Scene Grammars, Factor Graphs, and Belief Propagation
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We consider a class of probabilistic grammars for generating scenes with multiple objects. Probabilistic scene grammars capture relationships between objects using compositional rules that provide important contextual cues for inference with ambiguous data. We show how to represent the distribution defined by a probabilistic scene grammar using a factor graph. We also show how to efficiently perform message passing in this factor graph. This leads to an efficient approach for inference with a grammar model using belief propagation as the underlying computational engine. Inference with belief propagation naturally combines bottom-up and top-down contextual information and leads to a robust algorithm for aggregating evidence. We show experiments on two different applications to demonstrate the generality of the framework. The first application involves detecting curves in noisy images, and we address this problem using a grammar that generates a collection of curves using a first-order Markov process. The second application involves localizing faces and parts of faces in images. In this case, we use a grammar that captures spatial relationships between the parts of a face. In both applications the same framework leads to robust inference algorithms that can effectively combine weak local information to reason about a scene.
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