Stereo matching algorithms conventionally match over a range of disparities sufficient to encompass all visible 3D scene points. Human vision, however, works over a narrow band of disparities-Panum's fusional band-whose typical range may be as little as 1/20 of the full range of disparities for visible points. Only points inside the band are fused visually; the remainder of points are seen diplopically. A probabilistic approach is presented for dense stereo matching under the Panum band restriction. It is shown that existing dense stereo algorithms are inadequate in this problem setting and the main problem is segmentation, marking the image into the areas that fall inside the band. An approximation is derived that makes up for missing out-of-band information with a ??proxy?? based on image autocorrelation. It is shown that the Panum Proxy algorithm achieves accuracy close to what can be obtained when the full disparity band is available, and with gains of between one and two orders of magnitude in computation time. There are also substantial gains in computation space. Panum band processing is also demonstrated in an active stereopsis framework.