Handheld manipulable objects can often be found on flat surfaces within human environments. Researchers have previously demonstrated that perceptually segmenting a flat surface from the objects resting on it can enable robots to pick and place objects. However, methods for performing this segmentation can fail when applied to scenes with natural clutter. For example, low-profile objects and dense clutter that obscures the underlying surface can complicate the interpretation of the scene. As a first step towards characterizing the statistics of real-world clutter in human environments, we have collected and hand labeled 104 scans of cluttered tables using a tilting laser range finder (LIDAR) and a camera. Within this paper, we describe our method of data collection, present notable statistics from the dataset, and introduce a perceptual algorithm that uses machine learning to discriminate surface from clutter. We also present a method that enables a humanoid robot to place objects on uncluttered parts of flat surfaces using this perceptual algorithm. In cross-validation tests, the perceptual algorithm achieved a correct classification rate of 78.70% for surface and 90.66% for clutter, and outperformed our previously published algorithm. Our humanoid robot succeeded in 16 out of 20 object placing trials on 9 different unaltered tables, and performed successfully in several high-clutter situations. 3 out of 4 failures resulted from placing objects too close to the edge of the table.