© 2019, Springer-Verlag London Ltd., part of Springer Nature.In recent decades, the need for efficient and effective image search from large databases has increased. In this paper, we present a novel shape matching framework based on structures common to similar shapes. After representing shapes as medial axis graphs, in which nodes show skeleton points and edges connect nearby points, we determine the critical nodes connecting or representing a shape’s different parts. By using the shortest path distance from each skeleton (node) to each of the critical nodes, we effectively retrieve shapes similar to a given query through a transportation-based distance function. To improve the effectiveness of the proposed approach, we employ a unified framework that takes advantage of the feature representation of the proposed algorithm and the classification capability of a supervised machine learning algorithm. A set of shape retrieval experiments including a comparison with several well-known approaches demonstrate the proposed algorithm’s efficacy and perturbation experiments show its robustness.