Stereo matching algorithms conventionally match over a range of disparities sufficient to encompass all visible 3D scene points. Human vision however does not do this. It 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. Points inside the band are fused visually and the remainder of points are seen as "diplopic" -- that is with double vision. The Panum band restriction is important also in machine vision, both with active (pan/tilt) cameras, and with high resolution cameras and digital pan/tilt. A probabilistic approach is presented for dense stereo matching under the Panum band restriction. First it is shown that existing dense stereo algorithms are inadequate in this problem setting. Secondly it is shown that the main problem is segmentation, separating the (left) image into the areas that fall respectively inside and outside the band. Thirdly, an approx...