Optimizing queries that involve operations on spatial data requires estimating the selectivity and cost of these operations. In this paper, we focus on estimating the cost of spatial selections, or window queries, where the query windows and data objects are general polygons. Cost estimation techniques previously proposed in the literature only handle rectangular query windows over rectangular data objects, thus ignoring the very significant cost of exact geometry comparison (the refinement step in a ``filter and refine'' query processing strategy). The cost of the exact geometry comparison depends on the selectivity of the filtering step and the average number of vertices in the candidate objects identified by this step.In this paper, we introduce a new type of histogram for spatial data that captures the complexity and size of the spatial objects as well as their location. Capturing these attributes makes this type of histogram useful for accurate estimation, as we experimentally demonstrate. We also investigate sampling-based estimation approaches. Sampling can yield better selectivity estimates than histograms for polygon data, but at the high cost of performing exact geometry comparisons for all the sampled objects.