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Burt and Julesz experimentally demonstrated that, in addition to Panum's fusional area, a quantity defined by them and named disparity gradient also plays a crucial part in deciding whether the human visual system would be able to fuse the images seen by the left and right eyes. The physical meaning of this quantity remains obscure despite attempts to interpret it in terms of depth gradient. Nevertheless, it has been found to be an effective selector of matches in stereo correspondence algorithms. A proof is provided that a disparity gradient limit of less than 2 implies that the matches between the two images preserve the topology of the images. The result, which is invariant under rotations and under relative as well as overall magnifications, holds for pairs of points separated in any direction, not just along epipolar lines. This in turn can be shown to prevent correspondences being established between points which would have to be located in three dimensions on a surface invisible to one eye, assuming opaque surfaces.

Hitherto known formulas for the translation of exponential-type functions (ETF's) from one center to another (i.e., addition theorems) encounter serious difficulties of one kind or another in practical applications. In contrast, the recently derived new addition theorem of A functions appears to be free of many of those difficulties. The A functions are a special class of ETF's, defined by a product of an exponential, a Laguerre function, and a regular solid spherical harmonic:A"i(r, 6, $)=23' N(n, l)e 'L"' 'i 'i(2r)(2r)'Yt (8,$).We have examined the new one-range addition theorem for its applicability to quantummechanical multicenter problems from the computational point of view and found it very useful. Test calculations on molecular multicenter one-electron integrals are reported.Under term-by-term integration, accuracy of 10 could be achieved for all these integrals with an acceptable number of expansion terms.

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