Performance evaluation of content-based image retrieval (CBIR) systems is an important but still unsolved problem. The reason for its importance is that only performance evaluation allows for comparison and integration of different CBIR systems. We propose an image retrieval system that splits the retrieval process into two stages. Users are querying the system through image description using a set of local semantic concepts and the size of the image area to be covered by the particular concept. In Stage I of the system, only small patches of the image are analyzed whereas in the second stage the patch information is processed and the relevant images are retrieved. In this two-stage retrieval system, the retrieval performance, that is precision and recall, can be modeled statistically. Based on the model, we develop closed-form expressions that allow for the prediction as well as the optimization of the retrieval performance. As shown through experiments, the retrieval precision can b...