Adynamic texture is a spatio-temporal generative model for video, which represents video sequences as observations from a linear dynamical system. This work studies the mixture of dynamic textures, a statistical model for an ensemble of video sequences that is sampled from a finite collection of visual processes, each of which is a dynamic texture. An expectation-maximization (EM) algorithm is derived for learning the parameters of the model, and the model is related to previous works in linear systems, machine learning, time-series clustering, control theory, and computer vision. Through experimentation, it is shown that the mixture of dynamic textures is a suitable representation for both the appearance and dynamics of a variety of visual processes that have traditionally been challenging for computer vision (for example, fire, steam, water, vehicle and pedestrian traffic, and so forth). When compared with state-of-the-art methods in motion segmentation, including both temporal texture methods and traditional representations (for example, optical flow or other localized motion representations), the mixture of dynamic textures achieves superior performance in the problems of clustering and segmenting video of such processes.

A probabilistic formulation for semantic image annotation and retrieval is proposed. Annotation and retrieval are posed as classification problems where each class is defined as the group of database images labeled with a common semantic label. It is shown that, by establishing this one-to-one correspondence between semantic labels and semantic classes, a minimum probability of error annotation and retrieval are feasible with algorithms that are 1) conceptually simple, 2) computationally efficient, and 3) do not require prior semantic segmentation of training images. In particular, images are represented as bags of localized feature vectors, a mixture density estimated for each image, and the mixtures associated with all images annotated with a common semantic label pooled into a density estimate for the corresponding semantic class. This pooling is justified by a multiple instance learning argument and performed efficiently with a hierarchical extension of expectation-maximization. The benefits of the supervised formulation over the more complex, and currently popular, joint modeling of semantic label and visual feature distributions are illustrated through theoretical arguments and extensive experiments. The supervised formulation is shown to achieve higher accuracy than various previously published methods at a fraction of their computational cost. Finally, the proposed method is shown to be fairly robust to parameter tuning.