We derive an algorithm for compression of the currents and varifolds representations of shapes, using the Nystrom approximation in Reproducing Kernel Hilbert Spaces. Our method is faster than existing compression techniques, and comes with theoretical guarantees on the rate of convergence of the compressed approximation, as a function of the smoothness of the associated shape representation. The obtained compression are shown to be useful for down-line tasks such as nonlinear shape registration in the Large Deformation Metric Mapping (LDDMM) framework, even for very high compression ratios. The performance of our algorithm is demonstrated on large-scale shape data from modern geometry processing datasets, and is shown to be fast and scalable with rapid error decay.

翻译：本文提出一种基于再生核希尔伯特空间中Nystrom逼近的形状表示压缩算法，适用于电流与变差形式表示。该方法较现有压缩技术具有更快的计算速度，并从理论上保证了压缩逼近的收敛速率与形状表示光滑度的函数关系。实验表明，所获得的压缩表示在下游任务中具有实用价值，例如大变形微分同胚度量映射框架中的非线性形状配准任务，即使在高压缩比条件下仍保持良好性能。算法在现代几何处理数据集的大规模形状数据上得到验证，展现出快速的计算速度、良好的可扩展性以及误差的迅速衰减特性。