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We present a novel algorithmic approach to object categorization and detection that can learn category specific detectors, using Boosting, from a visual alphabet of shape and appearance. The alphabet itself is learnt incrementally during this process. The resulting representation consists of a set of category-specific descriptors--basic shape features are represented by boundary-fragments, and appearance is represented by patches--where each descriptor in combination with centroid vectors for possible object centroids (geometry) forms an alphabet entry. Our experimental results highlight several qualities of this novel representation. First, we demonstrate the power of purely shape-based representation with excellent categorization and detection results using a Boundary-Fragment-Model (BFM), and investigate the capabilities of such a model to handle changes in scale and viewpoint, as well as intra- and inter-class variability. Second, we show that incremental learning of a BFM for many categories leads to a sub-linear growth of visual alphabet entries by sharing of shape features, while this generalization over categories at the same time often improves categorization performance (over independently learning the categories). Finally, the combination of basic shape and appearance (boundary-fragments and patches) features can further improve results. Certain feature types are preferred by certain categories, and for some categories we achieve the lowest error rates that have been reported so far.