The last section of the paper has been entirely revised in the new draft. However there is a crucial part of the argument which must be understood if this model is to be given fair consideration. The following text is now included in the new draft:

There is an important general principle embodied in this model that must be clearly understood. The issues of shape-from-shading and perception of illumination are extremely challenging problems as long as these entities are to be computed in a two-dimensional or abstracted representation. The problem is enormously simplified however by moving into a fully spatial context, because in the spatial model the complex spatial pattern due to the illumination of a geometrcal surface is replicated spatially in the model itself. Although the initial construction of a spatial model is itself very complex, the subsequent computation of illumination within that model, and the calculation of the complex patterns of light and shadow on a surface due to that illuminant, becomes as simple as turning on a modeled light source in the modeled 3-D scene, and registering where the modeled light propagated within the model falls. This calculation is no different for arbitrarily complex three-dimensional surfaces than it is for simple planar surfaces, and even automatically calculates detatched shadows cast on the ground for example by objects hovering over the ground. The inverse problem of calculating the illuminant from a given illumination profile is likewise simplified by the reverse ray-tracing algorithm, as if "turning on" the illuminated surfaces and tracing backwards through the model to see where the light must be coming from. The general idea is that the most complex spatial aspect of the problem is solved by constructing a replica of the spatial configuration, which then duplicates the very complex interactions of surface geometry with the illuminant, by way of relatively simple local calculations that replicate the propagation of light in space.

This is the point made in the figure below. Assuming that we have the spatial mechanism described, and we "turn on" the modeled light source as shown in A below, there is no need to calculate the pattern of shading in the figure, whether attached shadows or cast shadows, these are calculated automatically in parallel by the system, regardless of how complex the shape of the illuminated surfaces, and even disconnected shadows are calculated the same way. The same kind of parallel calculation can work in the reverse direction, as suggested in B below, and as described in the paper. If it remains unclear to this reviewer how a spatial representation simplifies the computation of a spatial percept, then the reviewer is missing the whole point of this model.