Shape analysis is a key task in image processing. A common method for representing a 2D shape is via a polygon, where the latter is a discretized version of the contour outlining the shape. However, due to the problem of curve reparameterization (i. e., points “sliding” along the contour), even if several shapes are very similar, their representations might be misleadingly far from each other. This misalignment problem confounds shape analysis. As a remedy, we propose a deep-learning framework, based on the recently-proposed diffeomorphic transformers nets. The proposed method handles either a single class (in an unsupervised manner) or multiple classes (in a semi-supervised manner), and is amenable to the warp-around effect exhibited in closed contours. Moreover, unlike typical alignment methods unrelated to learning, the proposed method aligns not only the original (“training”) shapes but also generalizes to test shapes (even if no class labels are given during the test). Our code is publicly available at https://git;hub.com/BGU-CS-VIL/CDTNCA.