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Recent work in object categorization often uses local image descriptors such as SIFT to learn and detect object categories. Such descriptors explicitly code local appearance and have shown impressive results on objects with sufficient local appearance statistics. However, many important object classes such as tools, cups and other man-made artifacts seem to require features that capture the respective shape and geometric layout of those object classes. Therefore this paper compares, on a novel data collection of 10 geometric object classes, various shape-based features with appearance-based descriptors such as SIFT. The analysis includes a direct comparison of feature statistics as well as results within standard recognition frameworks, which are partly intuitive, but sometimes surprising.