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In this paper, we address the problems of deformable object matching (alignment) and segmentation with cluttered background. We propose a novel hierarchical log-linear model (HLLM) which represents both shape and appearance features at multiple levels of a hierarchy. This model enables us to combine appearance cues at multiple scales directly into the hierarchy and to model shape deformations at short-range, medium range, and long-range. We introduce the structure-perceptron algorithm to estimate the parameters of the HLLM in a discriminative way. The learning is able to estimate the appearance and shape parameters simultaneously in a global manner. Moreover, the structure-perceptron learning has a feature selection aspect (similar to AdaBoost) which enables us to specify a class of appearance/shape features and allow the algorithm to select which features to use and weight their importance. This method was applied to the tasks of deformable object localization, segmentation, matching (alignment), and parsing. We demonstrate that the algorithm achieves the state of the art performance by evaluation on public dataset (horse and multi-view face).