Textons refer to fundamental micro-structures in natural images (and videos) and are considered as the atoms of pre-attentive human visual perception (Julesz, 1981). Unfortunately, the word "texton" remains a vague concept in the literature for lack of a good mathematical model. In this article, we first present a three-level generative image model for learning textons from texture images. In this model, an image is a superposition of a number of image bases selected from an over-complete dictionary including various Gabor and Laplacian of Gaussian functions at various locations, scales, and orientations. These image bases are, in turn, generated by a smaller number of texton elements, selected from a dictionary of textons. By analogy to the waveform-phonemeword hierarchy in speech, the pixel-base-texton hierarchy presents an increasingly abstract visual description and leads to dimension reduction and variable decoupling. By fitting the generative model to observed images, we can learn the texton dictionary as parameters of the generative model. Then the paper proceeds to study the geometric, dynamic, and photometric structures of the texton representation by further extending the generative model to account for motion and illumination variations. (1) For the geometric structures, a texton consists of a number of image bases with deformable spatial configurations. The geometric structures are learned from static texture images.(2) For the dynamic structures, the motion of a texton is characterized by a Markov chain model in time which sometimes can switch geometric configurations during the movement. We call the moving textons as "motons". The dynamic models are learned using the trajectories of the textons inferred from video sequence. (3) For photometric structures, a texton represents the set of images of a 3D surface element under varying illuminations and is called a "lighton" in this paper. We adopt an illumination-cone representation where a lighton is a texton triplet. For a given light source, a lighton image is generated as a linear sum of the three texton bases. We present a sequence of experiments for learning the geometric, dynamic, and photometric structures from images and videos, and we also present some comparison studies with K-mean clustering, sparse coding, independent component analysis, and transformed component analysis. We shall discuss how general textons can be learned from generic natural images.

No abstract

Abstract. Vision can be considered a highly specialized data collection and analysis problem. We need to understand the special properties of natural image data in order to construct statistical models and develop statistical methods for representing and recognizing the wide variety of natural image patterns. One fundamental property of natural image data that distinguishes vision from other sensory tasks such as speech recognition is that scale plays a profound role in image formation and interpretation. Specifically, visual objects can appear at a wide range of scales in the images due to the change of viewing distance as well as camera resolution. The same objects appearing at different scales produce different image data with different statistical properties. In particular, we show that the entropy rate of the image data changes over scale. Moreover, the inferential uncertainty changes over scale too. We call these changes information scaling. We then examine both empirically and theoretically two prominent and yet largely isolated classes of image models, namely, wavelet sparse coding models and Markov random field models. Our results indicate that the two classes of models are appropriate for two different entropy regimes: sparse coding targets low entropy regimes, whereas Markov random fields are appropriate for high entropy regimes. Because information scaling connects different entropy regimes, both sparse coding and Markov random fields are necessary for representing natural image data, and information scaling triggers transitions between these two regimes. This motivates us to propose a modeling scheme that embraces both regimes of models in a common framework. The contribution of our work is two-fold. First, the study of information scaling provides a unifying perspective for the rich variety of natural image patterns. Second, the modeling scheme that we develop provides a natural integration of different regimes of image models.

No abstract

No abstract