In this paper, we identify some of the existing problems in shape context matching. We first identify the need for reflection invariance in shape context matching algorithms and propose a method to achieve the same. With the use of these reflection invariance techniques, we bring all the objects, in a database, to their canonical form, which halves the time required to match two shapes using their contexts. We then show how we can build better shape descriptors by the use of geodesic information from the shapes and hence improve upon the well-known Inner Distance Shape Context (IDSC). The IDSC is used by many pre- and post-processing algorithms as the baseline shape-matching algorithm. Our improvements to IDSC will remain compatible for use with those algorithms. Finally, we introduce new comparison metrics that can be used for the comparison of two or more algorithms. We have tested our proposals on the MPEG-7 database and show that our methods significantly outperform the IDSC.