Category-level object detection has a crucial need for informative object representations. This demand has led to feature descriptors of ever increasing dimensionality like co-occurrence statistics and self-similarity. In this paper we propose a new object representation based on curvature self-similarity that goes beyond the currently popular approximation of objects using straight lines. However, like all descriptors using second order statistics, ours also exhibits a high dimensionality. Although improving discriminability, the high dimensionality becomes a critical issue due to lack of generalization ability and curse of dimensionality. Given only a limited amount of training data, even sophisticated learning algorithms such as the popular kernel methods are not able to suppress noisy or superfluous dimensions of such high-dimensional data. Consequently, there is a natural need for feature selection when using present-day informative features and, particularly, curvature self-similarity. We therefore suggest an embedded feature selection method for SVMs that reduces complexity and improves generalization capability of object models. By successfully integrating the proposed curvature self-similarity representation together with the embedded feature selection in a widely used state-of-the-art object detection framework we show the general pertinence of the approach.