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This paper presents a framework for unsupervised learning of a hierarchical reconfigurable image template - the AND-OR Template (AOT) for visual objects. The AOT includes: 1) hierarchical composition as "AND" nodes, 2) deformation and articulation of parts as geometric "OR" nodes, and 3) multiple ways of composition as structural "OR" nodes. The terminal nodes are hybrid image templates (HIT)  that are fully generative to the pixels. We show that both the structures and parameters of the AOT model can be learned in an unsupervised way from images using an information projection principle. The learning algorithm consists of two steps: 1) a recursive block pursuit procedure to learn the hierarchical dictionary of primitives, parts, and objects, and 2) a graph compression procedure to minimize model structure for better generalizability. We investigate the factors that influence how well the learning algorithm can identify the underlying AOT. And we propose a number of ways to evaluate the performance of the learned AOTs through both synthesized examples and real-world images. Our model advances the state of the art for object detection by improving the accuracy of template matching.