This paper proposes two approaches to the skin lesion image segmentation problem. The first is a mainly region-based segmentation method where an optimal threshold is determined iteratively by an isodata algorithm. The second method proposed is based on neural network edge detection and a rational Gaussian curve that fits an approximate closed elastic curve between the recognized neural network edge patterns. A quantitative comparison of the techniques is enabled by the use of synthetic lesions to which Gaussian noise is added. The proposed techniques are also compared with an established automatic skin segmentation method. It is demonstrated that for lesions with a range of different border irregularity properties the iterative thresholding method provides the best performance over a range of signal to noise ratios. Iterative thresholding technique is also demonstrated to have similar performance when tested on real skin lesions.