Stereo algorithms for structure reconstruction demand accurate disparities with low mismatch errors 
and false positives. Mismatch errors in large textureless regions force most accurate algorithms  to 
be sparse, with disparities known only in textured  regions. We propose a novel method which uses 
characteristics of the multi-valued disparity to segregate image regions into unambiguous, occluded 
but textured and regions with low color variation. The disparity in the unambiguous region is calculated using stable matching with local disparity filtering.  The disparity is interpolated into other regions by diffusion using unstructured triangulation and method  of finite elements for rapid convergence. The boundary  conditions for each of the region are appropriately modified so that accurate discontinuities in the  disparity are preserved. A comparison of our method with some existing methods through experiments reveal  that this algorithm indeed performs significantly better 
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