An investigation of shape analysis methods is presented for application to remotely sensed images. The Method of Moments, in conjunction with linear pattern classification techniques, is shown to be suitable for the recognition of simple polygonal shapes in the absence of noise and in the presence of additive Gaussian noise with positive signal-to- noise ratios. The appropriate weight vectors for linear separation are presented and a suitable decision process is described for the recognition of desired shapes. The Method of Moments is successfully applied to a region which has been extracted from a real remotely sensed image using various segmentation thresholds. Finally, some recommendations are made for further work.