Images are ambiguous at each of many levels of a contextual hierarchy. Nevertheless, the high-level interpretation of most scenes is unambiguous, as evidenced by the superior performance of humans. This observation argues for global vision models, such as deformable templates. Unfortunately, such models are computationally intractable for unconstrained problems. We propose a compositional model in which primitives are recursively composed, subject to syntactic restrictions, to form tree-structured objects and object groupings. Ambiguity is propagated up the hierarchy in the form of multiple interpretations, which are later resolved by a Bayesian, equivalently minimum-description-length, cost functional. 1 Bayesian decision theory and compositionality In his Essay on Probability, Laplace (1812) devotes a short chapter---his "Sixth Principle"---to what we call today the Bayesian decision rule. Laplace observes that we interpret a "regular combination," e.g., an arrangement of objects th...

We present a novel probabilistic model for the hierarchical structure of an image and its regions. We call this model spatial random tree grammars (SRTGs). We develop algorithms for the exact computation of likelihood and maximum a posteriori (MAP) estimates and the exact expectation-maximization (EM) updates for model-parameter estimation. We collectively call these algorithms the center-surround algorithm. We use the center-surround algorithm to automatically estimate the maximum likelihood (ML) parameters of SRTGs and classify images based on their likelihood and based on the MAP estimate of the associated hierarchical structure. We apply our method to the task of classifying natural images and demonstrate that the addition of hierarchical structure significantly improves upon the performance of a baseline model that lacks such structure.

A new class of multiscale multidimensional stochastic processes called spatial random trees was recently introduced in [9]. The model is based on multiscale stochastic trees with stochastic structure as well as stochastic states. In this work, we describe a method for estimating the parameters of the process.

Abstract—We develop a new class of hierarchical stochastic image models called spatial random trees (SRTs) which admit polynomial-complexity exact inference algorithms. Our framework of multitree dictionaries is the starting point for this construction. SRTs are stochastic hidden tree models whose leaves are associated with image data. The states at the tree nodes are random variables, and, in addition, the structure of the tree is random and is generated by a probabilistic grammar. We describe an efficient recursive algorithm for obtaining the maximum a posteriori estimate of both the tree structure and the tree states given an image. We also develop an efficient procedure for performing one iteration of the expectation-maximization algorithm and use it to estimate the model parameters from a set of training images. We address other inference problems arising in applications such as maximization of posterior marginals and hypothesis testing. Our models and algorithms are illustrated through several image classification and segmentation experiments, ranging from the segmentation of synthetic images to the classification of natural photographs and the segmentation of scanned documents. In each case, we show that our method substantially improves accuracy over a variety of existing methods. Index Terms—Dictionary, estimation, grammar, hierarchical model, image classification, probabilistic context-free grammar, segmentation, statistical image model, stochastic context-free grammar, tree model. I.

A new class of multiscale multidimensional stochastic processes called spatial random trees is introduced. The model is based on multiscale stochastic trees with stochastic structure as well as stochastic states. Procedures are developed for exact likelihood calculation, MAP estimation of the process, and estimation of the parameters of the process. The new framework is illustrated through a simple binary image classification problem.

A new class of multiscale stochastic processes called spatial random trees (SRTs) is introduced and studied. As with previous multiscale stochastic processes, SRTs model multidimensional signals using random processes on trees. Our key innovation, however, is that the tree structure itself is random and is generated by a probabilistic context-free grammar (PCFG) [26]. While PCFGs have been used to model 1-D signals, the generalization to multiple dimensions is not direct because the leaves of a tree generated by a PCFG cannot be naturally mapped to a multidimensional lattice. We solve this problem by defining a new class of PCFGs which can produce trees whose leaves are naturally arranged in a multidimensional lattice. We call such trees admissible and show that each of them generates a unique multidimensional signal. Based on this framework, procedures are developed for likelihood calculation, MAP estimation of the processes, and parameter estimation. The new framework is illustrated through simple detection problems.

Model building by perturbation

We introduce a general information architecture for designing distributed inference algorithms in ad hoc sensor networks to support applications that monitor multiple, dynamic physical phenomena in a sensor field. The information architecture consists of a graphical information representation with processing mechanisms guided by sensor evidence and provides a global view of the set of computations occurring in the system. The information architecture can then be optimally mapped onto the sensor network via an agent assignment, thereby generating a resource aware distributed algorithm on the sensor network.

We present a method for imposing hierarchal structure on segmented images using probabilistic context-free grammars (PCFGs). The notion of PCFG, which has been used in the past to characterize 1D word strings, is extended to characterize 2D images as well. The inside-outside algorithm is then extended to support training, classification, and parsing on images with these extended PCFGs. The soundness and efficiency of these extensions rely on a novel notion of constituency that constrains the allowable ways to partition a parent segment into child subsegments during parsing. We successfully apply our method to the task of classifying natural images and also show that our method can learn the common hierarchal structure in such images, in an unsupervised fashion, from unlabeled training data.

Abstract—We present a novel probabilistic model for the hierarchical structure of an image and its regions. We call this model spatial random tree grammars (SRTGs). We develop algorithms for the exact computation of likelihood and maximum a posteriori (MAP) estimates and the exact expectation-maximization (EM) updates for model-parameter estimation. We collectively call these algorithms the center-surround algorithm. We use the center-surround algorithm to automatically estimate the maximum likelihood (ML) parameters of SRTGs and classify images based on their likelihood and based on the MAP estimate of the associated hierarchical structure. We apply our method to the task of classifying natural images and demonstrate that the addition of hierarchical structure significantly improves upon the performance of a baseline model that lacks such structure. Index Terms—Bayesian methods for image understanding, multiscale analysis. Ç