The delineation of important structures in chest radiographs is an essential preprocessing step in order to automatically analyze these images, e.g., for tuberculosis screening support or in computer assisted diagnosis. We present algorithms for the automatic segmentation of lung fields in chest radiographs. We compare several segmentation techniques: a matching approach; pixel classifiers based on several combinations of features; a new rule-based scheme that detects lung contours using a general framework for the detection of oriented edges and ridges in images; and a hybrid scheme. Each approach is discussed and the performance of nine systems is compared with interobserver variability and results available from the literature. The best performance is obtained by the hybrid scheme that combines the rule-based segmentation algorithm with a pixel classification approach. The combinations of two complementary techniques leads to robust performance; the accuracy is above 94\% for all 115 images in the test set. The average accuracy of the scheme is 0.969 +/- 0.0080, which is close to the interobserver variability of 0.984 +/- 0.0048. The methods are fast, and implemented on a standard PC platform.