Two central issues in stereo algorithm design are the matching criterion and the underlying smoothness assumptions. In this paper we propose a newstereo algorithm with novel approaches to both issues. We start with a careful analysis of the properties of the continuous disparity space image (DSI), and derive a new matching cost based on the reconstructed image signals.We then use a symmetric matching process that employs visibility constraints to assign disparities to a large fraction of pixels with minimal smoothness assumptions. While the matching operates on integer disparities, sub-pixel information is maintained throughout the process. Global smoothness assumptions are delayed until a later stage in which disparities are assigned in textureless and occluded areas.We validate our approach with experimental results on stereo images with ground truth.