We address the fundamental problem of matching in two static images. The remaining challenges are related to occlusion and lack of texture. Our approach addresses these difficulties within a perceptual organization framework, considering both binocular and monocular cues. Initially, matching candidates for all pixels are generated by a combination of matching techniques. The matching candidates are then embedded in disparity space, where perceptual organization takes place in 3D neighborhoods and, thus, does not suffer from problems associated with scanline or image neighborhoods. The assumption is that correct matches produce salient, coherent surfaces, while wrong ones do not. Matching candidates that are consistent with the surfaces are kept and grouped into smooth layers. Thus, we achieve surface segmentation based on geometric and not photometric properties. Surface overextensions, which are due to occlusion, can be corrected by removing matches whose projections are not consistent in color with their neighbors of the same surface in both images. Finally, the projections of the refined surfaces on both images are used to obtain disparity hypotheses for unmatched pixels. The final disparities are selected after a second tensor voting stage, during which information is propagated from more reliable pixels to less reliable ones. We present results on widely used benchmark stereo pairs.