the model, the spatial arrangements of the textons in the texton maps are characterized by minimax entropy principle, which leads to embellished versions of Gibbs point process models (Stoyan, D., Kendall, W.S., and Mecke, J. 1985. Stochastic Geometry and its Applications). The top level of the model is descriptive in nature. We demonstrate the integrated model by a set of experiments.

Statistical Modeling of Texture Sketch

Recent results on sparse coding and independent component analysis suggest that human vision first represents a visual image by a linear superposition of a relatively small number of localized, elongate, oriented image bases. With this representation, the sketch of an image consists of the locations, orientations, and elongations of the image bases, and the sketch can be visually illustrated by depicting each image base by a linelet of the same length and orientation. Built on the insight of sparse and independent component analysis, we propose a two-level generative model for textures. At the bottom-level, the texture image is represented by a linear superposition of image bases. At the top-level, a Markov model is assumed for the placement of the image bases or the sketch, and the model is characterized by a set of simple geometrical feature statistics.

Mathematical modeling of clutter: descriptive vs. generative models

In this article, we present two mathematical paradigms for clutter modeling. Both paradigms pose clutter modeling as a statistical inference problem, and pursue probabilistic models for characterizing observed training images. The two paradigms differ in the forms (or families) of models that they choose and in their philosophical assumptions on real world clutter patterns. The first paradigm studies descriptive models, such as Markov random field (MRF) models and the minimax entropy models (Zhu, Wu, and Mumford 1997). In this modeling paradigm, image features are first extracted from images, and statistics of these features are calculated. The latter define an image ensemble-called the Julesz ensemble which is an equivalence class where all images share the same feature statistics. For any large images from this ensemble, a local patch given its boundary condition is then Gibbs (or MRF) models. We shall review the recent conclusions about ensemble equivalence studied in (Wu, Zhu and Liu, 1999). The second paradigm studies generative model, such as the random collage model (Lee and Mumford, 1999). In contrast to a descriptive model, a generative model introduces hidden variables which are assumed to be the underlying causes producing the observed image. For example, trees and rock for clutter. The learning process makes inference about the hidden variables. We shall discuss a texton model for clutter and effective Markov chain Monte Carlo methods for stochastic inference. We shall also reveal the deep relationship between the two modeling paradigm.

Information Scaling Laws in Natural Scenes

In natural scenes, objects and patterns can appear at a wide variety of distances from the viewer. For the same visual pattern viewed at different distances, both the image and our perception of the pattern change over distance. We call the change of the image over distance as image scaling, and the change of our perception over distance as information scaling. While image scaling can be accounted for by the state space theory, information scaling has not been mathematically studied in computer vision. In this paper, we prove two information scaling laws: 1) the entropy rate of the image changes over distance, and 2) the entropy of the posterior distribution of the pattern also changes over distance. These two information scaling laws have deep implications in computer vision: they call for different models of the same visual pattern at different distances, as well as a model transition mechanism for switching models over different distance/scale regimes.