Ill this paper we apply neural network techniques and physically based models to determine the surface shape of chips from scanning electronic microscopy images. Deducing some specific feature's vertical cross-section within an integrated circuit from two-dimensional top down scanning electron microscope images of the feature surface is a difficult "inverse problem" which arises in semiconductor fabrication. This paper refines our previous work on the reconstruction of semiconductor wafer surface shapes from top down electron microscopy images. One of the approaches we have developed directly maps from the CD-SEM intensity waveforms to line profiles. The other novel method we describe is based on an approximate physical model, where we assume a simplified mathematical representation of the physical process that produces the SEM image from the electron beam's interaction with the feature surface. Our results are illustrated with a variety of real data sets.