We present a method for computing dense visual correspondence based on general assumptions about scene geometry. Our algorithm does not rely on correlation, and uses a variable region of support. We assume that images consist of a number of connected sets of pixels with the same disparity, which we call disparity components. Using maximum likelihood arguments, at each pixel we compute a small set of plausible disparities. A pixel is assigned a disparity $d$ based on connected components of pixels, where each pixel in a component considers $d$ to be plausible. Our implementation chooses the largest plausible disparity component; however, global contextual constraints can also be applied. While the algorithm was originally designed for visual correspondence, it can also be used for other early vision problems such as image restoration. It runs in a few seconds on traditional benchmark images with standard parameter settings, and gives quite promising results. (Visit our image gallery.)