This fascinating paper presents an important stage in the development of powerful integrated methods for remote determination of terrain such as the Venusian surface. The authors combine shape-from-shading (SFS) information with low-resolution digital terrain model information. The SFS is based on synthetic aperture radar (SAR) images.

The shape information obtained in SAR shading is obviously inexact, due to noise in the observed image intensity and, especially, imperfect modeling. The authors present a five-step procedure to generate satisfactory terrain models. The first step minimizes the sum of squared errors between the observed image and its prediction. Second, smoothness in the estimated surface is enforced by a regularization penalty constraint, based on the sum of squared values of the second partial derivatives of the surface. The third step enforces self-consistency of the estimated surface by constructing an integrable set of estimates from the generally nonintegrable surface slope estimates. Next, low-resolution surface height data are used to supplement the information extracted from the SAR imagery and to supply estimates of the reflectance model parameters. The last step incorporates the SAR image coordinates and reflectance models. The paper discusses details of each component of the procedure using simulated and real examples. The enforcement of consistency between observed shadows and shadows predicted by the constructed model is left for later study.

A valuable part of this paper is the “Conclusions and Extensions” section, which is much more interesting than the usual summary and conclusions that read like an extended abstract. I was particularly intrigued by the thought that “the precision of stereo matches can be improved by accounting for shading differences…. After shading compensation the stereo matching procedure is repeated with greater achievable accuracy.” The paper concludes with the following call for a definitive solution to shape estimation:

The full power of numerical methods for solving differential equations has not been fully utilized in…image analysis applications…. With the direct approach, it is possible to approximate the surface slopes consistent with a given intensity function, apply smoothness constraints, enforce fairly general boundary conditions, enforce integrability, and fuse shading information with stereo information in a unified algorithm….

The extensive bibliography appears quite up-to-date but does not neglect important early references.

Computer vision is included under the AI umbrella. When something works and you can see how, the “I” of AI is hard to see. We have here a well-thought-out and well-presented set of procedures to solve the title problem. But is it AI?