For identifying the disease-effected regions using medical images, it is important to bring all individual instances into the common space for comparison (between normal and abnormal groups). To achieve this, one way is to identify the shape-based correspondences between multiple instances of the same organ. The objective of shape correspondence then is to identify corresponding landmarks across a population of instances of the same shape. However, the non-rigid variation observed in naturally occurring 3D structures leads to a highly non-linear and complex problem. While various efforts have been made to address the problem of shape correspondence in previous research works, most existing methods are limited in their application to the smooth, closed-surface type of shape. Due to the importance of shape correspondence in various computer vision tasks, especially medical imaging-related applications, this work investigates the problem of shape correspondence for the case of open-surface shapes and highly convoluted surfaces. This work introduces a novel 3D landmark sliding framework which can be used to bring both closed-surface and open-surface shapes into correspondence. Further, this work introduces the concept of topological consistency of landmarks, which has previously not been included in shape correspondence research. The developed landmark sliding framework and topology consistency are able to perform shape correspondence more accurately and efficiently compared to existing methods. Finally, this work introduces a method of organizing a population of shape instances into a novel tree structure to minimize the shape correspondence errors by pairing similar instances together while constraining the height of the tree to minimize accumulation of errors.
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