Optimal Steps for Fast Diffeomorphic Shape Registration
1 Inria, Université Paris Cité, Inserm, HeKA, Paris 2 Hôpital Européen Georges Pompidou, AP-HP, Paris
Deep learning performs well on registration tasks, with fast inference. But three constraints limit its use in clinical studies: it requires a training corpus, which small clinical cohorts rarely provide; its accuracy degrades on anatomical variations absent from the training set; and each new anatomy carries a substantial retraining cost. Optimization-based methods are free of all three, but they remain substantially slower. That is the gap we address, with ideas drawn from the computer vision literature: a learning-free registration model that is diffeomorphic and roughly forty times faster than the geometric state of the art.
Table 1. Quantitative comparison on 757 vertebrae from the VerSe dataset. Our method achieves the highest surface alignment accuracy and preserves topological structure, without requiring access to a training dataset or the related computational overhead.
Computing this atlas from 978 vertebrae took 17 minutes on a single workstation.
The same pipeline also performs remarkably well out of the box on a completely different anatomy. We tested it on intra-patient lung vascular trees, registering inspiration to expiration. Without any tuning, and in just 20 seconds per pair for 40k points, it achieves a mean landmark error of 3.08 mm, compared to 2 mm for the state of the art.
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Code
We make our code available in scikit-shapes, the open-source library for shape analysis, under MIT license. Feel free to try it yourself!