We present an approach to match partially occluded plant leaves with databases of full plant leaves. Although contour based 2D shape matching has been studied extensively in the last couple of decades, matching occluded leaves with full leaf databases is an open and little worked on problem. Classifying occluded plant leaves is even more challenging than full leaf matching because of large variations and complexity of leaf structures. Matching an occluded contour with all the full contours in a database is an NP-hard problem [Su et al. ICCV2015], so our algorithm is necessarily suboptimal.First, we represent the 2D contour points as a β-Spline curve. We extract interest points on these curves via the Discrete Contour Evolution (DCE) algorithm. To find the best match of an occluded curve with segments of the full leaf curves in the database, we formulate our solution as a subgraph matching algorithm, using the feature points as graph nodes. This algorithm produces one or more open curves for each closed leaf contour considered. These open curves are matchable, to some degree, with the occluded curve. We then compute the affine parameters for each open curve and the occluded curve. After performing the inverse affine transform on the occluded curve, which allows the occluded curve and any subgraph curve to be "overlaid", we then compare the shapes using the Fréchet distance metric. We keep the best η matched curves. Since the Fréchet distance metric is cheap to compute but not perfectly correlated with the quality of the match, we formulate an energy functional that is well correlated with the quality of the match, but is considerably more expensive to compute. The functional uses local and global curvature, angular information and local geometric features. We minimize this energy functional using the well known convexconcave relaxation technique. The curve among the best η curves retained. that has the minimum energy, is considered to be the best overall match with the occluded leaf. Experiments on three publicly available leaf image database shows that our method is both effective and efficient, outperforming other current stateof-the-art methods. Occlusion is measured as a percentage of the overall contour (and not leaf area) that is missing. We show our algorithm can, for leaves that are up to 50% occluded, still identify the best full leaf match from the databases.